Videos_By_निलू

Prince of Persia

2010-06-15T10:12:00.001+05:30

My Love Story -part 1

2010-05-20T21:22:00.000+05:30

one day i was walking on beach. suddenly I saw a lady with beautiful eyes and smile. So i started looking at her for long time. Suddenly she noticed me, then smiled at me. i don't know then what happened to me. I gave her flirty smile. Even she gave me the same smile and started blushing at me. So i went to her and started conversation. Sooner or later we started talking to each other and got so involved that we didn't even noticed that it was almost late night. So i dropped her back to her home and asked for next meet. She agreed. Next day we met at coffee shop on beach, she was looking so HOT that day. We were just talking about our future plans .but suddenly she asked me, "do i like her?" Hearing those words i feel like in HEAVEN. Thinking that How Lucky guy am i????. I said "Yes, I do!!!" .Then we started taking walk on beach .She started and shared her future dreams- That how we'll be living together. How we’ll sharing our life. Then she started taking about her parents ,my parents. She was almost got involved into that dream that from next when we met she started pretending to be my WIFE and then she started DOMINATING on me. Even if any girl waved at me unknowingly also she started doubting on me, whether do I know her or having any affair with her??? …What the HELLL!!!! .Even if I tried to convince her she started crying and started blackmailing me emotionally. GOD help me out from this .. I almost started praying at GOD, why we MET ????? Oh GOD, Pls help me out!!!!

Suddenly God listened to me, and magic happened. I saw one HOT Girl on Beach and she was having gr8 Figure, WOOWWWWW !!!!! I was stunned at her. My GF noticed that I was looking at her, then she started quarrelling with me and taken decision to DUMPPED me. I said “OK, Good Bye forever”. Then She went and I went to that HOT Figure Girl. And this time I made strong decision. No need to waste time as earlier done and directly ask her “Will u Marry Me? I’ll fulfil all ur dreams”. She was stunned by hearing this and said “Do you think that am I going to say YES to u?”. I Said “No Worries to me, if u denied there are many girls on beach who will be ready to get marry with me as I m a Rich Person.” Listening to this she hugged me and kissed me and said “Yes ,I do Sweet heart .I’ll Want to Marry you” Her Hug was so tight that we fell into water (we were on beach remember na).

Then suddenly I woke up and found myself in Bath Tub… Wow !!! What a dream was that I had. I am still thinking ,if I went on beach am I going to get that Hot Figure girl ever in my life or That Stupid GF who was dominating on me.

Hmm thinking of these 2 girls ,I get crazy.. No more beach …. Try something else.. And Story Continues……

Mr. Perfect HD DVD Song ARYA 2 Allu Arjun Kajal Navadeep

2010-05-10T14:21:00.000+05:30

Incredible Talent

2010-05-10T14:20:00.000+05:30

मराठी भाषेत संवाद साधणे

2010-02-24T11:08:00.003+05:30

मराठी भाषेत संवाद साधणे जरी साधे असले तरी ते लिहिणे तेवढेच सोपे करण्याकरीता लिहिण्याची सवय केली पाहिजे

Tera Hone Laga Hoon- Ajab Prem ki Gazab Kahani

2010-02-04T11:57:00.000+05:30

What do you think about Global Warmin?

2010-01-30T15:15:00.000+05:30

Hi,

Kindly suggest any solutions or ways to avoid global warming?

Your suggests are valuables..

Get Together of DHL-Wipro on 4th Dec09

2009-12-05T11:07:00.001+05:30

Magic with Presto

2009-10-19T17:34:00.001+05:30

Parrot Talking

2009-09-27T19:48:00.000+05:30

Remeo's Intro

2009-01-13T10:07:00.000+05:30

To download above clip visit:

http://rapidshare.com/files/182302253/Remeo_s_Intro.3gp

Romeo's Saloon

2009-01-13T09:29:00.000+05:30

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http://rapidshare.com/files/182302592/Romeo_s_Saloon.3gp

Laila O Laila

2009-01-13T09:05:00.000+05:30

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http://rapidshare.com/files/182303038/Laila_O_Laila.3gp

Mujhe Pyar ho gaya

2009-01-13T08:52:00.000+05:30

To download above clip visit:

http://rapidshare.com/files/182303538/Mujhe_Pyar_ho_gaya.3gp

Girlfriend aur Tumharaa!!!

2009-01-13T08:29:00.000+05:30

To download above clip visit:

http://rapidshare.com/files/182304205/Girlfriend_aur_Tumharaa___.3gp

Love ka Rule- Be Cool

2009-01-12T09:28:00.000+05:30

To download above clip visit:

http://rapidshare.com/files/182304668/Love_ka_Rule-_Be_Cool.3gp

Iron Man Photo

2008-11-06T09:26:00.000+05:30

HOT PURSUIT FOR BOURNE

2008-11-05T14:26:00.000+05:30

Mr. Madhav Malvankar Golmal(Marathi)

2008-10-27T16:41:00.000+05:30

Hero's introduction in Golmal(Marathi)

2008-10-27T16:27:00.000+05:30

Heros get attacked by Music from Kung fu Hanstle

2008-10-27T16:10:00.000+05:30

Hee Gulabi Hawa --- Golmal(Marathi)

2008-10-27T15:58:00.000+05:30

GUSTAKH NIGAH by Riteish Deshmukh

2008-10-27T15:44:00.000+05:30

Fights of biker Girls

2008-10-27T15:35:00.000+05:30

Fights Between Gangs of Bikers

2008-10-27T15:20:00.000+05:30

EXCUSE ME..MERA DIL TERE PE FIDA RE

2008-10-27T15:06:00.000+05:30

DHOOM DHADAKA SONG

2008-10-27T14:54:00.000+05:30

Dhamaal - Title Song

2008-10-16T12:17:00.000+05:30

DAD QUESTIONING HIS SON

2008-10-16T12:10:00.000+05:30

CHOTA NIMBUDA

2008-10-16T11:00:00.000+05:30

BOURNE IDENTITY PARK FIGHT

2008-10-16T10:45:00.000+05:30

BOURNE IDENTITY ESCAPE FROM SECURITY

2008-10-15T11:24:00.000+05:30

BOURNE IDENTITY ESCAPE FROM POLICE

2008-10-15T11:10:00.000+05:30

BOURNE IDENTITY ATTACK ON JASON & MARIE

2008-10-15T10:53:00.000+05:30

graph one

2008-10-09T10:12:00.000+05:30

division fraction

2008-10-04T14:15:00.000+05:30

(x-2) | x^7+ 0x^6+0x^5+0x^4+0x^3+0x^2+0x-128| x^6+2x^5+4x^4+8x^3+16x^2+32x+64

x^7-2x^6

-------------------------------------------

2x^6+0x^5+0x^4+0x^3+0x^2+0x-128

2x^6-4x^5

--------------------------------------------------

4x^5+0x^4+0x^3+0x^2+0x-128

4x^5-8x^4

-------------------------------------

8x^4+0x^3+0x^2+0x-128

8x^4-16x^3

-------------------------------

16 x^3+0x^2+0x-128

16x^3-32x^2

-----------------------

32x^2+0x-128

32 x^2-64x

------------------

64x-128

-------------

Arithmetic Series

2008-10-04T10:01:00.000+05:30

Sum (the arithmetic series)

The sum of the components of an arithmetic progression is called an arithmetic series.

[edit] Formula (for the arithmetic series)

Express the arithmetic series in two different ways:

Add both sides of the two equations. All terms involving d cancel, and so we're left with:

Rearranging and remembering that an = a1 + (n − 1)d, we get:

[edit] Product

The product of the components of an arithmetic progression with an initial element a1, common difference d, and n elements in total, is determined in a closed expression by

where denotes the rising factorial and Γ denotes the Gamma function. (Note however that the formula is not valid when a1 / d is a negative integer or zero).

This is a generalization from the fact that the product of the progression is given by the factorial n! and that the product

for positive integers m and n is given by

Bharat Jadhav Trapped Golmal(Marathi)

2008-10-03T11:55:00.000+05:30

BALAJI'S K SERIAL PARADY

2008-10-03T11:09:00.000+05:30

Ishq ka Rog laaga-- AARTI DANCE

2008-10-03T10:41:00.000+05:30

123 Title Song

2008-10-03T10:16:00.000+05:30

Quadratic_equation

2008-10-02T19:46:00.001+05:30

Quadratic formula

A quadratic equation with real or complex coefficients has two, but not necessarily distinct, solutions, called roots, which may or may not be real, given by the quadratic formula:

where the symbol "±" indicates that both

are solutions.

[edit] Discriminant

0: 3⁄2x2+1⁄2x−4⁄3">0: 3⁄2x2+1⁄2x−4⁄3" src="http://upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Quadratic_equation_discriminant.png/180px-Quadratic_equation_discriminant.png" class="thumbimage" border="0" height="180" width="180">

Example discriminant signs
■ <0:>x²+¹⁄₂
■ =0: −⁴⁄₃x²+⁴⁄₃x−¹⁄₃
■ >0: ³⁄₂x²+¹⁄₂x−⁴⁄₃

In the above formula, the expression underneath the square root sign:

is called the discriminant of the quadratic equation.

A quadratic equation with real coefficients can have either one or two distinct real roots, or two distinct complex roots. In this case the discriminant determines the number and nature of the roots. There are three cases:

If the discriminant is positive, there are two distinct roots, both of which are real numbers. For quadratic equations with integer coefficients, if the discriminant is a perfect square, then the roots are rational numbers—in other cases they may be quadratic irrationals.
If the discriminant is zero, there is exactly one distinct root, and that root is a real number. Sometimes called a double root, its value is:
If the discriminant is negative, there are no real roots. Rather, there are two distinct (non-real) complex roots, which are complex conjugates of each other:

Thus the roots are distinct if and only if the discriminant is non-zero, and the roots are real if and only if the discriminant is non-negative.

[edit] Geometry

For the quadratic function:
f (x) = x² − x − 2 = (x + 1)(x − 2) of a real variable x, the x-coordinates of the points where the graph intersects the x-axis, x = −1 and x = 2, are the roots of the quadratic equation: x² − x − 2 = 0.

The roots of the quadratic equation

are also the zeros of the quadratic function:

since they are the values of x for which

If a, b, and c are real numbers and the domain of f is the set of real numbers, then the zeros of f are exactly the x-coordinates of the points where the graph touches the x-axis.

It follows from the above that, if the discriminant is positive, the graph touches the x-axis at two points, if zero, the graph touches at one point, and if negative, the graph does not touch the x-axis.

[edit] Examples

$7 x + 15 - 2 x 2 = 0$ has a strictly positive discriminant $Δ = 169$ and therefore has two real solutions : and .
$x 2 - 2 x + 1 = 0$ has a discriminant $Δ$ whose value is zero, therefore it has a double solution
$x 2 + 3 x + 3 = 0$ has no real solution because $Δ = - 3 <>. But it has two complex solutions x 1 and x 2 : and$

[edit] Quadratic factorization

The term

is a factor of the polynomial

if and only if r is a root of the quadratic equation

It follows from the quadratic formula that

In the special case where the quadratic has only one distinct root (i.e. the discriminant is zero), the quadratic polynomial can be factored as

Eigenvectors

2008-10-02T19:33:00.000+05:30

Left and right eigenvectors

The word eigenvector formally refers to the right eigenvector $x R$ . It is defined by the above eigenvalue equation $A x R = λ R x R$ , and is the most commonly used eigenvector. However, the left eigenvector $x L$ exists as well, and is defined by $x L A = λ L x L$ .

[edit] Characteristic equation

Main article: Characteristic polynomial

When a transformation is represented by a square matrix A, the eigenvalue equation can be expressed as

This can be rearranged to

If there exists an inverse

(A - λ I) - 1,

then both sides can be multiplied by the inverse to obtain the trivial solution: x = 0. Thus we require there to be no inverse by assuming from linear algebra that the determinant equals zero:

det(A - λ I) = 0.

The determinant requirement is called the characteristic equation (less often, secular equation) of A, and the left-hand side is called the characteristic polynomial. When expanded, this gives a polynomial equation for $λ$ . The eigenvector x or its components are not present in the characteristic equation.

[edit] Example

The matrix

defines a linear transformation of the real plane. The eigenvalues of this transformation are given by the characteristic equation

The roots of this equation (i.e. the values of $λ$ for which the equation holds) are $λ = 1$ and $λ = 3$ . Having found the eigenvalues, it is possible to find the eigenvectors. Considering first the eigenvalue $λ = 3$ , we have

Both rows of this matrix equation reduce to the single linear equation $x = y$ . To find an eigenvector, we are free to choose any value for x, so by picking x=1 and setting y=x, we find the eigenvector to be

We can check this is an eigenvector by checking that : For the eigenvalue $λ = 1,$ a similar process leads to the equation $x = - y$ , and hence the eigenvector is given by

The complexity of the problem for finding roots/eigenvalues of the characteristic polynomial increases rapidly with increasing the degree of the polynomial (the dimension of the vector space). There are exact solutions for dimensions below 5, but for higher dimensions there are generally no exact solutions and one has to resort to numerical methods to find them approximately. For large symmetric sparse matrices, Lanczos algorithm is used to compute eigenvalues and eigenvectors.

[edit] Existence and multiplicity of eigenvalues

For transformations on real vector spaces, the coefficients of the characteristic polynomial are all real. However, the roots are not necessarily real; they may well be complex numbers, or a mixture of real and complex numbers. For example, a matrix representing a planar rotation of 45 degrees will not leave any non-zero vector pointing in the same direction. Over a complex vector space, the fundamental theorem of algebra guarantees that the characteristic polynomial has at least one root, and thus the linear transformation has at least one eigenvalue.

As well as distinct roots, the characteristic equation may also have repeated roots. However, having repeated roots does not imply there are multiple distinct (i.e. linearly independent) eigenvectors with that eigenvalue. The algebraic multiplicity of an eigenvalue is defined as the multiplicity of the corresponding root of the characteristic polynomial. The geometric multiplicity of an eigenvalue is defined as the dimension of the associated eigenspace, i.e. number of linearly independent eigenvectors with that eigenvalue.

Over a complex space, the sum of the algebraic multiplicities will equal the dimension of the vector space, but the sum of the geometric multiplicities may be smaller. In a sense, then it is possible that there may not be sufficient eigenvectors to span the entire space. This is intimately related to the question of whether a given matrix may be diagonalized by a suitable choice of coordinates.

[edit] Shear

Horizontal shear. The shear angle φ is given by k = cot φ.

Shear in the plane is a transformation in which all points along a given line remain fixed while other points are shifted parallel to that line by a distance proportional to their perpendicular distance from the line.^[18] Shearing a plane figure does not change its area. Shear can be horizontal − along the X axis, or vertical − along the Y axis. In horizontal shear (see figure), a point P of the plane moves parallel to the X axis to the place P' so that its coordinate y does not change while the x coordinate increments to become x' = x + k y, where k is called the shear factor.

The matrix of a horizontal shear transformation is . The characteristic equation is λ² − 2 λ + 1 = (1 − λ)² = 0 which has a single, repeated root λ = 1. Therefore, the eigenvalue λ = 1 has algebraic multiplicity 2. The eigenvector(s) are found as solutions of

The last equation is equivalent to y = 0, which is a straight line along the x axis. This line represents the one-dimensional eigenspace. In the case of shear the algebraic multiplicity of the eigenvalue (2) is greater than its geometric multiplicity (1, the dimension of the eigenspace). The eigenvector is a vector along the x axis. The case of vertical shear with transformation matrix is dealt with in a similar way; the eigenvector in vertical shear is along the y axis. Applying repeatedly the shear transformation changes the direction of any vector in the plane closer and closer to the direction of the eigenvector.

[edit] Uniform scaling and reflection

Fig. 3. When a surface is stretching equally in all directions (a homothety) any one of the radial vectors can be the eigenvector.

As a one-dimensional vector space, consider a rubber string tied to unmoving support in one end, such as that on a child's sling. Pulling the string away from the point of attachment stretches it and elongates it by some scaling factor λ which is a real number. Each vector on the string is stretched equally, with the same scaling factor λ, and although elongated, it preserves its original direction. For a two-dimensional vector space, consider a rubber sheet stretched equally in all directions such as a small area of the surface of an inflating balloon (Fig. 3). All vectors originating at the fixed point on the balloon surface (the origin) are stretched equally with the same scaling factor λ. This transformation in two-dimensions is described by the 2×2 square matrix:

Expressed in words, the transformation is equivalent to multiplying the length of any vector by λ while preserving its original direction. Since the vector taken was arbitrary, every non-zero vector in the vector space is an eigenvector. Whether the transformation is stretching (elongation, extension, inflation), or shrinking (compression, deflation) depends on the scaling factor: if λ > 1, it is stretching; if λ <>

[edit] Unequal scaling

1) of a unit square. Eigenvectors are u1 and u2 and eigenvalues are λ1 = k1 and λ2 = k2. This transformation orients all vectors towards the principal eigenvector u1."> 1) of a unit square. Eigenvectors are u1 and u2 and eigenvalues are λ1 = k1 and λ2 = k2. This transformation orients all vectors towards the principal eigenvector u1." src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/be/Unequal_scaling.svg/250px-Unequal_scaling.svg.png" class="thumbimage" border="0" height="188" width="250">

Vertical shrink (k₂ <>k₁ > 1) of a unit square. Eigenvectors are u₁ and u₂ and eigenvalues are λ₁ = k₁ and λ₂ = k₂. This transformation orients all vectors towards the principal eigenvector u₁.

For a slightly more complicated example, consider a sheet that is stretched unequally in two perpendicular directions along the coordinate axes, or, similarly, stretched in one direction, and shrunk in the other direction. In this case, there are two different scaling factors: k₁ for the scaling in direction x, and k₂ for the scaling in direction y. The transformation matrix is , and the characteristic equation is $(k 1 - λ)(k 2 - λ) = 0$ . The eigenvalues, obtained as roots of this equation are λ₁ = k₁, and λ₂ = k₂ which means, as expected, that the two eigenvalues are the scaling factors in the two directions. Plugging k₁ back in the eigenvalue equation gives one of the eigenvectors:

or, more simply,

y = 0

Thus, the eigenspace is the x-axis. Similarly, substituting $λ = k 2$ shows that the corresponding eigenspace is the y-axis. In this case, both eigenvalues have algebraic and geometric multiplicities equal to 1. If a given eigenvalue is greater than 1, the vectors are stretched in the direction of the corresponding eigenvector; if less than 1, they are shrunken in that direction. Negative eigenvalues correspond to reflections followed by a stretch or shrink. In general, matrices that are diagonalizable over the real numbers represent scalings and reflections: the eigenvalues represent the scaling factors (and appear as the diagonal terms), and the eigenvectors are the directions of the scalings.

The figure shows the case where $k 1 > 1$ and $1 > k 2 > 0$ . The rubber sheet is stretched along the x axis and simultaneously shrunk along the y axis. After repeatedly applying this transformation of stretching/shrinking many times, almost any vector on the surface of the rubber sheet will be oriented closer and closer to the direction of the x axis (the direction of stretching). The exceptions are vectors along the y-axis, which will gradually shrink away to nothing.

[edit] Rotation

For more details on this topic, see Rotation matrix.

A rotation in a plane is a transformation that describes motion of a vector, plane, coordinates, etc., around a fixed point. Clearly, for rotations other than through 0° and 180°, every vector in the real plane will have its direction changed, and thus there cannot be any eigenvectors. But this is not necessarily true if we consider the same matrix over a complex vector space.

A counterclockwise rotation in the horizontal plane about the origin at an angle φ is represented by the matrix

The characteristic equation of R is λ² − 2λ cos φ + 1 = 0. This quadratic equation has a discriminant D = 4 (cos² φ − 1) = − 4 sin² φ which is a negative number whenever φ is not equal a multiple of 180°. A rotation of 0°, 360°, … is just the identity transformation, (a uniform scaling by +1) while a rotation of 180°, 540°, …, is a reflection (uniform scaling by -1). Otherwise, as expected, there are no real eigenvalues or eigenvectors for rotation in the plane.

[edit] Rotation matrices on complex vector spaces

The characteristic equation has two complex roots λ₁ and λ₂. If we choose to think of the rotation matrix as a linear operator on the complex two dimensional, we can consider these complex eigenvalues. The roots are complex conjugates of each other: λ_1,2 = cos φ ± i sin φ = e ^{± iφ}, each with an algebraic multiplicity equal to 1, where i is the imaginary unit.

The first eigenvector is found by substituting the first eigenvalue, λ₁, back in the eigenvalue equation:

The last equation is equivalent to the single equation $x = i y$ , and again we are free to set $x = 1$ to give the eigenvector

Similarly, substituting in the second eigenvalue gives the single equation $x = - i y$ and so the eigenvector is given by

Although not diagonalizable over the reals, the rotation matrix is diagonalizable over the complex numbers, and again the eigenvalues appear on the diagonal. Thus rotation matrices acting on complex spaces can be thought of as scaling matrices, with complex scaling factors.

GRAPH

2008-10-02T11:13:00.000+05:30

Current–voltage characteristic of Diodes

2008-10-01T22:20:00.001+05:30

Current–voltage characteristic

A semiconductor diode's current–voltage characteristic, or I–V curve, is related to the transport of carriers through the so-called depletion layer or depletion region that exists at the p-n junction between differing semiconductors. When a p-n junction is first created, conduction band (mobile) electrons from the N-doped region diffuse into the P-doped region where there is a large population of holes (places for electrons in which no electron is present) with which the electrons "recombine". When a mobile electron recombines with a hole, both hole and electron vanish, leaving behind an immobile positively charged donor on the N-side and negatively charged acceptor on the P-side. The region around the p-n junction becomes depleted of charge carriers and thus behaves as an insulator.

However, the depletion width cannot grow without limit. For each electron-hole pair that recombines, a positively-charged dopant ion is left behind in the N-doped region, and a negatively charged dopant ion is left behind in the P-doped region. As recombination proceeds and more ions are created, an increasing electric field develops through the depletion zone which acts to slow and then finally stop recombination. At this point, there is a "built-in" potential across the depletion zone.

If an external voltage is placed across the diode with the same polarity as the built-in potential, the depletion zone continues to act as an insulator, preventing any significant electric current flow. This is the reverse bias phenomenon. However, if the polarity of the external voltage opposes the built-in potential, recombination can once again proceed, resulting in substantial electric current through the p-n junction. For silicon diodes, the built-in potential is approximately 0.6 V. Thus, if an external current is passed through the diode, about 0.6 V will be developed across the diode such that the P-doped region is positive with respect to the N-doped region and the diode is said to be "turned on" as it has a forward bias.

Figure 5: I–V characteristics of a P-N junction diode (not to scale).

A diode’s I–V characteristic can be approximated by four regions of operation (see the figure at right).

At very large reverse bias, beyond the peak inverse voltage or PIV, a process called reverse breakdown occurs which causes a large increase in current that usually damages the device permanently. The avalanche diode is deliberately designed for use in the avalanche region. In the zener diode, the concept of PIV is not applicable. A zener diode contains a heavily doped p-n junction allowing electrons to tunnel from the valence band of the p-type material to the conduction band of the n-type material, such that the reverse voltage is "clamped" to a known value (called the zener voltage), and avalanche does not occur. Both devices, however, do have a limit to the maximum current and power in the clamped reverse voltage region. Also, following the end of forward conduction in any diode, there is reverse current for a short time. The device does not attain its full blocking capability until the reverse current ceases.

The second region, at reverse biases more positive than the PIV, has only a very small reverse saturation current. In the reverse bias region for a normal P-N rectifier diode, the current through the device is very low (in the µA range).

The third region is forward but small bias, where only a small forward current is conducted.

As the potential difference is increased above an arbitrarily defined "cut-in voltage" or "on-voltage" or "diode forward voltage drop (V_d)", the diode current becomes appreciable (the level of current considered "appreciable" and the value of cut-in voltage depends on the application), and the diode presents a very low resistance.

The current–voltage curve is exponential. In a normal silicon diode at rated currents, the arbitrary "cut-in" voltage is defined as 0.6 to 0.7 volts. The value is different for other diode types — Schottky diodes can be as low as 0.2 V and red light-emitting diodes (LEDs) can be 1.4 V or more and blue LEDs can be up to 4.0 V.

At higher currents the forward voltage drop of the diode increases. A drop of 1 V to 1.5 V is typical at full rated current for power diodes.

[edit] Shockley diode equation

The Shockley ideal diode equation or the diode law (named after transistor co-inventor William Bradford Shockley, not to be confused with tetrode inventor Walter H. Schottky) is the I–V characteristic of an ideal diode in either forward or reverse bias (or no bias). The equation is:

where

I is the diode current,

I_S is the reverse bias saturation current,

V_D is the voltage across the diode,

V_T is the thermal voltage,

and n is the emission coefficient, also known as the ideality factor. The emission coefficient n varies from about 1 to 2 depending on the fabrication process and semiconductor material and in many cases is assumed to be approximately equal to 1 (thus the notation

n

is omitted).

The thermal voltage V_T is approximately 25.85 mV at 300 K, a temperature close to “room temperature” commonly used in device simulation software. At any temperature it is a known constant defined by:

where

q is the magnitude of charge on an electron (the elementary charge),

k is Boltzmann’s constant,

T is the absolute temperature of the p-n junction in kelvins

The Shockley ideal diode equation or the diode law is derived with the assumption that the only processes giving rise to current in the diode are drift (due to electrical field), diffusion, and thermal recombination-generation. It also assumes that the recombination-generation (R-G) current in the depletion region is insignificant. This means that the Shockley equation doesn’t account for the processes involved in reverse breakdown and photon-assisted R-G. Additionally, it doesn’t describe the “leveling off” of the I–V curve at high forward bias due to internal resistance.

Under reverse bias voltages (see Figure 5) the exponential in the diode equation is negligible, and the current is a constant (negative) reverse current value of -I_S. The reverse breakdown region is not modeled by the Shockley diode equation.

For even rather small forward bias voltages (see Figure 5) the exponential is very large because the thermal voltage is very small, so the subtracted ‘1’ in the diode equation is negligible and the forward diode current is often approximated as

The use of the diode equation in circuit problems is illustrated in the article on diode modeling.

[edit] Small-signal behavior

For circuit design, a small-signal model of the diode behavior often proves useful. A specific example of diode modeling is discussed in the article on small-signal circuits.

[edit] Types of semiconductor diode


Diode	Zener diode	Schottky diode	Tunnel diode

Light-emitting diode	Photodiode	Varicap	Silicon controlled rectifier

Figure 7: Some diode symbols

There are several types of junction diodes, which either emphasize a different physical aspect of a diode often by geometric scaling, doping level, choosing the right electrodes, are just an application of a diode in a special circuit, or are really different devices like the Gunn and laser diode and the MOSFET:

Normal (p-n) diodes, which operate as described above, are usually made of doped silicon or, more rarely, germanium. Before the development of modern silicon power rectifier diodes, cuprous oxide and later selenium was used; its low efficiency gave it a much higher forward voltage drop (typically 1.4–1.7 V per “cell”, with multiple cells stacked to increase the peak inverse voltage rating in high voltage rectifiers), and required a large heat sink (often an extension of the diode’s metal substrate), much larger than a silicon diode of the same current ratings would require. The vast majority of all diodes are the p-n diodes found in CMOS integrated circuits, which include two diodes per pin and many other internal diodes.

Avalanche diodes

Diodes that conduct in the reverse direction when the reverse bias voltage exceeds the breakdown voltage. These are electrically very similar to Zener diodes, and are often mistakenly called Zener diodes, but break down by a different mechanism, the avalanche effect. This occurs when the reverse electric field across the p-n junction causes a wave of ionization, reminiscent of an avalanche, leading to a large current. Avalanche diodes are designed to break down at a well-defined reverse voltage without being destroyed. The difference between the avalanche diode (which has a reverse breakdown above about 6.2 V) and the Zener is that the channel length of the former exceeds the “mean free path” of the electrons, so there are collisions between them on the way out. The only practical difference is that the two types have temperature coefficients of opposite polarities.

Cat’s whisker or crystal diodes

These are a type of point contact diode. The cat’s whisker diode consists of a thin or sharpened metal wire pressed against a semiconducting crystal, typically galena or a piece of coal.[3] The wire forms the anode and the crystal forms the cathode. Cat’s whisker diodes were also called crystal diodes and found application in crystal radio receivers. Cat’s whisker diodes are obsolete.

Constant current diodes

These are actually a JFET with the gate shorted to the source, and function like a two-terminal current-limiter analog to the Zener diode, which is limiting voltage. They allow a current through them to rise to a certain value, and then level off at a specific value. Also called CLDs, constant-current diodes, diode-connected transistors, or current-regulating diodes.

Esaki or tunnel diodes

these have a region of operation showing negative resistance caused by quantum tunneling, thus allowing amplification of signals and very simple bistable circuits. These diodes are also the type most resistant to nuclear radiation.

Gunn diodes

These are similar to tunnel diodes in that they are made of materials such as GaAs or InP that exhibit a region of negative differential resistance. With appropriate biasing, dipole domains form and travel across the diode, allowing high frequency microwave oscillators to be built.

Light-emitting diodes (LEDs)

In a diode formed from a direct band-gap semiconductor, such as gallium arsenide, carriers that cross the junction emit photons when they recombine with the majority carrier on the other side. Depending on the material, wavelengths (or colors) from the infrared to the near ultraviolet may be produced. The forward potential of these diodes depends on the wavelength of the emitted photons: 1.2 V corresponds to red, 2.4 to violet. The first LEDs were red and yellow, and higher-frequency diodes have been developed over time. All LEDs produce incoherent, narrow-spectrum light; “white” LEDs are actually combinations of three LEDs of a different color, or a blue LED with a yellow scintillator coating. LEDs can also be used as low-efficiency photodiodes in signal applications. An LED may be paired with a photodiode or phototransistor in the same package, to form an opto-isolator.

Laser diodes

When an LED-like structure is contained in a resonant cavity formed by polishing the parallel end faces, a laser can be formed. Laser diodes are commonly used in optical storage devices and for high speed optical communication.

Peltier diodes

are used as sensors, heat engines for thermoelectric cooling. Charge carriers absorb and emit their band gap energies as heat.

Photodiodes

All semiconductors are subject to optical charge carrier generation. This is typically an undesired effect, so most semiconductors are packaged in light blocking material. Photodiodes are intended to sense light(photodetector), so they are packaged in materials that allow light to pass, and are usually PIN (the kind of diode most sensitive to light). A photodiode can be used in solar cells, in photometry, or in optical communications. Multiple photodiodes may be packaged in a single device, either as a linear array or as a two-dimensional array. These arrays should not be confused with charge-coupled devices.

Point-contact diodes

These work the same as the junction semiconductor diodes described above, but their construction is simpler. A block of n-type semiconductor is built, and a conducting sharp-point contact made with some group-3 metal is placed in contact with the semiconductor. Some metal migrates into the semiconductor to make a small region of p-type semiconductor near the contact. The long-popular 1N34 germanium version is still used in radio receivers as a detector and occasionally in specialized analog electronics.

PIN diodes

A PIN diode has a central un-doped, or intrinsic, layer, forming a p-type/intrinsic/n-type structure. They are used as radio frequency switches and attenuators. They are also used as large volume ionizing radiation detectors and as photodetectors. PIN diodes are also used in power electronics, as their central layer can withstand high voltages. Furthermore, the PIN structure can be found in many power semiconductor devices, such as IGBTs, power MOSFETs, and thyristors.

Schottky diodes

Schottky diodes are constructed from a metal to semiconductor contact. They have a lower forward voltage drop than p-n junction diodes. Their forward voltage drop at forward currents of about 1 mA is in the range 0.15 V to 0.45 V, which makes them useful in voltage clamping applications and prevention of transistor saturation. They can also be used as low loss rectifiers although their reverse leakage current is generally higher than that of other diodes. Schottky diodes are majority carrier devices and so do not suffer from minority carrier storage problems that slow down many other diodes — so they have a faster “reverse recovery” than p-n junction diodes. They also tend to have much lower junction capacitance than p-n diodes which provides for high switching speeds and their use in high-speed circuitry and RF devices such as switched-mode power supply, mixers and detectors.

Super Barrier Diodes

Super barrier diodes are rectifier diodes that incorporate the low forward voltage drop of the Schottky diode with the surge-handling capability and low reverse leakage current of a normal p-n junction diode.

Gold-doped” diodes

As a dopant, gold (or platinum) acts as recombination centers, which help a fast recombination of minority carriers. This allows the diode to operate at signal frequencies, at the expense of a higher forward voltage drop. Gold doped diodes are faster than other p-n diodes (but not as fast as Schottky diodes). They also have less reverse-current leakage than Schottky diodes (but not as good as other p-n diodes).[4].^[6] A typical example is the 1N914.

Snap-off or Step recovery diodes

The term ‘step recovery’ relates to the form of the reverse recovery characteristic of these devices. After a forward current has been passing in an SRD and the current is interrupted or reversed, the reverse conduction will cease very abruptly (as in a step waveform). SRDs can therefore provide very fast voltage transitions by the very sudden disappearance of the charge carriers.

Transient voltage suppression diode (TVS)

These are avalanche diodes designed specifically to protect other semiconductor devices from high-voltage transients. Their p-n junctions have a much larger cross-sectional area than those of a normal diode, allowing them to conduct large currents to ground without sustaining damage.

Varicap or varactor diodes

These are used as voltage-controlled capacitors. These are important in PLL (phase-locked loop) and FLL (frequency-locked loop) circuits, allowing tuning circuits, such as those in television receivers, to lock quickly, replacing older designs that took a long time to warm up and lock. A PLL is faster than an FLL, but prone to integer harmonic locking (if one attempts to lock to a broadband signal). They also enabled tunable oscillators in early discrete tuning of radios, where a cheap and stable, but fixed-frequency, crystal oscillator provided the reference frequency for a voltage-controlled oscillator.

Zener diodes

Diodes that can be made to conduct backwards. This effect, called Zener breakdown, occurs at a precisely defined voltage, allowing the diode to be used as a precision voltage reference. In practical voltage reference circuits Zener and switching diodes are connected in series and opposite directions to balance the temperature coefficient to near zero. Some devices labeled as high-voltage Zener diodes are actually avalanche diodes (see below). Two (equivalent) Zeners in series and in reverse order, in the same package, constitute a transient absorber (or Transorb, a registered trademark). The Zener diode is named for Dr. Clarence Melvin Zener of Southern Illinois University, inventor of the device.

Types of Viscosity

2008-10-01T22:11:00.000+05:30

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or extensional stress. In general terms it is the resistance of a liquid to flow, or its "thickness". Viscosity describes a fluid's internal resistance to flow and may be thought of as a measure of fluid friction. Thus, water is "thin", having a lower viscosity, while vegetable oil is "thick" having a higher viscosity. All real fluids (except superfluids) have some resistance to stress, but a fluid which has no resistance to shear stress is known as an ideal fluid or inviscid fluid. For example, a high viscosity magma will create a tall volcano, because it cannot spread fast enough; low viscosity lava will create a shield volcano, which is large and wide.^[1] The study of viscosity is known as rheology.

Etymology

The word "viscosity" derives from the Latin word "viscum" for mistletoe. A viscous glue was made from mistletoe berries and used for lime-twigs to catch birds.^[2]

Viscosity coefficients

When looking at a value for viscosity, the number that one most often sees is the coefficient of viscosity. There are several different viscosity coefficients depending on the nature of applied stress and nature of the fluid. They are introduced in the main books on hydrodynamics^[3]^[4] and rheology.^[5]

Dynamic viscosity (or absolute viscosity) determines the dynamics of an incompressible Newtonian fluid;
Kinematic viscosity is the dynamic viscosity divided by the density for a Newtonian fluid;
Volume viscosity (or bulk viscosity) determines the dynamics of a compressible Newtonian fluid;
Shear viscosity is the viscosity coefficient when the applied stress is a shear stress (valid for non-Newtonian fluids);
Extensional viscosity is the viscosity coefficient when the applied stress is an extensional stress (valid for non-Newtonian fluids).

Shear viscosity and dynamic viscosity are much better known than the others. That is why they are often referred to as simply viscosity. Simply put, this quantity is the ratio between the pressure exerted on the surface of a fluid, in the lateral or horizontal direction, to the change in velocity of the fluid as you move down in the fluid (this is what is referred to as a velocity gradient). For example, at room temperature, water has a nominal viscosity of 1.0 × 10^-3 Pa∙s and motor oil has a nominal apparent viscosity of 250 × 10^-3 Pa∙s.^[6]

Extensional viscosity is widely used for characterizing polymers.

Volume viscosity is essential for Acoustics in fluids, see Stokes' law (sound attenuation) ^[7]

Newton's theory

Laminar shear of fluid between two plates. Friction between the fluid and the moving boundaries causes the fluid to shear. The force required for this action is a measure of the fluid's viscosity. This type of flow is known as a Couette flow.

Laminar shear, the non-constant gradient, is a result of the geometry the fluid is flowing through (e.g. a pipe).

In general, in any flow, layers move at different velocities and the fluid's viscosity arises from the shear stress between the layers that ultimately opposes any applied force.

Isaac Newton postulated that, for straight, parallel and uniform flow, the shear stress, τ, between layers is proportional to the velocity gradient, ∂u/∂y, in the direction perpendicular to the layers.

Here, the constant $μ$ is known as the coefficient of viscosity, the viscosity, the dynamic viscosity, or the Newtonian viscosity. Many fluids, such as water and most gases, satisfy Newton's criterion and are known as Newtonian fluids. Non-Newtonian fluids exhibit a more complicated relationship between shear stress and velocity gradient than simple linearity.

The relationship between the shear stress and the velocity gradient can also be obtained by considering two plates closely spaced apart at a distance y, and separated by a homogeneous substance. Assuming that the plates are very large, with a large area A, such that edge effects may be ignored, and that the lower plate is fixed, let a force F be applied to the upper plate. If this force causes the substance between the plates to undergo shear flow (as opposed to just shearing elastically until the shear stress in the substance balances the applied force), the substance is called a fluid. The applied force is proportional to the area and velocity of the plate and inversely proportional to the distance between the plates. Combining these three relations results in the equation $F = μ(A u / y)$ , where $μ$ is the proportionality factor called the dynamic viscosity (also called absolute viscosity, or simply viscosity). The equation can be expressed in terms of shear stress; $τ = F / A = μ(u / y)$ . The rate of shear deformation is $u / y$ and can be also written as a shear velocity, du/dy. Hence, through this method, the relation between the shear stress and the velocity gradient can be obtained.

James Clerk Maxwell called viscosity fugitive elasticity because of the analogy that elastic deformation opposes shear stress in solids, while in viscous fluids, shear stress is opposed by rate of deformation.

Viscosity measurement

Dynamic viscosity is measured with various types of rheometer. Close temperature control of the fluid is essential to accurate measurements, particularly in materials like lubricants, whose viscosity can double with a change of only 5 °C. For some fluids, it is a constant over a wide range of shear rates. These are Newtonian fluids.

The fluids without a constant viscosity are called Non-Newtonian fluids. Their viscosity cannot be described by a single number. Non-Newtonian fluids exhibit a variety of different correlations between shear stress and shear rate.

One of the most common instruments for measuring kinematic viscosity is the glass capillary viscometer.

In paint industries, viscosity is commonly measured with a Zahn cup, in which the efflux time is determined and given to customers. The efflux time can also be converted to kinematic viscosities (cSt) through the conversion equations.

Also used in paint, a Stormer viscometer uses load-based rotation in order to determine viscosity. The viscosity is reported in Krebs units (KU), which are unique to Stormer viscometers.

Vibrating viscometers can also be used to measure viscosity. These models such as the Dynatrol use vibration rather than rotation to measure viscosity.

Extensional viscosity can be measured with various rheometers that apply extensional stress

Volume viscosity can be measured with acoustic rheometer.

Units of measure

Dynamic viscosity

The usual symbol for dynamic viscosity used by mechanical engineers, fluid dynamicists and ASHRAE is the Greek letter mu ( $μ$ )^[8]^[9]^[10]^[11]. The symbol $η$ is also used by chemists and IUPAC^[12]. The SI physical unit of dynamic viscosity is the pascal-second (Pa·s), which is identical to kg·m⁻¹·s⁻¹. If a fluid with a viscosity of one Pa·s is placed between two plates, and one plate is pushed sideways with a shear stress of one pascal, it moves a distance equal to the thickness of the layer between the plates in one second.

The cgs physical unit for dynamic viscosity is the poise^[13] (P), named after Jean Louis Marie Poiseuille. It is more commonly expressed, particularly in ASTM standards, as centipoise (cP). Water at 20 °C has a viscosity of 1.0020 cP.

1 P = 1 g·cm⁻¹·s⁻¹

The relation between poise and pascal-seconds is:

10 P = 1 kg·m⁻¹·s⁻¹ = 1 Pa·s

1 cP = 0.001 Pa·s = 1 mPa·s

The name 'poiseuille' (Pl) was proposed for this unit (after Jean Louis Marie Poiseuille who formulated Poiseuille's law of viscous flow), but not accepted internationally.^{[citation needed]} Care must be taken in not confusing the poiseuille with the poise named after the same person.

Kinematic viscosity

In many situations, we are concerned with the ratio of the viscous force to the inertial force, the latter characterised by the fluid density ρ. This ratio is characterised by the kinematic viscosity (Greek letter nu, $ν$ ), defined as follows:

where $μ$ is the dynamic viscosity (Pa·s) and $ρ$ is the density (kg/m³), and $ν$ is the kinematic viscosity (m²/s).

The obsolete cgs physical unit for kinematic viscosity is the stokes (St), named after George Gabriel Stokes. It is sometimes expressed in terms of centistokes (cSt or ctsk). In U.S. usage, stoke is sometimes used as the singular form.

1 stokes = 100 centistokes = 1 cm²·s⁻¹ = 0.0001 m²·s⁻¹.

1 centistokes = 1 mm²·s^-1 = 10^-6m²·s⁻¹

The kinematic viscosity is sometimes referred to as diffusivity of momentum, because it is comparable to and has the same unit (m²s⁻¹) as diffusivity of heat and diffusivity of mass. It is therefore used in dimensionless numbers which compare the ratio of the diffusivities.

Saybolt Universal Viscosity

At one time the petroleum industry relied on measuring kinematic viscosity by means of the Saybolt viscometer, and expressing kinematic viscosity in units of Saybolt Universal Seconds (SUS). ^[14] Kinematic viscosity in centistoke can be converted from SUS according to the arithmetic and the reference tabel provided in ASTM D 2161. It can also be converted in computerized method, or vice versa.^[15]

Relation to Mean Free Path of Diffusing Particles

In relation to diffusion, the kinematic viscosity provides a better understanding of the behavior of mass transport of a dilute species. Viscosity is related to shear stress and the rate of shear in a fluid, which illustrates its dependence on the mean free path, $λ$ , of the diffusing particles.

From fluid mechanics, shear stress, $τ$ , is the rate of change of velocity with distance perpendicular to the direction of movement.

Interpreting shear stress as the time rate of change of momentum,p, per unit area (rate of momentum flux) of an arbitrary control surface gives

Further manipulation will show

where

is the rate of change of mass

ρ

is the density of the fluid

is the average molecular speed

μ

is the dynamic viscosity.

Dynamic versus kinematic viscosity

Conversion between kinematic and dynamic viscosity is given by $νρ = μ$ .

For example,

ν =

0.0001 m²·s^-1 and

ρ =

1000 kg m^-3 then

μ = νρ =

0.1 kg·m⁻¹·s⁻¹ = 0.1 Pa·s

ν =

1 St (= 1 cm²·s⁻¹) and

ρ =

1 g cm^-3 then

μ = νρ =

1 g·cm⁻¹·s⁻¹ = 1 P

Example: viscosity of water

Because of its density of $ρ$ = 1 g/cm³ (varies slightly with temperature), and its dynamic viscosity is near 1 mPa·s (see #Viscosity of water section), the viscosity values of water are, to rough precision, all powers of ten:

Dynamic viscosity:

μ

= 1 mPa·s = 10^-3 Pa·s = 1 cP = 10^-2 poise

Kinematic viscosity:

ν

= 1 cSt = 10^-2 stokes = 1 mm²/s

Molecular origins

Pitch has a viscosity approximately 100 billion times that of water.

The viscosity of a system is determined by how molecules constituting the system interact. There are no simple but correct expressions for the viscosity of a fluid. The simplest exact expressions are the Green-Kubo relations for the linear shear viscosity or the Transient Time Correlation Function expressions derived by Evans and Morriss in 1985. Although these expressions are each exact in order to calculate the viscosity of a dense fluid, using these relations requires the use of molecular dynamics computer simulations.

Gases

Viscosity in gases arises principally from the molecular diffusion that transports momentum between layers of flow. The kinetic theory of gases allows accurate prediction of the behavior of gaseous viscosity.

Within the regime where the theory is applicable:

Viscosity is independent of pressure and
Viscosity increases as temperature increases.

James Clerk Maxwell published a famous paper in 1866 using the kinetic theory of gases to study gaseous viscosity.^[16]

Effect of temperature on the viscosity of a gas

Sutherland's formula can be used to derive the dynamic viscosity of an ideal gas as a function of the temperature:

where:

$μ$ = dynamic viscosity in (Pa·s) at input temperature $T$
$μ 0$ = reference viscosity in (Pa·s) at reference temperature $T 0$
$T$ = input temperature in kelvin
$T 0$ = reference temperature in kelvin
$C$ = Sutherland's constant for the gaseous material in question

Valid for temperatures between 0 < $T$ <>

Sutherland's constant and reference temperature for some gases

Gas	$C$ [K]	$T 0$ [K]	$μ 0$ [10^-6 Pa s]
air	120	291.15	18.27
nitrogen	111	300.55	17.81
oxygen	127	292.25	20.18
carbon dioxide	240	293.15	14.8
carbon monoxide	118	288.15	17.2
hydrogen	72	293.85	8.76
ammonia	370	293.15	9.82
sulfur dioxide	416	293.65	12.54
helium	79.4 ^[17]	273	19 ^[18]

(also see: ^[19])

Viscosity of a dilute gas

The Chapman-Enskog equation^[20] may be used to estimate viscosity for a dilute gas. This equation is based on semi-theorethical assumption by Chapman and Enskoq. The equation requires three empirically determined parameters: the collision diameter (σ), the maximum energy of attraction divided by the Boltzmann constant (є/к) and the collision integral (ω(T*)).

T*=κT/ε Reduced temperature (dimensionless)
$μ 0$ = viscosity for dilute gas (uP)
$M$ = molecular mass (g/mol)
$T$ = temperature (K)
$σ$ = the collision diameter (Å)
$ε / κ$ = the maximum energy of attraction divided by the Boltzmann constant (K)
$ω μ$ = the collision integral

Liquids

In liquids, the additional forces between molecules become important. This leads to an additional contribution to the shear stress though the exact mechanics of this are still controversial.^{[citation needed]} Thus, in liquids:

Viscosity is independent of pressure (except at very high pressure); and
Viscosity tends to fall as temperature increases (for example, water viscosity goes from 1.79 cP to 0.28 cP in the temperature range from 0 °C to 100 °C); see temperature dependence of liquid viscosity for more details.

The dynamic viscosities of liquids are typically several orders of magnitude higher than dynamic viscosities of gases.

Viscosity of blends of liquids

The viscosity of the blend of two or more liquids can be estimated using the Refutas equation^[21]^[22]. The calculation is carried out in three steps.

The first step is to calculate the Viscosity Blending Number (VBN) (also called the Viscosity Blending Index) of each component of the blend:

(1)

where v is the kinematic viscosity in centistokes (cSt). It is important that the kinematic viscosity of each component of the blend be obtained at the same temperature.

The next step is to calculate the VBN of the blend, using this equation:

(2)

where $x X$ is the mass fraction of each component of the blend.

Once the viscosity blending number of a blend has been calculated using equation (2), the final step is to determine the kinematic viscosity of the blend by solving equation (1) for v:

(3)

where $V B N B l e n d$ is the viscosity blending number of the blend.

Viscosity of selected substances

The viscosity of air and water are by far the two most important materials for aviation aerodynamics and shipping fluid dynamics. Temperature plays the main role in determining viscosity.

Viscosity of air

The viscosity of air depends mostly on the temperature. At 15.0 °C, the viscosity of air is 1.78 × 10⁻⁵ kg/(m·s) or 1.78 × 10⁻⁴ P. One can get the viscosity of air as a function of temperature from the Gas Viscosity Calculator

Viscosity of water

The viscosity of water is 8.90 × 10⁻⁴ Pa·s or 8.90 × 10⁻³ dyn·s/cm² or 0.890 cP at about 25 °C.
As a function of temperature T (K): μ(Pa·s) = A × 10^B/(T−C)
where A=2.414 × 10⁻⁵ Pa·s ; B = 247.8 K ; and C = 140 K.

Viscosity of water at different temperatures is listed below.

Temperature [°C]	viscosity [Pa·s]
10	1.308 × 10⁻³
20	1.003 × 10⁻³
30	7.978 × 10⁻⁴
40	6.531 × 10⁻⁴
50	5.471 × 10⁻⁴
60	4.668 × 10⁻⁴
70	4.044 × 10⁻⁴
80	3.550 × 10⁻⁴
90	3.150 × 10⁻⁴
100	2.822 × 10⁻⁴

Viscosity of various materials

Example of the viscosity of milk and water. Liquids with higher viscosities will not make such a splash when poured at the same velocity.

Honey being drizzled.

Peanut butter is a semi-solid and so can hold peaks.

Some dynamic viscosities of Newtonian fluids are listed below:

Gases (at 0 °C):

	viscosity [Pa·s]
hydrogen	8.4 × 10⁻⁶
air	17.4 × 10⁻⁶
xenon	2.12 × 10⁻⁵

Liquids (at 25 °C):

	viscosity [Pa·s]	viscosity [cP]
liquid nitrogen @ 77K	1.58 × 10⁻⁴	0.158
acetone*	3.06 × 10⁻⁴	0.306
methanol*	5.44 × 10⁻⁴	0.544
benzene*	6.04 × 10⁻⁴	0.604
blood	3 to 4 × 10⁻³^[23]	1,37^[24]
water	8.94 × 10⁻⁴	0.894
ethanol*	1.074 × 10⁻³	1.074
mercury*	1.526 × 10⁻³	1.526
nitrobenzene*	1.863 × 10⁻³	1.863
propanol*	1.945 × 10⁻³	1.945
Ethylene glycol	1.61 × 10⁻²	16.1
sulfuric acid*	2.42 × 10⁻²	24.2
olive oil	.081	81
glycerol	1.5	1500
castor oil*	.985	985
corn syrup*	1.3806	1380.6
HFO-380	2.022	2022
pitch	2.3 × 10⁸	2.3 × 10¹¹

* Data from CRC Handbook of Chemistry and Physics, 73^rd edition, 1992-1993.

Fluids with variable compositions, such as honey, can have a wide range of viscosities.

A more complete table can be found at Transwiki, including the following:

	viscosity [cP]
honey	2,000–10,000
molasses	5,000–10,000
molten glass	10,000–1,000,000
chocolate syrup	10,000–25,000
molten chocolate^*	45,000–130,000 ^[25]
ketchup^*	50,000–100,000
peanut butter	~250,000
shortening^*	~250,000

* These materials are highly non-Newtonian.

Viscosity of solids

On the basis that all solids, such as granite^[26] flow to a small extent in response to shear stress some researchers^[27] have contended that substances known as amorphous solids, such as glass and many polymers, may be considered to have viscosity. This has led some to the view that solids are simply liquids with a very high viscosity, typically greater than 10¹² Pa·s. This position is often adopted by supporters of the widely held misconception that glass flow can be observed in old buildings. This distortion is more likely the result of the glass making process rather than the viscosity of glass.^[28]

However, others argue that solids are, in general, elastic for small stresses while fluids are not.^[29] Even if solids flow at higher stresses, they are characterized by their low-stress behavior. Viscosity may be an appropriate characteristic for solids in a plastic regime. The situation becomes somewhat confused as the term viscosity is sometimes used for solid materials, for example Maxwell materials, to describe the relationship between stress and the rate of change of strain, rather than rate of shear.

These distinctions may be largely resolved by considering the constitutive equations of the material in question, which take into account both its viscous and elastic behaviors. Materials for which both their viscosity and their elasticity are important in a particular range of deformation and deformation rate are called viscoelastic. In geology, earth materials that exhibit viscous deformation at least three times greater than their elastic deformation are sometimes called rheids.

Viscosity of amorphous materials

Common glass viscosity curves.^[30]

Viscous flow in amorphous materials (e.g. in glasses and melts)^[31]^[32]^[33] is a thermally activated process:

where $Q$ is activation energy, $T$ is temperature, $R$ is the molar gas constant and $A$ is approximately a constant.

The viscous flow in amorphous materials is characterized by a deviation from the Arrhenius-type behavior: $Q$ changes from a high value $Q H$ at low temperatures (in the glassy state) to a low value $Q L$ at high temperatures (in the liquid state). Depending on this change, amorphous materials are classified as either

strong when: $Q H - Q L < Q L$ or
fragile when:

The fragility of amorphous materials is numerically characterized by the Doremus’ fragility ratio:

$R D = Q H / Q L$

and strong material have whereas fragile materials have

The viscosity of amorphous materials is quite exactly described by a two-exponential equation:

with constants $A 1, A 2, B, C$ and $D$ related to thermodynamic parameters of joining bonds of an amorphous material.

Not very far from the glass transition temperature, $T g$ , this equation can be approximated by a Vogel-Tammann-Fulcher (VTF) equation or a Kohlrausch-type stretched-exponential law.

If the temperature is significantly lower than the glass transition temperature, $T < T g$ , then the two-exponential equation simplifies to an Arrhenius type equation:

with:

$Q H = H d + H m$

where $H d$ is the enthalpy of formation of broken bonds (termed configurons) and $H m$ is the enthalpy of their motion. When the temperature is less than the glass transition temperature, $T < T g$ , the activation energy of viscosity is high because the amorphous materials are in the glassy state and most of their joining bonds are intact.

If the temperature is highly above the glass transition temperature, $T > T g$ , the two-exponential equation also simplifies to an Arrhenius type equation:

with:

$Q L = H m$

When the temperature is higher than the glass transition temperature, $T > T g$ , the activation energy of viscosity is low because amorphous materials are melt and have most of their joining bonds broken which facilitates flow.

Volume (bulk) viscosity

The negative-one-third of the trace of the stress tensor is often identified with the thermodynamic pressure,

,

which only depends upon the equilibrium state potentials like temperature and density (equation of state). In general, the trace of the stress tensor is the sum of thermodynamic pressure contribution plus another contribution which is proportional to the divergence of the velocity field. This constant of proportionality is called the volume viscosity.

Eddy viscosity

In the study of turbulence in fluids, a common practical strategy for calculation is to ignore the small-scale vortices (or eddies) in the motion and to calculate a large-scale motion with an eddy viscosity that characterizes the transport and dissipation of energy in the smaller-scale flow (see large eddy simulation). Values of eddy viscosity used in modeling ocean circulation may be from 5x10⁴ to 10⁶ Pa·s depending upon the resolution of the numerical grid.

Fluidity

The reciprocal of viscosity is fluidity, usually symbolized by $φ = 1 / μ$ or $F = 1 / μ$ , depending on the convention used, measured in reciprocal poise (cm·s·g^-1), sometimes called the rhe. Fluidity is seldom used in engineering practice.

The concept of fluidity can be used to determine the viscosity of an ideal solution. For two components $a$ and $b$ , the fluidity when $a$ and $b$ are mixed is

which is only slightly simpler than the equivalent equation in terms of viscosity:

where $χ a$ and $χ b$ is the mole fraction of component $a$ and $b$ respectively, and $μ a$ and $μ b$ are the components pure viscosities.

The linear viscous stress tensor

(See Hooke's law and strain tensor for an analogous development for linearly elastic materials.)

Viscous forces in a fluid are a function of the rate at which the fluid velocity is changing over distance. The velocity at any point is specified by the velocity field . The velocity at a small distance from point may be written as a Taylor series:

where is shorthand for the dyadic product of the del operator and the velocity:

This is just the Jacobian of the velocity field. Viscous forces are the result of relative motion between elements of the fluid, and so are expressible as a function of the velocity field. In other words, the forces at are a function of and all derivatives of at that point. In the case of linear viscosity, the viscous force will be a function of the Jacobian tensor alone. For almost all practical situations, the linear approximation is sufficient.

If we represent x, y, and z by indices 1, 2, and 3 respectively, the i,j component of the Jacobian may be written as where is shorthand for . Note that when the first and higher derivative terms are zero, the velocity of all fluid elements is parallel, and there are no viscous forces.

Any matrix may be written as the sum of an antisymmetric matrix and a symmetric matrix, and this decomposition is independent of coordinate system, and so has physical significance. The velocity field may be approximated as:

where Einstein notation is now being used in which repeated indices in a product are implicitly summed. The second term from the right is the asymmetric part of the first derivative term, and it represents a rigid rotation of the fluid about with angular velocity $ω$ where:

For such a rigid rotation, there is no change in the relative positions of the fluid elements, and so there is no viscous force associated with this term. The remaining symmetric term is responsible for the viscous forces in the fluid. Assuming the fluid is isotropic (i.e. its properties are the same in all directions), then the most general way that the symmetric term (the rate-of-strain tensor) can be broken down in a coordinate-independent (and therefore physically real) way is as the sum of a constant tensor (the rate-of-expansion tensor) and a traceless symmetric tensor (the rate-of-shear tensor):

where $δ i j$ is the unit tensor. The most general linear relationship between the stress tensor and the rate-of-strain tensor is then a linear combination of these two tensors:^[34]

where $ζ$ is the coefficient of bulk viscosity (or "second viscosity") and $μ$ is the coefficient of (shear) viscosity.

The forces in the fluid are due to the velocities of the individual molecules. The velocity of a molecule may be thought of as the sum of the fluid velocity and the thermal velocity. The viscous stress tensor described above gives the force due to the fluid velocity only. The force on an area element in the fluid due to the thermal velocities of the molecules is just the hydrostatic pressure. This pressure term ( $- p δ i j$ ) must be added to the viscous stress tensor to obtain the total stress tensor for the fluid.

The infinitesimal force $d F i$ on an infinitesimal area $d A i$ is then given by the usual relationship:

Types of Plating

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Gold plating

Main article: Gold plating

Gold plating is a method of depositing a thin layer of gold on the surface of other metal, most often copper or silver.

Gold plating is often used in electronics, to provide a corrosion-resistant electrically conductive layer on copper, typically in electrical connectors and printed circuit boards. With direct gold-on-copper plating, the copper atoms have the tendency to diffuse through the gold layer, causing tarnishing of its surface and formation of an oxide/sulfide layer. A layer of a suitable barrier metal, usually nickel, has therefore to be deposited on the copper substrate, forming a copper-nickel-gold sandwich.

Metals may also be coated with gold for ornamental purposes, using a number of different processes usually referred to as gilding.

[edit] Silver plating

For less demanding applications in electronics, silver is often used as a cheaper replacement for gold. Care should be used for parts exposed to high humidity environments. When the silver layer is porous or contains cracks, the underlying copper undergoes rapid galvanic corrosion, flaking off the bell end crust the plating and exposing the copper itself; a process known as red plague.

Historically, silver plate was used to provide a cheaper version of items that might otherwise be made of silver, including cutlery and candlesticks. The earliest kind was Old Sheffield Plate, but in the 19th century new methods of production (including electroplating) were introduced: see Sheffield Plate.

Another method that can be used to apply a thin layer of silver to several objects, such as glass, is the Tollen's Test method, which usually is prepared as follows. Using this method the final reaction can occur by placing Tollen's Reagent in a glass and then adding Glucose/Dextrose and shaking the bottle to perform the reaction.

AgNO₃ + KOH -> AgOH + KNO₃

AgOH + 2NH₃ -> [Ag(NH₃)₂]¹⁺ + [OH]^1- (Note: See Tollen's Reagent)

[Ag(NH₃)₂]¹⁺ + [OH]^1- + Aldehyde(Usually Glucose/Dextrose) -> Ag + 2NH₃ + H₂O

[edit] Rhodium plating

Rhodium plating is occasionally used on white gold, silver or copper and its alloys. A barrier layer of nickel is usually deposited on silver first, though in this case it is not to prevent migration of silver through rhodium, but to prevent contamination of the rhodium bath with silver and copper, which slightly dissolve in the sulfuric acid, usually present in the bath composition.

[edit] Chrome plating

Main article: Chrome plating

Chrome plating is a finishing treatment utilizing the electrolytic deposition of chromium. The most common form of chrome plating is the thin, decorative bright chrome, which is typically a 10-µm layer over an underlying nickel plate. When plating on iron or steel, an underlying plating of copper allows the nickel to adhere. The pores (tiny holes) in the nickel and chromium layers also promote corrosion resistance. Bright chrome imparts a mirror-like finish to items such as metal furniture frames and automotive trim. Thicker deposits, up to 1000 µm, are called hard chrome and are used in industrial equipment to reduce friction and wear.

The traditional solution used for industrial hard chrome plating is made up of about 250 g/l of Cr0₃ and about 2.5 g/l of S0₄^-. In solution, the chrome exists as chromic acid, known as hexavalent chromium. A high current is used, in part to stabilize a thin layer of chromium(+2) at the surface of the plated work. Acid chrome has poor throwing power, fine details or holes are further away and receive less current resulting in poor plating.

[edit] Zinc plating

Main article: Galvanization

Zinc coatings prevent oxidation of the protected metal by forming a barrier and by acting as a sacrificial anode if this barrier is damaged. Zinc oxide is a fine white dust that (in contrast to iron oxide) does not cause a breakdown of the substrate's surface integrity as it is formed. Indeed the zinc oxide, if undisturbed, can act as a barrier to further oxidation, in a way similar to the protection afforded to aluminum and stainless steels by their oxide layers.

[edit] Tin plating

See also: Tinplate

The tin-plating process is used extensively to protect both ferrous and nonferrous surfaces. Tin is a useful metal for the food processing industry since it is non-toxic, ductile and corrosion resistant. The excellent ductility of tin allows a tin coated base metal sheet to be formed into a variety of shapes without damage to the surface tin layer. It provides sacrificial protection for copper, nickel and other non-ferrous metals, but not for steel.

Tin is also widely used in the electronics industry because of its ability to protect the base metal from oxidation thus preserving its solderability. In electronic applications, lead may be added to prevent the growth of metallic "whiskers" in compression stressed deposits, which would otherwise cause electrical shorting

[edit] Alloy plating

In some cases, it is desirable to co-deposit two or more metals resulting in an electroplated alloy deposit. Depending on the alloy system, an electroplated alloy may be solid solution strengthened or precipitation hardened by heat treatment to improve the plating's physical and chemical properties. Nickel-Cobalt is a common electroplated alloy.

[edit] Composite plating

Metal matrix composite plating can be manufactured when a substrate is plated in a bath containing a suspension of ceramic particles. Careful selection of the size and composition of the particles can fine-tune the deposit for wear resistance, high temperature performance, or mechanical strength. Tungsten Carbide, Silicon carbide, Chromium carbide, and Aluminum Oxide (alumina) are commonly used in composite electroplating.

[edit] Cadmium plating

Cadmium plating is under scrutiny because of the environmental toxicity of the cadmium metal. However, cadmium plating is still widely unreplaced in some applications such as aerospace fasteners and it remains in military and aviation specs.^[1] Cadmium plating (or "cad plating") has technical advantages such as excellent corrosion resistance even at relatively low thickness and in salt atmospheres, can be dyed to many colors and clear, has good lubricity and solderability, and works well either as a final finish or as a paint base

Form follows function

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Form follows function is a principle associated with modern architecture and industrial design in the 20th Century, which states that the shape of a building or object should be predicated by or based upon its intended function or purpose.

Wainwright Building by Louis Sullivan

In the context of design professions form follows function seems like good sense but on closer examination it becomes problematic and open to interpretation. Linking the relationship between the form of an object and its intended purpose is a good idea for designers and architects, but it is not always by itself a complete design solution. Defining the precise meaning(s) of the phrase 'form follows function' opens a discussion of design integrity that remains an important, lively debate.^[1]

[hide]

[edit] Origins of the phrase

The origin of the phrase is traced back to the American sculptor Horatio Greenough^[2], but it was American architectural giant Louis Sullivan who adopted it and made it famous. Sullivan actually said 'form ever follows function', but the simpler (and less emphatic) phrase is the one usually remembered. For Sullivan this was distilled wisdom, an aesthetic credo, the single "rule that shall permit of no exception". The full quote is thus:

"It is the pervading law of all things organic and inorganic,

Of all things physical and metaphysical,

Of all things human and all things super-human,

Of all true manifestations of the head,

Of the heart, of the soul,

That the life is recognizable in its expression,

That form ever follows function. This is the law.”^[3]

Sullivan developed the shape of the tall steel skyscraper in late 19th Century Chicago at the very moment when technology, taste and economic forces converged violently and made it necessary to drop the established styles of the past. If the shape of the building wasn't going to be chosen out of the old pattern book something had to determine form, and according to Sullivan it was going to be the purpose of the building. It was 'form follows function', as opposed to 'form follows precedent'. Sullivan's assistant Frank Lloyd Wright adopted and professed the same principle in slightly different form—perhaps because shaking off the old styles gave them more freedom and latitude. There is a song for teaching this^[4].

[edit] Is ornament functional?

In 1908 the Austrian architect Adolf Loos famously proclaimed that architectural ornament was criminal, and his essay on that topic would become foundational to Modernism and eventually trigger the careers of Le Corbusier, Walter Gropius, Alvar Aalto, Mies van der Rohe and Gerrit Rietveld. The Modernists adopted both of these equations—form follows function, ornament is a crime—as moral principles, and they celebrated industrial artifacts like steel water towers as brilliant and beautiful examples of plain, simple design integrity. Between 1945 and 1984 Modernism stood as the only respected architectural form in the mainstream of the profession. Everything else was illegitimate.

These two principles—form follows function, ornament is crime—are often invoked on the same occasions for the same reasons, but they do not mean the same thing. If ornament on a building may have social usefulness like aiding wayfinding, announcing the identity of the building, signaling scale, or attracting new customers inside, then ornament can be seen as functional, which puts those two articles of dogma at odds with each other.

Conversely the argument ‘ornament is crime’ doesn’t say anything about function. It is an aesthetic preference inspired by the machine age. While human performance may be enhanced by a sense of well-being endowed by aesthetic pleasure, machines have no such need of beauty to perform their work tirelessly. Ornament becomes an unnecessary relic, or worse, an impediment to optimal engineering design and equipment maintenance. Other stylistic ‘non-functional’ features may rest untouched (e.g., the feeling of space, the composition of the volumes) as we can see in the subsequent abstracted and non-ornamented styles. Much of the confusion between these two concepts comes from the fact that ornament traditionally derives from a function becoming a stylistic character (e.g., the gargoyle from Gothic cathedrals).

Modernism in architecture began as a disciplined effort to allow the shape and organization of a building to be determined only by functional requirements, instead of by traditional aesthetic concepts. It assumes that the designer will determine empirically (or decide arbitrarily) what is or is not a functional requirement. The resulting architecture tended to be shockingly simpler, flatter, and lighter than its older neighbors, possibly due to the limited number of functional requirements upon which the designs were based; their functionality and refreshing nakedness looked as honest and inevitable as an airplane. Modernists believed, perhaps incorrectly, that airplane design did not involve any aesthetic decisions by the airplane designers. A recognizable Modern vocabulary began to develop.

[edit] Application in different fields

[edit] Architecture

Louis Sullivan is credited with coining the phrase "form follows function," which would become the great battle-cry of modernist architects. This credo, which placed the demands of practical use above aesthetics, would later be taken by influential designers to imply that decorative elements, which architects call "ornament," were superfluous in modern buildings. But Sullivan himself neither thought nor designed along such dogmatic lines during the peak of his career. Indeed, while his buildings could be spare and crisp in their principal masses, he often punctuated their plain surfaces with eruptions of lush Art Nouveau and something like Celtic Revival decorations, usually cast in iron or terra cotta, and ranging from organic forms like vines and ivy, to more geometric designs, and interlace, inspired by his Irish design heritage. Probably the most famous example is the writhing green ironwork that covers the entrance canopies of the Carson Pirie Scott store on South State Street. These ornaments, often executed by the talented younger draftsman in Sullivan's employ, would eventually become Sullivan's trademark; to students of architecture, they are his instantly-recognizable signature.

[edit] Product design

In the late 1910s the two principles of “form follows function” and “ornament is a crime” were effectively adopted by the designers of the Bauhaus and applied to the production of everyday objects like chairs, bedframes, toothbrushes, tunics, and teapots. Some of those forms were refined and purified to such an extreme degree that they became unusable by humans^{[citation needed]}, but generally the Bauhaus still constructively influences the look, feel and function of consumer goods down to the present day.

One quiet landmark in the history of the inherent conflict between functional design and the demands of the marketplace happened in 1935^{[citation needed]}, after the introduction of the streamlined Chrysler Airflow, when the auto industry halted serious aerodynamic research. As documented in Jeffrey Meikle’s “Twentieth Century Limited: Industrial Design in America, 1925 – 1939”, carmakers realized that optimal aerodynamic efficiency would result in a single optimal auto-body shape, a "teardrop" shape, which would not be good for unit sales.^{[citation needed]} GM thereafter adopted two different positions on streamlining, one meant for its internal engineering community, the other meant for its customers. Like the annual model year change, so-called aerodynamic styling is often meaningless in terms of technical performance.

The American industrial designers of the 1930s and '40s like Raymond Loewy, Norman bel Geddes and Henry Dreyfuss grappled with the inherent contradictions of 'form follows function' as they redesigned blenders and locomotives and duplicating machines for mass-market consumption. Loewy formulated his ‘MAYA’ (Most Advanced Yet Acceptable) principle to express that product designs are bounded by functional constraints of math and materials and logic, but their acceptance is constrained by social expectations.

By honestly applying ‘form follows function’, industrial designers had the potential to advance their clients right out of business.^{[citation needed]} Some simple single-purpose objects like screwdrivers and pencils and teapots might be reducible to a single optimal form, and through the eyes of a teapot maker that’s simply unacceptable. Some objects made too durable would prevent sales of replacements. From the standpoint of functionality some products are flatly unnecessary, and through the eyes of an electric carving knife maker that’s quite unacceptable.

Victor Papanek (died 1999) was an influential recent designer and design philosopher who taught and wrote as a proponent of "form follows function."

Formula One cars Aerodynamics

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Engines

Main article: Formula One engines

A BMW Sauber P86 V8 engine, which powered the 2006 BMW Sauber F1.06.

For a decade F1 cars had run with 3.0 litre naturally-aspirated V10 engines, but in an attempt to slow the cars down, the FIA mandated that as of the 2006 season the cars must be powered by 2.4 litre naturally-aspirated engines in the V8 configuration that have no more than four valves per cylinder. Further technical restrictions such as a ban on variable intake trumpets have also been introduced with the new 2.4 L V8 formula to prevent the teams from achieving higher rpm and horsepower too quickly. As of the start of the 2007 season all engines are now limited to 19,000 rpm in an effort to improve engine reliability and to cut costs down in general.

Once the teams started using exotic alloys in the late 1990s, the FIA banned the use of exotic materials in engine construction, and only aluminum and iron alloys were allowed for the pistons, cylinders, connecting rods, and crankshafts. Nevertheless through engineering on the limit and the use of such devices as pneumatic valves, modern F1 engines have revved up to over 18,000 rpm since approximately the 2000 season. Almost each year the FIA has enforced material and design restrictions to limit power, otherwise the 3.0L V10 engines would easily have exceeded 22,000 rpm^{[citation needed]} and well over 1,000 hp (745 kW)^{[citation needed]}. Even with the restrictions the V10s in the 2005 season were reputed to develop 960 hp (715 kW)^{[citation needed]}. The new 2.4L V8 engines are reported to develop between 700 hp (520 kW) and 780 hp (582 kW).^{[citation needed]}

The more poorly funded teams (Ferrari spends hundreds of millions of pounds a year developing their car, while the former Minardi team spent less than 50 million) had the option of keeping the current V10 for another season, but with a rev limiter to keep them from being competitive with the most powerful V8 engines. The only team to take this option was the Toro Rosso team, which was the reformed and regrouped Minardi.

The engines produce over 100,000 BTU per minute (1,750 kW)^{[citation needed]} of heat that must be dumped, usually to the atmosphere via radiators and the exhaust, which can reach temperatures over 1,000 degrees Celsius^{[citation needed]}(1,800 to 2,000 degrees Fahrenheit). They consume around 650 liters (23 ft³) of air per second^{[citation needed]}. Race fuel consumption rate is normally around 75 liters per 100 kilometers traveled (3.1 US mpg - 3.8 UK mpg - 1.3 km/l). Nonetheless a Formula One engine is over 20% more efficient at turning fuel into power than most small commuter cars, considering their craftsmanship.

All cars have the engine located between the driver and the rear axle. The engines are a stressed member in most cars, meaning that the engine is part of the structural support framework; being bolted to the cockpit at the front end, and transmission and rear suspension at the back end.

In the 2004 championship, engines were required to last a full race weekend; in the 2005 championship, they are required to last two full race weekends and if a team changes an engine between the two races, they incur a penalty of 10 grid positions. In 2007 this rule was altered slightly and an engine now only has to last for Saturday and Sunday running. This was to promote Friday running. In 2006, teams avoided running for long stints in an effort to save the engine and avoid a 10 place drop on the grid.

As of the 2006 Chinese Grand Prix all engine development was frozen until 2009, meaning that the teams must use existing engine specs for the next two seasons.^[1] FIA President Max Mosley has suggested the possible introduction of bio-fuel and reintroduction of turbochargers to F1 to improve the efficiency of future engines developed after the freeze is lifted.^[2]

[edit] Transmission

Formula One cars use semi-automatic sequential gearboxes with six or seven forward gears and one reverse gear. The driver initiates gear changes using paddles mounted on the back of the steering wheel and electro-hydraulics perform the actual change as well as throttle control. Clutch control is also performed electro-hydraulically except from and to a standstill when the driver must operate the clutch using a lever mounted on the back of the steering wheel. By regulation the cars use rear wheel drive. A modern F1 clutch is a multi-plate carbon design with a diameter of less than four inches (100 mm)^{[citation needed]}, weighing less than 2.20 lb (1.00 kg)^{[citation needed]} and handling 900 hp (670 kW) or so^{[citation needed]}.

Continuously variable transmissions have long been banned, thus creating contention in the introduction of the new seamless shift gearbox, a type of dual-clutch transmission which nearly eliminates the brief power interruption during a gear change. The ultimate advantage of this is said to be from five to ten seconds over a complete race distance, which is a significant gain when races are sometimes only won by three seconds or less. As of the 2007 race season, most of the top teams are using seamless shift transmissions. Shift times are around .05 seconds^{[citation needed]} for the 2007 season.

As of 2008 race season, all gearboxes must endure for four consecutive events, although gear ratios can be changed for each race. Changing a gearbox before the allowed time will cause a five places drop on the starting grid.^[3]

[edit] Aerodynamics

The rear wing of a modern Formula One car, with three aerodynamic elements (1, 2, 3). The rows of holes for adjustment of the angle of attack (4) and installation of another element (5) are visible on the wing's endplate.

The use of aerodynamics to increase the cars' grip was pioneered in Formula One in the late 1960s by Lotus, Ferrari and Brabham.

[edit] Wings

Early designs linked wings directly to the suspension, but several accidents led to rules stating that wings must be fixed rigidly to the chassis. The cars' aerodynamics are designed to provide maximum downforce with a minimum of drag; every part of the bodywork is designed with this aim in mind. Like most open wheeler cars they feature large front and rear aerofoils, but they are far more developed than American open wheel racers, which depend more on suspension tuning; for instance, the nose is raised above the centre of the front aerofoil, allowing its entire width to provide downforce. The front and rear wings are highly sculpted and extremely fine 'tuned', along with the rest of the body such as the turning vanes beneath the nose, bargeboards, sidepods, underbody, and the rear diffuser. They also feature aerodynamic appendages that direct the airflow. Such an extreme level of aerodynamic development means that an F1 car produces much more downforce than any other open-wheel formula; for example the Indycars produce downforce equal to their weight at 190 km/h (118 mph), while an F1 car achieves the same downforce:weight ratio of 1:1 at 125 km/h (78 mph) to 130 km/h (81 mph), and at 190 km/h (118 mph) the ratio is roughly 2:1. Therefore, theoretically, F1 cars can drive upside down from 130 km/h (81 mph).^[4]

The 'barge boards' in particular are designed, shaped, configured, adjusted and positioned not to create downforce directly, as with a conventional wing or underbody venturi, but to create vortices from the air spillage at their edges. The use of vortices is a significant feature of the latest breeds of F1 cars. Since a vortex is a rotating fluid that creates a low pressure zone at its centre, creating vortices lowers the overall local pressure of the air. Since low pressure is what is desired under the car, as it allows normal atmospheric pressure to press the car down from the top, by creating vortices downforce can be augmented while still staying within the rules prohibiting ground effects.^{[dubious – discuss]}

[edit] Ground effects

F1 regulations heavily limit the use of ground effect aerodynamics, which are a highly efficient means of creating downforce with a relatively small drag penalty. The underside of the vehicle, the undertray, must be flat between the axles. A 10mm^[5] thick wooden plank or skidblock runs down the middle of the car to prevent the cars from running low enough to contact the track surface; this skidblock is measured before and after a race. Should the plank be less than 9mm thick after the race, the car is disqualified.

A substantial amount of downforce is provided by using a rear diffuser which rises from the undertray at the rear axle to the actual rear of the bodywork. The limitations on ground effects, limited size of the wings (requiring use at high angles of attack to create sufficient downforce), and vortices created by open wheels lead to a high aerodynamic drag coefficient (about 1 according to Minardi's technical director Gabriele Tredozi^[6]; compare with the average modern saloon car (sedan in the USA), which has a C_d value between 0.25-0.35), so that, despite the enormous power output of the engines, the top speed of these cars is less than that of World War II vintage Mercedes-Benz and Auto Union Silver Arrows racers. However, this drag is more than compensated for by the ability to corner at extremely high speed. The aerodynamics are adjusted for each track; with a relatively low drag configuration for tracks where high speed is relatively more important like Autodromo Nazionale Monza, and a high traction configuration for tracks where cornering is more important, like the Circuit de Monaco.

[edit] Regulations

The FIA is hoping to rid F1 of small winglets and other parts of the car (minus the front and rear wing) used to manipulate the airflow of the car. This is in order to not only decrease downforce, but also to increase drag. As it is now, the front wing is shaped specifically to push air towards all the winglets and bargeboards so that the airflow is smooth. Should these be removed, various parts of the car will cause great drag when the front wing is unable to shape the air past the body of the car. New regulations coming into effect in 2009 have halved the width of the rear wing, and standardised the centre section of the front wing to prevent teams developing the front wing.

[edit] Construction

The cars are constructed from composites of carbon fibre and similar ultra-lightweight (and incredibly expensive to manufacture) materials. The minimum weight permissible is 605 kg (1334 lb) including the driver, fluids and on-board cameras. However, all F1 cars weigh significantly less than this (some as little as 440 kg) so teams add ballast to the cars to bring them up to the minimum legal weight. The advantage of using ballast is that it can be placed anywhere in the car to provide ideal weight distribution.

[edit] Steering wheel

A modern Ferrari steering wheel, with a complex array of dials, knobs and buttons.

The driver has the ability to fine tune many elements of the race car from within the machine using the steering wheel. The wheel can be used to change gears, apply rev limiter, adjust fuel air mix, change brake pressure and call the radio. Data such as rpm, laptimes, speed and gear is displayed on an LCD screen. The wheel alone can cost about $40,000, and with carbon fibre construction, weighs in at 1.3 kilograms.

[edit] Fuel

The fuel used in F1 cars is fairly similar to ordinary gasoline, albeit with a far more tightly controlled mix. Formula One fuel cannot contain compounds that are not found in commercial gasoline, in contrast to alcohol-based fuels used in American open-wheel racing. Blends are tuned for maximum performance in given weather conditions or different circuits. During the period when teams were limited to a specific volume of fuel during a race, exotic high-density fuel blends were used which were actually heavier than water, since the energy content of a fuel depends on its mass density.

To make sure that the teams and fuel suppliers are not violating the fuel regulations, the FIA requires Elf, Shell, Mobil, and the other fuel teams to submit a sample of the fuel they are providing for a race. At any time, FIA inspectors can request a sample from the fueling rig to compare the "fingerprint" of what is in the car during the race with what was submitted. The teams usually abide by this rule, but in 1997, Mika Häkkinen was stripped of his third place finish at Spa-Francorchamps in Belgium after the FIA determined that his fuel was not the correct formula, as well as in 1976, both McLaren and Penske cars were forced to the rear of the Italian Grand Prix after the octane mixture was found to be too high.

[edit] Tyres

Main article: Formula One tyres

A BMW Sauber's right-rear Bridgestone tires.

By regulation, the tyres feature a minimum of four grooves in them, with the intention of slowing down the cars (a slick tyre, with no indentations, is best in dry conditions). They can be no wider than 355 mm (14 in) and 380 mm (15 in) at the front and rear respectively. Unlike the fuel, the tyres bear only a superficial resemblance to a normal road tyre. Whereas a roadcar tyre has a useful life of up to 80,000 km (49,710 mi), in 2005, a Formula One tyre is built to last just one race distance (a little over 300 km (186 mi)). This is the result of a drive to maximize the road-holding ability, leading to the use of very soft compounds (to ensure that the tyre surface conforms to the road surface as closely as possible). However, tyre changes were re-instated in 2006, following the dramatic and highly political 2005 United States Grand Prix.

Since the start of the 2007 season Bridgestone is the sole tyre supplier and have introduced four compounds of tyre, two of which will be made available at each race. The harder tyre is more durable but gives less grip, and the softer tyre gives more grip but is less durable. Both compounds have to be used by teams in a race and the softer tyre has a painted white stripe in the second groove. This was introduced after the first race of the season when confusion occurred because a small dot was put instead of the white stripe. Each team must use each specification during the race, unless wet or intermediate tyres are used during the race, in which case this rule no longer applies.

Slick tyres will return as a part of revisions to the rules for the 2009 season.

[edit] Brakes

Brake discs on the Williams FW27.

Disc brakes consist of a rotor and caliper at each wheel. Expensive carbon-carbon (the same material used on the Space Shuttle) composite rotors - introduced by the Brabham team in 1976 - are used instead of steel or cast iron because of their superior frictional, thermal, and anti-warping properties, as well as significant weight savings. These brakes are designed and manufactured to work in extreme temperatures, up to 1,000 degrees Celsius. The driver can control brake force distribution fore and aft to compensate for changes in track conditions or fuel load. Regulations specify this control has to be manual, not electronic.

An average F1 car can decelerate from 100-0 km/h (62-0 mph) in about 17 metres (55 ft), compared with a 2007 Porsche 911 Turbo which takes 31.4 metres (103 feet).^{[citation needed]} When braking from higher speeds, aerodynamic downforce enables tremendous deceleration: 4.5 g to 5.0 g (44.1 to 49 m/s²), and up to 5.5 g at the high-speed circuits such as the Circuit Gilles Villeneuve (Canadian GP) and the Autodromo Nazionale Monza (Italian GP). This contrasts with 1.0 g to 1.5 g for the best sports cars (the Bugatti Veyron is claimed to be able to brake at 1.3 g). An F1 car can brake from 200 km/h (124 mph) to a complete stop in just 2.9 seconds, using only 65 meters (213 ft).^[7]

[edit] Performance

Grand Prix cars and the cutting edge technology that constitute them produce an unprecedented combination of outright speed and quickness for the drivers. Every F1 car on the grid is capable of going from 0 to 160 km/h (100 mph) and back to 0 in less than five seconds. During a demonstration at the Silverstone circuit in Britain, an F1 McLaren-Mercedes car driven by David Coulthard gave a pair of Mercedes-Benz street cars a head start of seventy seconds, and was able to beat the cars to the finish line from a standing start.

As well as being fast in a straight line, F1 cars also have incredible cornering ability. Grand Prix cars can negotiate corners at significantly higher speeds than other racing cars because of the intense levels of grip and downforce. Cornering speed is so high that Formula One drivers have strength training routines just for the neck muscles . Former F1 driver Juan Pablo Montoya claims to be able to perform 300 reps of 50 pounds with his neck. Since most tracks are clockwise, most drivers have the neck muscles built up on one side of their neck^{[citation needed]}, thus making counter-clockwise tracks (such as Imola, Istanbul Park and Interlagos) a much more testing race than even the high speed Monza or the tight and narrow Monaco.

The combination of light weight (605 kg in race trim), power (950 bhp with the 3.0 L V10, 730 bhp (544 kW) with the 2007 regulation 2.4 L V8), aerodynamics, and ultra-high performance tyres is what gives the F1 car its performance figures. The principal consideration for F1 designers is acceleration, and not simply top speed. Acceleration is not just linear forward acceleration, but three types of acceleration can be considered for an F1 car's, and all cars' in general, performance:

Forward acceleration
Forward deceleration (under braking)
Turning acceleration (centripetal acceleration)

Unless a car is to be raced solely on high-speed ovals (where only top speed matters), all three accelerations should be maximised. The way these three accelerations are obtained and their values are:

[edit] Forward acceleration

The 2006 F1 cars have a power-to-weight ratio of 1,250 hp (932 kW)/tonne (0.9 kW/kg). Theoretically this would allow the car to reach 100 km/h (62 mph) in less than 1 second. However the massive power cannot be converted to motion at low speeds due to traction loss, and the usual figure is 2 seconds to reach 100 km/h (62 mph). After about 130 km/h (81 mph) traction loss is minimal due to the combined effect of the car moving faster and the downforce, hence the car continues accelerating at a very high rate. The figures are (for the 2006 Renault R26):

0 to 100 km/h (62 mph): 1.7 seconds

0 to 200 km/h (124 mph): 3.8 seconds

0 to 300 km/h (186 mph): 8.6 seconds*

Figures may alter slightly depending on the aerodynamic setup.

The acceleration figure is usually 1.45 g (14.25 m/s²) up to 200 km/h (124 mph), which means the driver is pushed back in the seat with 1.45 times his bodyweight.

[edit] Deceleration

The carbon brakes in combination with the aerodynamics produces truly remarkable braking forces. The deceleration force under braking is usually 4 g (39 m/s²), and can be as high as 5-6 g when braking from extreme speeds, for instance at the Gilles Villeneuve circuit or at Indianapolis. Here the aerodynamic drag actually helps, and can contribute as much as 1.0 g of braking force, which is the equivalent of the brakes on most sports cars. In other words, if the throttle is let go, the F1 car will slow down under drag at the same rate as most sports cars do with braking, at least at speeds above 150 km/h (93 mph). The drivers do not utilise engine or compression braking, although it may seem this way. The only reason they change down gears prior to entering the corner is to be in the correct gear for maximum acceleration on the exit of the corner.

There are three companies who manufacture brakes for Formula One. They are Hitco, (based in the US, part of the SGL Carbon Group), Brembo in Italy and Carbone Industrie of France. Whilst Hitco manufacture their own carbon/carbon, Brembo sources theirs from Honeywell, and Carbone Industrie purchases their carbon from Messier Bugatti.

Carbon/Carbon is a short name for carbon fibre reinforced carbon. This means carbon fibres strengthening a matrix of carbon, which is added to the fibres by way of matrix deposition (CVI or CVD) or by pyrolosis of a resin binder.

F1 brakes are 278 mm (10.9 in) in diameter and a maximum of 28 mm (1.1 in) thick. The carbon/carbon brake pads are actuated by 6-piston opposed calipers provided by Akebono, AP Racing or Brembo. The calipers are aluminium alloy bodied with titanium pistons. The regulation limits the modulus of the caliper material to 80GPa in order to prevent teams using exotic, high specific stiffness materials for example Beryllium. Titanium pistons save weight, but also have a low thermal conductivity, reducing the heat flow into the brake fluid.

[edit] Turning acceleration

As mentioned above, the car can accelerate to 300 km/h (190 mph) very quickly, however the top speeds are not much higher than 330 km/h (205 mph) at most circuits, being highest at Monza (360 km/h in 2006), Indianapolis (about 335 km/h (208 mph)) and Gilles Villeneuve (about 325 km/h (202 mph)). This is because the top speeds are sacrificed for the turning speeds. An F1 car is designed principally for high-speed cornering, thus the aerodynamic elements can produce as much as three times the car's weight in downforce, at the expense of drag. In fact, at a speed of just 130 km/h (81 mph), the downforce equals the weight of the car. As the speed of the car rises, the downforce increases. The turning force at low speeds (below 70 to about 100 km/h) mostly comes from the so-called 'mechanical grip' of the tyres themselves. At such low speeds the car can turn at 2.0 g. At 210 km/h (130 mph) already the turning acceleration is 3.0g, as evidenced by the famous esses (turns 3 and 4) at the Suzuka circuit. Higher-speed corners such as Blanchimont (Circuit de Spa-Francorchamps) and Copse (Silverstone Circuit) are taken at above 5.0g, and 6.0g has been recorded at Suzuka's 130-R corner^[8]. This contrasts with 1g for the Enzo Ferrari, one of the best racing sports cars.

These turning accelerative forces allow an F1 car to corner at amazing speeds, seeming to defy the laws of physics. As an example of the extreme cornering speeds, the Blanchimont and Eau Rouge corners at Spa-Francorchamps are taken flat-out at above 300 km/h (186 mph), whereas the race-spec touring cars can only do so at 150–160 km/h. A newer and perhaps even more extreme example is the Turn 8 at the Istanbul Park circuit, a 190° relatively tight 4-apex corner, in which the cars maintain speeds between 265 km/h (165 mph) and 285 km/h (in 2006) and experience between 4.5g and 5.5g for 7 seconds - the longest sustained hard cornering in Formula 1.

[edit] Top Speeds

Top speeds are in practice limited by the longest straight at the track and by the need to balance the car's aerodynamic configuration between high straight line speed (low aerodynamic drag) and high cornering speed (high downforce) to achieve the fastest lap time.^[9] During the 2006 season, the top speeds of Formula 1 cars are a little over 300 km/h (186 mph) at high-downforce tracks such as Albert Park, Australia and Sepang, Malaysia. These speeds are down by some 10 km/h (6 mph) from the 2005 speeds, and 15 km/h (9 mph) from the 2004 speeds, due to the recent performance restrictions (see below). On low-downforce circuits greater top speeds are registered: at Gilles-Villeneuve (Canada) 325 km/h (203 mph), at Indianapolis (USA) 335 km/h (210 mph), and at Monza (Italy) 360 km/h (225 mph). In the Italian Grand Prix 2004, Antônio Pizzonia of BMW WilliamsF1 team recorded a top speed of 369.9 kilometers per hour (229 mph).^[10]

Away from the track, the BAR Honda team used a modified BAR 007 car, which they claim complied with FIA Formula One regulations, to set an unofficial speed record of 413 km/h (257 mph) on a one way straight line run on 6 November 2005 during a shakedown ahead of their Bonneville 400 record attempt. The car was optimised for top speed with only enough downforce to prevent it from leaving the ground. The car, badged as a Honda following their takeover of BAR at the end of 2005, set an FIA ratified record of 400 km/h (249 mph) on a one way run on 21 July 2006 at Bonneville Salt Flats.^[11] On this occasion the car did not fully meet FIA Formula One regulations, as it used a moveable aerodynamic rudder for stability control, breaching article 3.15 of the 2006 Formula One technical regulations which states that any specific part of the car influencing its aerodynamic performance must be rigidly secured.^[12]

[edit] Recent FIA performance restrictions

In an effort to reduce speeds and increase driver safety, the FIA has continuously introduced new rules for F1 constructors since the 80s.

These rules have included the banning of such things as the "wing car" (ground effect) in 1983, the turbo in 1989, active suspension and traction control in 1994, the introduction of grooved tyres in 1998 and the reduction in engine capacity from 3.0 to 2.4 litres in 2006. Yet despite these changes, constructors continued to extract performance gains by increasing power and aerodynamic efficiency. As a result, the pole position speed at many circuits in comparable weather conditions dropped between 1.5 and 3 seconds in 2004 over the prior year's times. In 2006 the engine power was reduced from 950 bhp to 750 bhp (710 to 560 kW) by going from the 3.0 L V10s, used for over a decade, to 2.4 L V8s. These new engines are capable of achieving over 20,000 rpm. The aerodynamic restrictions introduced in 2005 were meant to reduce downforce by about 30%, however most teams were able to successfully reduce this to a mere 5 to 10% downforce loss. For the 2007 season, teams are not allowed to make modification to the engines and they have been limited to 19,000 rpm.

In 2008, the FIA has further strengthened its cost-cutting measures by asking that gearboxes are to last for 4 grand prix weekends in addition to the 2-race engine lives. Further, all teams are required to use a standardised ECU supplied by MES (McLaren Electronic Systems) made in conjunction with Microsoft. These ECU's have placed restrictions on the use of electronic driver aids such as Traction Control and engine braking. The emphasis being on reducing costs as well as placing the focus back onto driver skills as opposed to the so-called 'electronic gizmo's' controlling the cars. Proposed changes for the 2009 season include a return to slick tyres, as well as considerable reduction in aerodynamic grip via the banning of winglets and other aero devices now currently being used to better direct airflow over and under the cars.

Due to increasing environmental pressures from lobby groups and the like, many have brought into speculation the relevance of Formula 1 as an innovating force towards future technological advances (particularly those concerned with 'greener' cars). The FIA has been asked to consider how it can persuade the sport to moving down a more environmentally friendly path. Therefore, in addition to the above changes outlined for the 2009 season, teams will also be asked to construct a KERS (Kinetic Energy Recovery System) device, encompassing certain types of regenerative braking systems to be fitted to the cars in time for the 2009 season. The system aims to reduce the amount of kinetic energy converted to waste heat in braking, converting it instead to a useful form (such as electrical energy or energy in a flywheel) to be later fed back through the engine to create a power boost. Such technology is highly likely to become a staple in the design and construction of road cars within the next 10 to 15 years, with increasing fuel costs and environmental concerns. It is through these technological breakthroughs that Formula 1 is striving to not only be the peak of what is technically possible, but also a platform from which environmentally friendly solutions for future use may be obtained, in a similar way to the development of technologies that have improved performance and efficiency in ordinary vehicles in the past.

Hertzsprung-Russell Diagram

2008-10-01T21:29:00.000+05:30

The Hertzsprung-Russell diagram (usually referred to by the abbreviation H-R diagram or HRD, also known as a colour-magnitude diagram, or CMD) shows the relationship between absolute magnitude, luminosity, classification, and effective temperature of stars. The diagram was created circa 1910 by Ejnar Hertzsprung and Henry Norris Russell, and represented a huge leap forward in understanding stellar evolution, or the 'lives of stars'.

[hide]

[edit] Diagram

Hertzsprung-Russell diagram by Richard Powell with permission. 22 000 stars are plotted from the Hipparcos catalog and 1000 from the Gliese catalog of nearby stars. An examination of the diagram shows that stars tend to fall only into certain regions on the diagram. The most predominant is the diagonal, going from the upper-left (hot and bright) to the lower-right (cooler and less bright), called the main sequence. In the lower-left is where white dwarfs are found, and above the main sequence are the subgiants, giants and supergiants. The Sun is found on the main sequence at luminosity 1 (absolute magnitude 4.8) and B-V color index 0.66 (temperature 5780K, spectral type G2).

[edit] Forms of diagram

HR diagrams for two open clusters, M67 and NGC 188, showing the main sequence turn-off at different ages.

There are several forms of the Hertzsprung-Russell diagram, and the nomenclature is not very well defined. The original diagram displayed the spectral type of stars on the horizontal axis and the absolute magnitude on the vertical axis. The first quantity (i.e. spectral type) is difficult to determine unambiguously and is therefore often replaced by the B-V colour index of the stars. This type of diagram is called a Hertzsprung-Russell diagram, or colour-magnitude diagram, and it is often used by observers. However, colour-magnitude diagram is also used in some cases to describe a plot with the vertical axis depicting the apparent, rather than the absolute, magnitude. Another form of the diagram plots the effective temperature of the star on one axis and the luminosity of the star on the other. This is what theoreticians calculate using computer models that describe the evolution of stars. This type of diagram should probably be called temperature-luminosity diagram, but this term is hardly ever used, the term Hertzsprung-Russell diagram being preferred instead. Despite some confusion regarding the nomenclature, astrophysicists make a strict distinction between these types of diagrams.

The reason for this distinction is that the exact transformation from one to the other is not trivial, and depends on the stellar-atmosphere model being used and its parameters (like composition and pressure, apart from temperature and luminosity). Also, one needs to know the distance to the observed objects and the interstellar reddening. Empirical transformation between various colour indices and effective temperature are available in literature (Sekiguchi 2000, Casagrande 2006).

The H-R diagram can be used to define different types of stars and to match theoretical predictions of stellar evolution using computer models with observations of actual stars. It is then necessary to convert either the calculated quantities to observables, or the other way around, thus introducing an extra uncertainty.

[edit] Interpretation

Most of the stars occupy the region in the diagram along the line called main sequence. During that stage stars are fusing hydrogen in their cores. The next concentration of stars is on the horizontal branch (helium fusion in the core and hydrogen burning in a shell surrounding the core). Another prominent feature is the Hertzsprung gap located in the region between A5 and G0 spectral type and between +1 and −3 absolute magnitudes (i.e. between the top of the main sequence and the giants in the horizontal branch). RR Lyrae stars can be found in the left of this gap. Cepheid variables reside in the upper section of the instability strip.

The H-R diagram can also be used by scientists to roughly measure how far away a star cluster is from Earth. This can be done by comparing the apparent magnitudes of the stars in the cluster to the absolute magnitudes of stars with known distances (or of model stars). The observed group is then shifted in the vertical direction, until the two main sequences overlap. The difference in magnitude that was bridged in order to match the two groups is called the distance modulus and is a direct measure for the distance. This technique is known as main-sequence fitting, or, confusingly, as the spectroscopic parallax.

[edit] The diagram's role in the development of stellar physics

Contemplation of the diagram led astronomers to speculate that it might demonstrate stellar evolution, a main suggestion being that stars collapsed from red giants to dwarf stars, then moving down along the line of the main sequence in the course of their lifetimes. However, following Russell's presentation of the diagram to a meeting of the Royal Astronomical Society in 1912, Arthur Eddington was inspired to use it as a basis for developing ideas on stellar physics (Porter, 2003). In 1926, in his book The Internal Constitution of the Stars he explained the physics of how stars fit on the diagram. This was a particularly remarkable development since at that time the major problem of stellar theory, the source of a star's energy, was still unsolved. Thermonuclear energy, and even that stars are largely composed of hydrogen, had yet to be discovered. Eddington managed to sidestep this problem by concentrating on the thermodynamics of radiative transport of energy in stellar interiors (Smith, 1995). So, Eddington predicted that dwarf stars remain in an essentially static position on the main sequence for most of their lives. In the 1930s and 1940s, with a understanding of hydrogen fusion, came a physically-based theory of evolution to red giants, and white dwarfs. By this time, study of the Hertzsprung-Russell diagram did not drive such developments but merely allowed stellar evolution to be presented graphically.

Electrical impedance RLC

2008-10-01T21:23:00.000+05:30

Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current (AC). Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative amplitudes of the voltage and current, but also the relative phases. Impedance is a complex quantity and the term complex impedance may be used interchangeably; the polar form conveniently captures both magnitude and phase characteristics,

where the magnitude represents the ratio of the voltage difference amplitude to the current amplitude, while the argument gives the phase difference between voltage and current. In Cartesian form,

where the real part of impedance is the resistance and the imaginary part is the reactance . Dimensionally, impedance is the same as resistance; the SI unit is the ohm. The term impedance was coined by Oliver Heaviside in July 1886.

The reciprocal of impedance is admittance.

A graphical representation of the complex impedance plane. Note that while reactance can be either positive or negative, resistance is always positive.

[edit] Ohm's law

An AC supply applying a voltage , across a load , driving a current .

Main article: Ohm's law

The meaning of electrical impedance can be understood by substituting it into Ohm's law.^[1]^[2]

The magnitude of the impedance acts just like resistance, giving the drop in voltage amplitude across an impedance for a given current . The phase factor tells us that the current lags the voltage by a phase of $θ$ (i.e. in the time domain, the current signal is shifted to the right with respect to the voltage signal).^[3]

Just as impedance extends Ohm's law to cover AC circuits, other results from DC circuit analysis such as voltage division, current division, Thevenin's theorem, and Norton's theorem, can also be extended to AC circuits by replacing resistance with impedance.

[edit] Complex voltage and current

Generalized impedances in a circuit can be drawn with the same symbol as a resistor (US ANSI or DIN Euro) or with a labeled box.

In order to simplify calculations, sinusoidal voltage and current waves are commonly represented as complex-valued functions of time denoted as and .^[4]^[5]

Impedance is defined as the ratio of these quantities.

Substituting these into Ohm's law we have

Noting that this must hold for all $t$ , we may equate the magnitudes and phases to obtain

The magnitude equation is the familiar Ohm's law applied to the voltage and current amplitudes, while the second equation defines the phase relationship.

[edit] Validity of complex representation

This representation using complex exponentials may be justified by noting that (by Euler's formula):

i.e. a real-valued sinusoidal function (which may represent our voltage or current waveform) may be broken into two complex-valued functions. By the principle of superposition, we may analyse the behaviour of the sinusoid on the left-hand side by analysing the behaviour of the two complex terms on the right-hand side. Given the symmetry, we only need to perform the analysis for one right-hand term; the results will be identical for the other. At the end of any calculation, we may return to real-valued sinusoids by further noting that

In other words, we simply take the real part of the result.

[edit] Phasors

Main article: Phasor (electronics)

A phasor is a constant complex number, usually expressed in exponential form, representing the complex amplitude (magnitude and phase) of a sinusoidal function of time. Phasors are used by electrical engineers to simplify computations involving sinusoids, where they can often reduce a differential equation problem to an algebraic one.

The impedance of a circuit element can be defined as the ratio of the phasor voltage across the element to the phasor current through the element, as determined by the relative amplitudes and phases of the voltage and current. This is identical to the definition from Ohm's law given above, recognising that the factors of cancel.

[edit] Device examples

Main article: Impedance of different devices (derivations)

The phase angles in the equations for the impedance of inductors and capacitors indicate that the voltage across a capacitor lags the current through it by a phase of , while the voltage across an inductor leads the current through it by . The identical voltage and current amplitudes tell us that the magnitude of the impedance is equal to one.

The impedance of a resistor is purely real and is referred to as a resistive impedance.

Inductors and capacitors have a purely imaginary reactive impedance.

Note the following identities for the imaginary unit and its reciprocal.

Thus we can rewrite the inductor and capacitor impedance equations in polar form

The magnitude tells us the change in voltage amplitude for a given current amplitude through our impedance, while the exponential factors give the phase relationship.

[edit] Deriving the device specific impedances

What follows below is a derivation of impedance for each of the three basic circuit elements, the resistor, the capacitor, and the inductor. Although the idea can be extended to define the relationship between the voltage and current of any arbitrary signal, these derivations will assume sinusoidal signals, since any arbitrary signal can be approximated as a sum of sinusoids through Fourier Analysis.

[show] Resistor
For a resistor, we have the relation: . This is simply a statement of Ohm's Law. Considering the voltage signal to be it follows that This tells us that the ratio of AC voltage amplitude to AC current amplitude across a resistor is $R$ , and that the AC voltage leads the AC current across a resistor by 0 degrees. This result is commonly expressed as

[show] Resistor

[show] Capacitor
For a capacitor, we have the relation: Considering the voltage signal to be it follows that And thus This tells us that the ratio of AC voltage amplitude to AC current amplitude across a capacitor is , and that the AC voltage leads the AC current across a capacitor by -90 degrees (or the AC current leads the AC voltage across a capacitor by 90 degrees). This result is commonly expressed in polar form, as or, more simply, using of Euler's formula, as

[show] Capacitor

[show] Inductor
For the inductor, we have the relation: This time, considering the current signal to be it follows that And thus This tells us that the ratio of AC voltage amplitude to AC current amplitude across an inductor is $ω L$ , and that the AC voltage leads the AC current across an inductor by 90 degrees. This result is commonly expressed in polar form, as or, more simply, using Euler's formula, as

[show] Inductor

[edit] Resistance vs reactance

It is important to realize that resistance and reactance are not individually significant; together they determine the magnitude and phase of the impedance, through the following relations:

In many applications the relative phase of the voltage and current is not critical so only the magnitude of the impedance is significant.

[edit] Resistance

Main article: Electrical resistance

Resistance is the real part of impedance; a device with a purely resistive impedance exhibits no phase shift between the voltage and current.

[edit] Reactance

Main article: Reactance (electronics)

Reactance is the imaginary part of the impedance; a component with a finite reactance induces a phase shift $θ$ between the voltage across it and the current through it.

A reactive component is distinguished by the fact that the sinusoidal voltage across the component is in quadrature with the sinusoidal current through the component. This implies that the component alternately absorbs energy from the circuit and then returns energy to the circuit. A pure reactance will not dissipate any power.

[edit] Capacitive reactance

Main article: Capacitor

A capacitor has a purely reactive impedance which is inversely proportional to the signal frequency. A capacitor consists of two conductors separated by an insulator, also known as a dielectric.

At low frequencies a capacitor is open circuit, as no charge flows in the dielectric. A DC voltage applied across a capacitor causes charge to accumulate on one side; the electric field due to the accumulated charge is the source of the opposition to the current. When the potential associated with the charge exactly balances the applied voltage, the current goes to zero.

Driven by an AC supply, a capacitor will only accumulate a limited amount of charge before the potential difference changes sign and the charge dissipates. The higher the frequency, the less charge will accumulate and the smaller the opposition to the current.

[edit] Inductive reactance

Main article: Inductor

An inductor has a purely reactive impedance which is proportional to the signal frequency. An inductor consists of a coiled conductor. Faraday's law of electromagnetic induction gives the back emf (voltage opposing current) due to a rate-of-change of magnetic field through a current loop.

For an inductor consisting of a coil with $N$ loops this gives.

The back-emf is the source of the opposition to current flow. A constant direct current has a zero rate-of-change, and sees an inductor as a short-circuit (it is typically made from a material with a low resistivity). An alternating current has a time rate-of-change that is proportional to frequency and so the inductive reactance is proportional to frequency.

[edit] Combining impedances

Main article: Series and parallel circuits

The total impedance of any network of components can be calculated using the rules for combining impedances in series and parallel. The rules are identical to those used for combining resistances, although they require some familiarity with complex numbers.

[edit] Series combination

For components connected in series, the current through each circuit element is the same; the ratio of voltages across any two elements is the inverse ratio of their impedances.

[edit] Parallel combination

For components connected in parallel, the voltage across each circuit element is the same; the ratio of currents through any two elements is the inverse ratio of their impedances.

The equivalent impedance can be calculated in terms of the equivalent resistance and reactance .^[6]

[edit] Measuring Impedance

According to Ohm’s law the impedance of a device can be calculated by complex division of the voltage and current. The impedance of the device can be calculated by applying a sinusoidal voltage to the device in series with a resistor, and measuring the voltage across the resistor and across the device. Performing this measurement by sweeping the frequencies of the applied signal provides the impedance phase and magnitude.^[7]

[edit] Impulse impedance spectroscopy

The use of an impulse response may be used in combintation with the fast Fourier transform (FFT) to rapidly measure the electrical impedance of various electrical devices. The technique compares well to other methodologies such as network and impedance analyzers while providing additional versatility in the electrical impedance measurement. The technique is theoretically simple, easy to implement and completed with ordinary laboratory instrumentation for minimal cost

Is ur PC Virus infected ???

2008-09-26T09:19:00.000+05:30

Boot your system in Safemode
Go to command prompt, in Drive C do the following commands.
Type -> ATTRIB -H -R -S AUTORUN.INF then press enter
Type -> DEL AUTORUN.INF then press enter
Type -> ATTRIB -H -R -S Recycled then press enter
In Windows Explorer in Safemode, remove the folder Recycled in drive C use Shift-Delete to delete the folder.
Repeat Step 3 to 6 for all drives of your system including the USB drive.
Search for CTFMON.EXE in your system using the Search of Windows found in Start Menu. If you find a file that is not located in C:\WINDOWS\SYSTEM32, delete it immediately. Dont forget to empty the recycle bin afterwards (Usually the virus will copy itself in the Startup folder of the Startmenu. Check if the file is present there and delete it then.)
To disable autorun of drives (i.e. everytime you double-click a drive or cd or usb, it is auto open) follow the following step:
Click Start->Run->type REGEDIT.EXE
Go to this key from the register HKEY_CURRENT_USER\Software\ Microsoft\Windows\CurrentVersion\Policies\Explorer
Look for the entry NoDriveTypeAutoRun, double click the entry
Type a new value : 0FF (Hex) for the NoDriveTypeAutoRun, this will turn off the AutoRun for all drives, and press ENTER
Reboot the system.
Viruses that uses Autorun.INF
There are several viruses that uses the autorun.inf to spread itself such as the Bacalid (hides itself in ctfmon.exe) and the RavMon.EXE. These viruses set its file attributes to System+Hidden+Read-Only attributes so some anti-viruses will have a hard time detecting or finding them. These viruses save itself in the root directory of every available drives of the current infected computer and runs itself every time you Double-Click the drive. In USB Sticks and CDs that are infected by the virus runs automatically especially if drive autorun is enabled for the current drives (which is usually by default, autorun for drives are enabled).
Disable AUTORUN from Registry
Now you can disable the AUTORUN for all drives by configuring the registry. Open the registry by typing regedit.exe to the command prompt (if your still at the command prompt) or execute it in Run. Look for the HKEY_CURRENT_USER\Software\ Microsoft\Windows\CurrentVersion\Policies\Explorer as shown below:
Double-click the NoDriveAutorun DWORD entry and type the value HEX: FF (255 in Decimal). (If the NoDriveAutorun does not exists, you can creat it by right-clicking the right side area of the regedit window, then click New->DWord Value -> type NoDriveAutorun) Close the registry and restart the computer. This procedure will disable all the autorun for all drives of your computer and at least will prevent the autorun function of infected USB drives or CDs and avoid the infection of viruses like the Bacalid and RavMon.exe
If you want to prevent viruses that uses autorun.inf to infect your USB flash drive, try to do this:
1. Open your flash drive via Command Prompt (do this via Start->Run->cmd.exe)
2. Change your logged drive to your USB flash drive (e.g. if your drive is at drive E: then type E: on the command prompt then press enter)
3. Create a folder named: AUTORUN.INF on the root directory of your flash drive. (to do this type the command: MD\AUTORUN.INF). If an error: a subdirectory already exists… shows, try to follow the instruction above to remove existing autorun.inf before doing this instruction.
The reason why this will avoid future infection is that autorun.inf viruses usually generates a file autorun.inf. Having an AUTORUN.INF folder on the root directory of your drives will make virus programs unable to create their own autorun.inf file, virus can’t even overwrite it because it’s a folder and not a file…

Lines

2008-09-25T22:58:00.000+05:30

Multiplication of 3 eqations

2008-09-25T22:41:00.000+05:30

(X+2)(X-1)(X+3)
=(x^2+x-2)(x+3)
=(x^3+x^2-2x+3x^2+3x-6)
=(x^3+4x^2+x-6)

Derivative of (u/v)

2008-09-25T22:36:00.000+05:30

f(x)= y= (x^2-6x+9)/(5-x)

use derivative formula as

d(u/v)= [v*d(u)-u*d(v)]/(v^2)
put u=(x^2-6x+9) and v= (5-x)

hence derivative r
d(u)= 2x-6 and d(v)= (-1)

so
f'(x)= {[(5-x)(2x-6)]-[(x^2-6x+9)(-1)]}/ (5-x)^2
= {[10x-30-2x^2+6x]-[6x-9-x^2]}/(25+x^2-10x)
= {10x-21-x^2}/(25+x^2-10x)
= {(-1)(x^2-10x+21)}/(x-5)^2
= [(3-x)(x-7)]/(x-5)^2

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Quadratic_equation

Quadratic formula

[edit] Discriminant

[edit] Geometry

[edit] Examples

[edit] Quadratic factorization

Eigenvectors

Left and right eigenvectors

[edit] Characteristic equation

[edit] Example

[edit] Existence and multiplicity of eigenvalues

[edit] Shear

[edit] Uniform scaling and reflection

[edit] Unequal scaling

[edit] Rotation

[edit] Rotation matrices on complex vector spaces

GRAPH

Current–voltage characteristic of Diodes

Current–voltage characteristic

[edit] Shockley diode equation

[edit] Small-signal behavior

[edit] Types of semiconductor diode

Types of Viscosity

Contents

Etymology

Viscosity coefficients

Newton's theory

Viscosity measurement

Units of measure

Dynamic viscosity

Kinematic viscosity

Saybolt Universal Viscosity

Relation to Mean Free Path of Diffusing Particles

Dynamic versus kinematic viscosity

Example: viscosity of water

Molecular origins

Gases

Effect of temperature on the viscosity of a gas