April 10, 2009

Viscosities of Pure Gases at low Pressure-1

Finding or calculating almost good estimate of any physical property is very important for young engineers & therefore I emphasise a lot on these methods which are time tested and proven and gives sufficient approximations in calculated numbers. So I am writing few such post in the next coming weeks on properties or other quick methods.

I have already posted following useful posts on different properties estimation on this blog.

The two co-relatons are those of Chapman & Enskog and of Yoon & Thodos. Both of them require temperature, molecular weight, critical temperature, critical pressure of the pure gas.

First method of Chapman Enskog also require accentric factor w. Both the methods can handle polar gases also but then they need more physical constants. These correlations are valid only for low pressures may be upto 5 atm or less.

Viscosity by Chapman & Enskog correlation
There are two things to remember - 1 Polar Gas, 2 Non Polar Gas.

So for Polar Gas the equation is -

Vis = (5/16) x (pi x M R T)^0.5 / (pi x Sigma^2) / CI

Which can be simplified as below.

Vis = 26.69 x (M T)^0.5 / (Sigma^2) / CI

M = Mol Wt of gas
T = Temperature of gas
Sigma is given by the following equation

Sigma = (2.3551 - 0.087 w) x Tc/Pc

w = accentric factor of gas(This is a std property & available in any good reference)
Tc = Critical Temperature of Gas
Pc = Critical Pressure of Gas

CI in the above equation is given as below by Lennard Jones method

CI = ( A / TT^ B) + ( C / exp(D * TT) + E / exp(F * TT)

Where TT = (k /epsilon) * T

For TT calculation k / epsilon is available from below equation.

(epsilon/k) = (0.7915 + 0.1693 * w) * Tc

Now for Non Polar Gases the equation is -

Yes the basic equation is same, the first one you read in the beginning however CI constant evaluation changes. Now the balance method remains same except calculate CI from the following Stockmayer equation.

CI (Stockmayer) = CI (Lennard Jones) + 0.2 * delta^2 / TT

TT is already given above, & delta is polarity of the gas.

Oops! I forgot to mention that viscosity is in micropoise here.
Yoon Thodos method shall be covered in next part of this post.

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