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October 12th, 2016, 10:52 AM   #1
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Dimensional Analysis

Please help out with the following question on dimensional analysis.And if any notes are available on the same topic,please give them to me.

a)
In Vander Waals equation

(p+a/v^2)(v-b)=RT

where p is the pressure, v is the volume,R is the universal gas constant and T the temperature.
what are the dimensions of the 'a' and 'b' ?

b)
The viscosity n of a gas depends on the mass m, the effective diameter d and the mean speed of the molecules v. Use dimensional analysis to find an expression for n
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October 13th, 2016, 03:27 AM   #2
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Math Focus: Physics, mathematical modelling, numerical and computational solutions
This should probably be moved to the physics sub forum

a) This question can be answered by understanding that when adding or subtracting quantities, those quantities must have the same units. Therefore

$\displaystyle \left[\frac{a}{v^2}\right] = \left[p\right]$

$\displaystyle \left[a\right] = \left[p v^2\right]$

and

$\displaystyle \left[v\right] = \left[b\right]$

where the square brackets here denote "units of"

b) To answer this one, we have

$\displaystyle [\nu] = [m]^a [d]^b [v]^c$

so replace the quantities with their units and then find a, b and c such that the equation is balanced (basically using simultaneous equations)
Thanks from skeeter and topsquark

Last edited by Benit13; October 13th, 2016 at 03:33 AM.
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October 22nd, 2016, 07:30 AM   #3
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thanks very much sir
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