quick dimensional analysis question check

[jianxu]

Hi, I haven't looked at math/physics in awhile and want to make sure I did this correctly lol

1. The problem statement, all variables and given/known data

The viscosity of a gas depends on the mass(m), the effective diamtere(d) of the gas and the mean speed(v) of the gas molecules. The unit of viscosity is (pascal * second). use dimensional analysis to derive an expression dependent on m,d and v.

2. Relevant equations
I know that 1 Pascal = 1 Newton / area(I assume this is the surface area of a gas molecule)




3. The attempt at a solution
My thought is to just solve and break the Newton part into mass*acceleration, so I canceled all the powers and ended up with:
pascal * second = (mass*meters)/(meter^2(for surface area of a sphere) * second) which after substituting all the units for the variables, I got:
(m*v)/(8*pi*d^2)


I've become really rusty with this and any help/suggestions is greatly appreciated. Thanks so much!! ^_^

[jianxu]

anyone able to confirm if I've done this correctly or not? thanks

[mgb_phys]

viscosity = pa s = pressure * time
pressure = force / area = mass * accelaration / area = kg m s-2 /m2 = kg s-2 m-1

so viscosity = kg s-2 m-1 s = kg s-1 m-1 = mass / (length * time)

[Chrisas]

Equations involving dimensional analysis should not have coefficients in them. The idea is to guess what the Viscosity is proportional to by consideration of units only. Even if you get it right, you can't say what the proportionality constant is without experiment. So in your first attempt at a solution, there shouldn't be any pi or 8 in it. I should only have the m, d, or v in the solution. The only numbers should be what you need for the exponents on m, d, or v.

[jianxu]

Oh I see so it's just pretty much converting what the units are into their corresponding variables? In that case, the answer would just be (m*v)/(d^2) correct? To make it dependent on mass(m), speed(v), and diameter(d).

[Chrisas]

Since the units of your answer seem to match the units of viscosity demonstrated by mgb, in my opinion it would be an acceptable answer.

[jianxu]

Thanks for your help ^_^

[mgb_phys]

You're welcome!
Dimensional analysis is a much underated skill, apart form letting you check your answer it provides a good way of guessing the equation (give or take 2pi).