Making use of Poiseuille's equation `(1.7 d)`, find the mass `mu` of gas flowing per unit time through the pipe of length `l` and radius `a` if constant pressures `p_1` and `p_2` are maintained at its ends.

Explanation

Take an infinitesimal section of length `dx` and apply Poiseuilles equation to this. Then
`(dV)/(dt) = (-pi a^4)/(8 eta) (del p)/(del x)`
From the formula `pV = RT. (m)/(M)`
`pdV = (RT)/(M) dm`
or `(dm)/(dt) = mu = -(pi a^4 M)/(8 eta RT) (pdp)/(dx)`
This equation implies that if the flow is isothermal then `p (dp)/(dx)` must be a constant and so equals `(|p_2^2 - p_1^2|)/(2 l)` in magnitude.
Thus, `mu = (pi a^4 M)/(16 eta RT) (|p_2^2 - p_1^2|)/(l)`.