Question

In Poiseuille’s law of flow, the variation of the velocity is given by _______

(a) v = \(\frac{hγ_w}{4ηL}(r^2-R^2)\)

(b) v = \(\frac{hγ_w}{14ηL}(R^2-r^2)\)

(c) v = \(\frac{hγ_w}{4ηL}(R^2-r^2)\)

(d) v = \(\frac{hγ_w}{8ηL}(R^2-r^2)\)

The question was asked by my school teacher while I was bunking the class.

Enquiry is from Poiseuille’s Law in section Permeability of Geotechnical Engineering I

Answer 1

Right answer is (c) v = \(\frac{hγ_w}{4ηL}(R^2-r^2)\)

The explanation: Consider a capillary tube of length L and radius R.

In equilibrium the sum of the forces is zero,

πr^2h1γw– πr^2h1γw-τ(2πrL)=0

on simplification, \(dv=-\frac{hγ_w}{2ηL}rdr\)

on integration,

\(v =- \frac{hγ_w}{4ηL}r^2 + C                     \,where\, C=\frac{hγ_w}{4ηL} R^2\)

∴ \(v = \frac{hγ_w}{4ηL}(R^2-r^2).\)