Question

The quantity of water flowing in thin cylindrical sheet of thickness dr is ____________

(a) \(dq=\frac{hγ_w}{4ηL}(R^2-r^2)2πrdr\)

(b) \(dq=\frac{hγ_w}{4ηL}(R^2-r^2)4πrdr\)

(c) \(dq=\frac{hγ_w}{4ηL}(R^2-r^2)8πrdr\)

(d) \(dq=\frac{hγ_w}{4ηL}(R^2-r^2)12πrdr\)

I got this question in a national level competition.

Query is from Poiseuille’s Law in chapter Permeability of Geotechnical Engineering I

Answer 1

Correct option is (a) \(dq=\frac{hγ_w}{4ηL}(R^2-r^2)2πrdr\)

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

dq=(2πrdr)v

substituting for velocity,

\(dq=(2πrdr)*\frac{hγ_w}{4ηL}(R^2-r^2)\)

\( ∴ dq=\frac{hγ_w}{4ηL}(R^2-r^2)2πrdr.\)