Question

The total quantity of water with respect to the hydraulic gradient flowing through the capillary tube is given by _________

(a) \( q=\frac{hiγ_w}{4ηL} R^2 \)

(b) \( q=\frac{hγ_w}{4ηL} R^4/i\)

(c) \( q=\frac{iγ_w}{8η} π R^2\)

(d) \( q=\frac{iγ_w}{8η} πR^4\)

This question was posed to me in an internship interview.

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

Answer 1

Right choice is (d) \( q=\frac{iγ_w}{8η} πR^4\)

Easy explanation: The hydraulic gradient i is the head loss divided by the length travelled,

i=h/L

\( ∴ q=\frac{hγ_w}{8ηL} πR^4 = \frac{iγ_w}{8η}πR4.\)