Question

The total quantity of water flowing through the capillary tube is given by _________

(a) \(q=\frac{hγ_w}{4ηL} R^2 \)

(b) \(q=\frac{hγ_w}{4ηL} R^4\)

(c) \(q=\frac{hγ_w}{8ηL} R^2\)

(d) \(q=\frac{hγ_w}{8ηL} πR^4\)

I had been asked this question in an online quiz.

I'm obligated to ask this question of Poiseuille’s Law in chapter Permeability of Geotechnical Engineering I

Answer 1

Right answer is (d) \(q=\frac{hγ_w}{8ηL} πR^4\)

Best explanation: The total quantity of flow is obtained by integrating with the limits 0 to R in the differential discharge.

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

\(q=\frac{hγ_w}{4ηL}\int_0^R (R^2-r^2)2πrdr\)

\( ∴ q=\frac{hγ_w}{8ηL} πR^4\)