Question

The relationship between the quantity of flow with respect to the hydraulic radius and the voids ratio is given by ________

(a) \(q=\frac{γ_w R_H^2}{η}\frac{e}{1+e}iA\)

(b) \(=C_S\frac{γ_w R_H^2}{η}\frac{e}{1+e}\)

(c) \(=C_S\frac{γ_w R_H^2}{η}iA\)

(d) \(=C_S\frac{γ_w R_H^2}{η}\frac{e}{1+e}iA\)

The question was posed to me during a job interview.

My doubt is from Poiseuille’s Law topic in portion Permeability of Geotechnical Engineering I

Answer 1

Correct option is (d) \(=C_S\frac{γ_w R_H^2}{η}\frac{e}{1+e}iA\)

Easy explanation: Let the total cross-section of the soil be A and the porosity be n,

∴ a=nA

∴ \(q=\frac{1}{2}\frac{γ_w R_H^2}{η}ia=\frac{1}{2}\frac{γ_w R_H^2}{η}inA\)

Since n=e/(1+e),

∴ \(q=C_S \frac{γ_w R_H^2}{η}\frac{e}{1+e}iA.\)