Question

The formula for the pumping out test in an unconfined aquifer is given by _________

(a) \(k=\frac{qπ}{1.36(H^2-h^2)}log_{10}\frac{R}{r} \)

(b) \(k=\frac{q}{1.36(H^2-h^2)}log_{10}\frac{R}{r} \)

(c) \(k=\frac{q}{2.72b(H-h)}log_{10}\frac{R}{r} \)

(d) \(k=\frac{q}{1.36(H^2-h^2)} \)

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

My query is from Well Hydraulics in division Well Hydraulics of Geotechnical Engineering I

Answer 1

Correct answer is (c) \(k=\frac{q}{2.72b(H-h)}log_{10}\frac{R}{r} \)

To explain I would say: From Darcy’s law,

q=kAi

A=2πxb

Where b=thickness of confined aquifer

\(i=\frac{dy}{dx}  \)

q=k2πxb \(\frac{dx}{x} \,or\, \frac{dx}{x}= k2πbdy\)

integrating between (R,r) for x and (H,h) for y,

\(∫_r^R q \frac{dx}{x} =2kπb∫_h^H dy \)

∴ \(k=\frac{q}{2.72b(H^2-h^2)}log_{10}\frac{R}{r}. \)