# Soil Mechanics Questions and Answers – Well Hydraulics – Pumping In and Pumping Out Tests – 2

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This set of Soil Mechanics Interview Questions and Answers for Freshers focuses on “Well Hydraulics – Pumping In and Pumping Out Tests – 2”.

1. 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) $$k=\frac{q}{π(H^2-h^2)}log_{10}\frac{R}{r}$$
d) $$k=\frac{q}{1.36(H^2-h^2)}$$

Explanation: From Darcy’s law,
q=kAi
A=2πxy
$$i=\frac{dy}{dx}$$
$$q=k2πxy \frac{dy}{dx} \,or\, \frac{dx}{x}= k2πydy$$
integrating between (R,r) for x and (H,h) for y,
$$\int_r^R q \frac{dx}{x} =2kπ∫_h^H ydy$$
∴ $$k=\frac{q}{1.36(H^2-h^2)}log_{10}\frac{R}{r}$$

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

Explanation: 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,
$$∫_r^R q \frac{dx}{x} =2kπb∫_h^H dy$$
∴ $$k=\frac{q}{2.72b(H^2-h^2)}log_{10}\frac{R}{r}.$$

3. The permeability of the aquifer is ________ if the drawdown is 4m, discharge is 40litres/sec, thickness of confined aquifer is 30m and the radius of the well is 0.1m. The radius of influence is taken as 245m.
a) 36 m/day
b) 30 m/day
c) 26 m/day
d) 20 m/day

Explanation: Given,
Drawdown=4m
Discharge q=40litres/sec
thickness of confined aquifer b=30m
the permeability is given by,
$$k=\frac{q}{2.72b(H-h)} log_{10}\frac{R}{r}$$
$$k=\frac{0.04}{(2.72*30*4)}log10\frac{245}{0.1}$$
∴k=36 m/day.

4. In the field determination, pumping must continue at a ________
a) uniform rate for sufficient time to approach steady state
b) non- uniform rate for sufficient time to approach steady state
c) uniform rate until just before time to approach steady state
d) non-uniform rate until just before time to approach steady state

Explanation: The steady state condition is the one in which the drawdown changes negligibly with time. In order to get accurate results, pumping must continue at a uniform rate for sufficient time in the field determination to approach steady state.

5. The U.S. Bureau of Reclamation (Earth manual 1960) has devised two types of pumping-in tests _________
a) open-end test and packer test
b) permeability test and radio test
c) dupin test and influence test

Explanation: The pumping-in tests includes open-end test and packer test. The falling head and constant head permeability test are also used to determine the permeability but are laboratory tests.

6. The formula for the open-end test is given by _________
a) $$k=\frac{q}{5.5rh}$$
b) $$k=\frac{5.5rh}{q}$$
c) $$k=\frac{q}{5rh}$$
d) $$k=\frac{q}{0.5rh}$$

Explanation: The permeability can be calculated from,
$$k=\frac{q}{5.5rh}$$ where k=permeability
q=discharge or constant rate of flow

7. The coefficient of permeability by Packer for length greater than ten times the radius test is given by ________
a) $$k=\frac{q}{2πh}log_{10} \frac{L}{r}$$
b) $$k=\frac{v}{2πLh}log_{10} \frac{L}{r}$$
c) $$k=\frac{q}{2Lh}log_{10} \frac{L}{r}$$
d) $$k=\frac{q}{2πLh}log_{10} \frac{L}{r}$$

Explanation: The coefficient of permeability k for L ≥ 10r is given by,
$$k=\frac{q}{2πLh}log_{10} \frac{L}{r}$$
where, q=discharge or constant rate of flow
L=length of portion of hole tested.

8. The coefficient of permeability by Packer for length in the range 10r > L ≥r test is given by ________
a) $$k=\frac{q}{2πh}log_{10} \frac{L}{r}$$
b) $$k=\frac{q}{2πLh}log_{10} \frac{L}{r}$$
c) $$k=\frac{q}{2Lh}log_{10} \frac{L}{r}$$
d) $$k=\frac{q}{2πLh}sinh^{-1}\frac{L}{2r}$$

Explanation: The coefficient of permeability k for 10r > L ≥r is given by,
$$k=\frac{q}{2πLh}sinh^{-1}\frac{L}{2r}$$
where, q=discharge or constant rate of flow
L=length of portion of hole tested.

Sanfoundry Global Education & Learning Series – Soil Mechanics.