This set of Soil Mechanics Questions and Answers 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) \(k=\frac{q}{1.36(H^2-h^2)} \)
View Answer
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) \(k=\frac{q}{1.36(H^2-h^2)} \)
View Answer
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
View Answer
Explanation: Given,
Drawdown=4m
Discharge q=40litres/sec
thickness of confined aquifer b=30m
radius of the well r=0.1m
radius of influence=245m
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
View Answer
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
d) falling head and constant head permeability test
View Answer
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) \(k=\frac{q}{0.5rh} \)
View Answer
Explanation: The permeability can be calculated from,
\(k=\frac{q}{5.5rh}\) where k=permeability
q=discharge or constant rate of flow
r=radius of casing
h=differential head of water.
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) \(k=\frac{q}{2πLh}log_{10} \frac{L}{r}\)
View Answer
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
r=radius of casing
h=differential head of water
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) \(k=\frac{q}{2πLh}sinh^{-1}\frac{L}{2r} \)
View Answer
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
r=radius of casing
h=differential head of water
L=length of portion of hole tested.
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