# Geotechnical Engineering Questions and Answers – Well Hydraulics – Interference among Wells

This set of Soil Mechanics Questions and Answers for Experienced people focuses on “Well Hydraulics – Interference among Wells”.

1. When two wells are situated near each other, the discharge in individual well is ________
a) increased
b) decreased
c) not effected
d) remains same with respect to each other

Explanation: When two wells are situated near each other, their drawdown curves intersect within their radii of zero drawdown. Thus, the discharge in individual well is decreased.

2. The discharge for drawdown of well is given by _______
a) $$q=\frac{2πkb(H-h)}{log_{10}\frac{R}{r}}$$
b) $$q=\frac{2πkb(H-h)}{log_e\frac{r}{R}}$$
c) $$q=\frac{2πkb(H-h)}{log_e\frac{R}{r}}$$
d) $$q=\frac{kb(H-h)}{log_e\frac{R}{r}}$$

Explanation: The formula for discharge for drawdown of well is given by,
$$q=\frac{2πkb(H-h)}{log_e\frac{R}{r}}$$
where, q=discharge
k=coefficient of permeability
b=aquifer thickness
(H-h)=drawdown.

3. The formula for discharge for two wells at distance B is given by ____________
a) $$q_1=q_2=\frac{2πkb(H-h)}{log_e \frac{R^2}{rB}}$$
b) $$q_1=q_2=\frac{2πkb(H-h)B}{log_e \frac{r}{R}}$$
c) $$q_1=q_2=\frac{2πkb(H-h)}{log_e \frac{RB}{r}}$$
d) $$q_1=q_2=\frac{kb(H-h)}{log_e \frac{R}{rB}}$$

Explanation: The formula for discharge for two wells at distance B is given by,
$$q_1=q_2=\frac{2πkb(H-h)}{log_e \frac{R^2}{rB}}$$
where, q1=q2=discharge in wells 1 and 2 respectively
k=coefficient of permeability
b=aquifer thickness
(H-h)=drawdown.

4. The formula for discharge for three wells forming an equilateral triangle at distance B on side is given by ____________
a) $$q_1=q_2=q_3= \frac{2πkb(H-h)}{log_e \frac{R^2}{rB}}$$
b) $$q_1=q_2=q_3= \frac{2πkb(H-h)}{log_e \frac{R^3}{rB^2}}$$
c) $$q_1=q_2=q_3= \frac{2πkb(H-h)}{log_e \frac{RB}{r}}$$
d) $$q_1=q_2=q_3= \frac{kb(H-h)}{log_e \frac{R}{rB}}$$

Explanation: The formula for discharge for three wells forming an equilateral triangle at distance B on side is given by,
$$q_1=q_2=q_3= \frac{2πkb(H-h)}{log_e \frac{R^3}{rB^2}},$$
where, q1=q2=q3=discharge in wells 1 and 2 respectively
k=coefficient of permeability
b=aquifer thickness
(H-h)=drawdown.

5. Two tube wells of 20cm diameter each are 100m apart. The coefficient of permeability is 4.15 * 10-4 m/s, drawdown is 4m and aquifer is 30m thick. If radius of influence is 245m, what is the discharge in each well?
a) 0.033 m3/s
b) 0.040 m3/s
c) 0.036 m3/s
d) 0.042 m3/s

Explanation: Given,
Interface among two wells,
B=100m
coefficient of permeability is 4.15 * 10-4 m/s
drawdown (H-h)=4m
aquifer=30m
the discharge is given by,
$$q_1=q_2=\frac{2πkb(H-h)}{log_e \frac{R^2}{rB}}$$
$$q_1=q_2=\frac{2π*4.15 * 10^(-4)*30*4}{log_e \frac{245^2}{0.1*100}}$$
∴ q1=q2=0.036 m3/s.
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6. In a tube well of 20cm diameter in a soil with coefficient of permeability of 4.15 * 10-4m/s, drawdown is 4m and aquifer is 30m thick. If radius of influence is 245m, what is the discharge in each well?
a) 0.033 m3/s
b) 0.040 m3/s
c) 0.036 m3/s
d) 0.042 m3/s

Explanation: Given,
coefficient of permeability is 4.15 * 10-4 m/s
drawdown (H-h)=4m
aquifer=30m
the discharge is given by,
$$q=\frac{2πkb(H-h)}{log_e \frac{R}{r}}$$
$$q=\frac{2π*4.15 * 10^{-4}*30*4}{log_e \frac{245}{0.1}}$$
∴ q=0.040 m3/s.

7. Three tube wells of 20cm diameter each forming an equilateral triangle at distance 100m on side. The coefficient of permeability is 4.15 * 10-4 m/s, drawdown is 4m and aquifer is 30m thick. If radius of influence is 245m, what is the discharge in each well?
a) 0.033 m3/s
b) 0.040 m3/s
c) 0.036 m3/s
d) 0.042 m3/s

Explanation: Given,
Interface among three wells,
B=100m
coefficient of permeability is 4.15 * 10-4 m/s
drawdown (H-h)=4m
aquifer=30m
the discharge is given by,
$$q_1=q_2=q_3= \frac{2πkb(H-h)}{log_e \frac{R^3}{rB^2}}$$
$$q_1=q_2=q_3= \frac{2π*4.15 * 10^{-4}*30*4}{log_e \frac{245^3}{0.1*100^2}}$$
∴ q1=q2=q3=0.033 m3/s.

8. In a artesian well, when water level falls below the top of confined aquifer, then this type of well is known as ______
a) well in unconfined aquifer
b) gravity well
c) combined artesian gravity well
d) artesian well

Explanation: In an artesian well, when water level falls below the top of confined aquifer, the flow pattern close to the well is similar to that of gravity well. Hence, it is also known as combined artesian gravity well.

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