This set of Engineering Hydrology Multiple Choice Questions & Answers (MCQs) focuses on “Steady Flow into a Well – Set 3”.

1. What is the definition of interference in discharge wells?

a) Overlapping zones of influence

b) Pumping from one well leads to discharge from nearby well

c) Two or more wells intersecting each other

d) Dependent recuperation of nearby wells

View Answer

Explanation: When two or more wells are located close to each other in an aquifer, their zones of influence may overlap each other. This intersecting of the drawdown curves is known as interference among wells.

2. A 50 cm diameter well completely penetrates a confined aquifer of thickness 18 m and permeability 100 m/day. The radius of influence is 250 m and the steady state well drawdown is 7.5 m. What is the discharge from the well, if it is affected by interference from another well 50 m away?

a) 415 m^{3}/hr

b) 512 m^{3}/hr

c) 770 m^{3}/hr

d) 1029 m^{3}/hr

View Answer

Explanation: Given r = 50/2 = 25 cm = 0.25 m, B = 18 m, R = 250 m, S = 7.5 m, K = 100 m/day, D = 50 m.

The discharge is given as,

Q=\(\frac{2πKBS}{ln \frac{R^2}{rD}} =\frac{2π*100*18*7.5}{ln(\frac{250^2}{0.25*50})}=\frac{27000π}{ln5000}\)=9959 m

^{3}/day≅415 m

^{3}/hr

3. Three identical wells are installed in a confined aquifer, equally spaced in a straight line. If the wells discharge over the same time for the same drawdown, then the discharge from each well due to interference will be equal.

a) True

b) False

View Answer

Explanation: For three wells installed in a straight line in an aquifer, the discharges for the outer two wells will be same. However, the discharge for the middle well will be different as it will be interfering with the drawdown curves of two wells.

4. Which of the following is true with respect to the discharge from wells due to interference between two identical wells completely penetrating an aquifer?

a) The total discharge of the wells remain same

b) The individual discharge of each well remains same

c) The total discharge of the wells decreases

d) The individual discharge of each well decreases

View Answer

Explanation: It has been observed that due to interference between wells, the discharge from each individual well decrease. However, the total discharge obtained from the combined system of wells increase due to interference.

5. Two well systems are installed in the same aquifer at different locations. Each system comprises of two identical wells with a radius of influence 200 m and same drawdown. If the distance between wells is 20 m and 25 m for each system respectively, what will be the ratio of well discharges of both systems?

a) 0.81

b) 0.97

c) 1.03

d) Data insufficient

View Answer

Explanation: Given K, B, S, R and r is same for both systems. Also, R = 200 m, D

_{1}= 20 m, D

_{2}= 25 m.

Since the distance between wells in both cases is less than R, there will be interference. Now,

\(\frac{Q_1}{Q_2} =\frac{ln(\frac{R^2}{rD_2})}{ln(\frac{R^2}{rD_1})}=\frac{ln(\frac{200^2}{r*25})}{ln(\frac{200^2}{r*20})} =\frac{ln(\frac{1600}{r})}{ln(\frac{2000}{r})}\) <1

The data regarding the well size is not given and hence the ratio cannot be computed. However, it can be seen that the wells in the system with the spacing farther apart will have a higher individual discharge.

6. The data regarding a two-well system in confined aquifers A and B is given.

Aquifer A | Aquifer B | |
---|---|---|

Thickness (in m) | 10 | 12 |

Permeability (in m/sec) | 1.5 x 10-4 | 4.5 x 10-4 |

Radius of wells (in cm) | 40 | 40 |

Radius of influence (in km) | 0.25 | 0.45 |

Spacing of wells (in m) | 100 | 100 |

If the steady state drawdown in both systems is same, what is the ratio of total discharge from aquifer A to total discharge of aquifer B?

a) 0.09

b) 0.24

c) 0.32

d) 0.46

View Answer

Explanation: This is a case of interference among wells for both systems since R > D.

Aquifer A – Given B

_{A}= 10 m, K

_{A}=1.5 x 10

^{-4}m/sec, r

_{A}=0.4 m, R

_{A}= 250 m, D

_{A}= 100 m.

Aquifer B – Given B

_{B}= 12 m, K

_{B}=4.5 x 10

^{-4}m/sec, r

_{B}=0.4 m, R

_{B}= 450 m, D

_{B}= 100 m.

Also, S

_{A}= S

_{B}.

The ratio of total discharges is given as,

\(\frac{Q_A}{Q_B} = \frac{2 \left(\frac{2\pi K_A B_A S_A}{\ln\left(\frac{R_A^2}{r_A D_A}\right)}\right)}{2 \left(\frac{2\pi K_B B_B S_B}{\ln\left(\frac{R_B^2}{r_B D_B}\right)}\right)} = \frac{\frac{K_A B_A}{\ln \frac{R_A^2}{r_A D_A}}}{\frac{K_B B_B}{\ln \frac{R_B^2}{r_B D_B}}} = \frac{K_A}{K_B} \cdot \frac{B_A}{B_B} \cdot \frac{\ln \frac{R_B^2}{r_B D_B}}{\ln \frac{R_A^2}{r_A D_A}}\)

\(\frac{Q_A}{Q_B} = \frac{1.5 \times 10^{-4}}{4.5 \times 10^{-4}} \times \frac{10}{12} \frac{\ln\left(\frac{450^2}{0.4 \times 100}\right)}{\ln\left(\frac{250^2}{0.4 \times 100}\right)} = \frac{1}{12} \frac{ln(5062.5)}{ln(1562.5)} = 0.32\)

7. Two wells 90 m apart completely penetrate an 8 m thick confined aquifer of permeability 4 m/hr. The diameter of the wells is 45 cm and their radius of influence is 270 m. If the steady state drawdown in the wells is 2.8 m, what is the percentage reduction in discharge from a well due to interference?

a) 9.7%

b) 13.4%

c) 15.5%

d) 17.4%

View Answer

Explanation: Given r = 45/2 = 22.5 cm = 0.225 m, B = 8 m, R = 270 m, S = 2.8 m, K = 4 m/hr, D = 90 m.

For no interference, the discharge is given as,

Q=\(\frac{2πKBS}{ln \frac{R}{r}} =\frac{2π*4*8*2.8}{ln \frac{270}{0.225}}\) =79.403 m

^{3}/hr

For interference, the discharge is given as,

Q

^{‘}=\(\frac{2πKBS}{ln \frac{R^2}{rD}} = \frac{2π*4*8*2.8}{ln \frac{270^2}{0.225*90}}\) =68.75 m

^{3}/hr

∴Percentage reduction=\(\frac{Q-Q’}{Q}*100=\frac{79.403-68.75}{79.403}*100\)=13.4%

8. A well is installed into the ground only upto the top surface of a confined aquifer. What is the nature of groundwater inflow into the well in this case?

a) Radial

b) Only from bottom

c) Spherical

d) Conical

View Answer

Explanation: When a well is penetrated only upto the top surface of a confined aquifer, the drawdown happens normally, but the groundwater recharge into the well is in the form of spherical flow. The discharge from such type of arrangement is very low and inefficient compared to radial flow.

9. Three wells each of radius r are installed in an unconfined aquifer (permeability K and saturated thickness B) in the pattern of an equilateral triangle of side a. All the wells discharge over the same time for a drawdown of (H – h) and radius of influence R. What is the discharge of an individual well in the system due to interference?

a) \(\frac{2πKB(H-h)}{ln(\frac{R^3}{r^2 a})}\)

b) \(\frac{2πKB(H-h)}{ln(\frac{R^3}{ra^2})}\)

c) \(\frac{πK(H^2-h^2)}{ln(\frac{R^3}{r^2 a})}\)

d) \(\frac{πK(H^2-h^2)}{ln(\frac{R^3}{ra^2 })}\)

View Answer

Explanation: The given case is of an equilateral triangle well system in an unconfined aquifer. Each of the three wells is equally influenced by the neighboring two wells and will give equal individual discharge. This discharge is given as,

Q=\(\frac{πK(H^2-h^2)}{ln(\frac{R^3}{ra^2 })}\).

10. What is the equation for discharge from a well with spherical flow? Take K = permeability of aquifer, S = drawdown in well, r = radius of well, R = radius of influence, B = aquifer thickness.

a) πKRS

b) 2πKRS

c) 2πKrS

d) 2πKBS

View Answer

Explanation: The discharge for spherical flow into a well is given as,

Q

_{s}=2πKrS

This depends upon the radius of the well apart form aquifer and drawdown. Unlike radial flow, it is independent of aquifer thickness and radius of influence as inflow takes place below the well. This discharge is very low compared to same well with radial flow conditions.

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