A fully penetrating well in a confined sandy aquifer has a maximum discharge capacity of 1200 l/min. The aquifer is overlain and underlain by impervious formations. The thickness of the aquifer is 20 m. Assume the percentage of the open area of an available strainer to be 15% and bore hole diameter as 15 cm. What is the length of the well screen? (Take safe entrance velocity as 0.02 m/s)
- A10.5 m
- B12.3 m
- C13.1 m
- D14.1 mCorrect
Solution
Concept
Screen length is chosen so that water enters the screen openings at a safe (low) entrance velocity.
Formula
Q = (open area fraction × π × d × L) × Ve, so L = Q / (p × π × d × Ve)
Step-by-step solution
1. Discharge Q = 1200 l/min = 1200/(1000 × 60) = 0.02 m³/s. 2. Required open area = Q / Ve = 0.02 / 0.02 = 1.0 m². 3. Open area per metre of screen = p × π × d = 0.15 × π × 0.15 = 0.0707 m²/m. 4. Screen length L = 1.0 / 0.0707 = 14.15 m ≈ 14.1 m.
Explanation
Water must enter the well through the open slots of the strainer at a safe velocity. The total open area needed is Q divided by the safe velocity. Dividing this area by the open area per metre of screen gives the length, which is about 14.1 m and less than the 20 m aquifer thickness.
Why the other options are wrong
(A) 10.5 m, (B) 12.3 m and (C) 13.1 m are too short. They give entrance velocity above 0.02 m/s, or come from wrong unit conversion or a wrong open area.
Shortcut
L = Q / (0.15 × π × 0.15 × 0.02) = 0.02 / 0.001414 ≈ 14.1 m
Common mistake
Not converting l/min to m³/s, or forgetting to multiply by the 15% open area.
Correct answer: D) 14.1 m