A double-acting reciprocating pump, running at 40 r.p.m., is discharging 1·0 m³ of water per minute. The pump has a stroke of 400 mm. The diameter of piston is 200 mm. The delivery and suction head are 20 m and 5 m respectively. The theoretical discharge for the double-acting pump is
- A1·6π/300 m³/sCorrect
- B0·8π/300 m³/s
- C2·4π/300 m³/s
- D0·4π/300 m³/s
Solution
Concept
Discharge of a double-acting pump
Formula
Qth = 2 A L N / 60
Step-by-step solution
1. A = (π/4)(0.2)² = 0.01π m². 2. Qth = 2 × 0.01π × 0.4 × 40 / 60 = 0.32π / 60 = 1.6π / 300 m³/s.
Explanation
In a double-acting pump delivery occurs in both strokes, so the theoretical discharge is twice that of a single-acting pump.
Why the other options are wrong
0.8π/300 is the single-acting value, and the other options are 1.5 and 0.25 times the correct value.
Shortcut
Double acting: 2ALN/60.
Common mistake
Using the single-acting formula.
Correct answer: A) 1·6π/300 m³/s