A double-acting reciprocating pump having piston area 0·1 m² has a stroke 0·30 m long. If the pump is discharging 2·4 m³ of water per minute at 45 r.p.m. through a height of 10 m, the power required to drive the pump will be nearly
- A4·98 kW
- B4·86 kW
- C4·64 kW
- D4·42 kWCorrect
Solution
Concept
Theoretical discharge and power of a reciprocating pump
Formula
Qth = 2 A L N / 60; P = ρ g Qth H
Step-by-step solution
1. Theoretical discharge Qth = 2 × 0.1 × 0.30 × 45 / 60 = 0.045 m³/s (2.7 m³/min). 2. Power required to drive the pump = ρ g Qth H = 9810 × 0.045 × 10 = 4414 W ≈ 4.42 kW. (The actual discharge of 2.4 m³/min shows 11% slip.)
Explanation
The piston sweeps the theoretical volume every stroke, so the driving power is based on the theoretical discharge, even though the actual discharge is lower because of slip.
Why the other options are wrong
The actual discharge gives only 3.92 kW. 4.98, 4.86 and 4.64 kW do not follow from either discharge.
Shortcut
Driving power uses Qtheoretical.
Common mistake
Using the actual discharge (3.92 kW).
Correct answer: D) 4·42 kW