A five cylinders reciprocating pump raises the water level by 100 m and the theoretical discharge is 0.2 m³/s. The velocity in the delivery pipe is 2 m/s. Total head loss in pipes is 20 m. What would be the mechanical loss (in head of water) if the mechanical efficiency of the pump is 0.8 (assume, g = 10 m/s²)?
- A20.20 m
- B30.05 mCorrect
- C36.08 m
- D39.30 m
Solution
Concept
Mechanical efficiency and head loss
Formula
ηm = Hwater/Hshaft
Step-by-step solution
1. Head given to the water = 100 + 20 + v²/2g = 120 + 4/20 = 120.2 m. 2. Head supplied at the shaft = 120.2/0.8 = 150.25 m. 3. Mechanical loss = 150.25 − 120.2 = 30.05 m.
Explanation
The delivery velocity head is included in the head given to the water.
Why the other options are wrong
Other values omit the velocity head or use a different basis.
Shortcut
Loss = H(1/η − 1).
Correct answer: B) 30.05 m