Question
Download Solution PDFFind the efficiency of a pump (rated 400 W) that can lift 500 kg of water by 30 m in 10 minutes. (Use g = 10m/s2)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Pump:
- A pump is a mechanical device used to force a fluid (a liquid or a gas) to move forward inside a pipeline or hose.
- They are also used to produce pressure by the creation of a suction (partial vacuum), which causes the fluid to rise to a higher altitude.
The efficiency of the pump, \(\eta =\frac{Useful ~power}{Power~rating}\)
Calculation:
Given:
Power rating = 400 W, Mass of water lifted = 500 kg, H = 30 m, time = 10 minutes = 60 × 10 = 600 seconds, g = 10 m/s2
Force, F = m × g = 500 × 10 = 5000 N
Work = Force × displacement (H) = 5000 × 30 = 150 kJ
\(Power=\frac{Work}{Time}\)
\(Power=\frac{150}{600}=0.25 ~kW=250~W\)
⇒ Useful work = 250 W
\(\eta=\frac{Useful ~power}{Power~rating}\)
\(\eta=\frac{250}{400}=0.625\)
⇒ η = 62.5%
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