Question

A pump can take out 7200kg of water per hour from a 100m deep well. Calculate the power of pump assuming it's efficiency to be 50%


Take g=10m/s

Answer 1

Given:

• mass= m= 7200kg
• height = h = 100m
• Efficiency = 50%
• g= 10m/${s}^{2}$

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Need to find:

• Power =?

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Solution :

Output Power:

= $\dfrac{work \: done}{time \: taken}$

= $\dfrac{mgh}{time}$

= $\dfrac{7200 \times 10 \times 100}{3600} watt$

$\bold{\purple{\boxed{ = 2000 \: watt}}}$

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We know,

• Efficiency = Output Power÷ Input Power

• Given Efficiency = 50% = (50÷100)

• We also know, Output Power = 2000 watt

Substitute the values!

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Efficiency = Output Power÷ Input Power

$\implies \dfrac{50}{100} = \dfrac{2000}{{Power}_{i}}$

$\implies {Power}_{I}= \dfrac{2000}{50} \times 100$

$\red{\bold{\large{\boxed{\implies {Power}_{i}= 4000\: watt }}}}$

Here i denotes: Input