Question

An electric motor is used to fill an overhead tank of capacity $10m^2$ kept at a height of $20m$ above the ground. If the pump takes $6$ minutes to fill the tank by consuming $20kW$ power, the efficiency of the pump should be $(g=10m/s^2)$

• A. $27.78\%$
• B. $30\%$
• C. $32\%$
• D. $40\%$

Answer 1

Answer: (A)

$27.78\%$

The mass of water filled in the tank is given as,

$m=dV$

$={10}^3\times 10$

$={10}^{4}kg$

The rise in potential energy of the water is given as,

$E=mgh$

$={10}^4\times 10\times 20$

$=2\times {10}^{6}J$

Power of the pump is given as,

$P_p=\frac{E}{t}$

$=\frac{2\times {10}^{6}J}{360}$

$=\frac{{10}^5}{18}W$

The efficiency of the pump is given as,

$\eta =\frac{P_p}{P_c}$

$=\frac{\frac{{10}^5}{18}}{20\times {10}^3}\times 100$

$=27.78\%$

Thus, the efficiency of the pump should be $27.78\%$.