Correct Answer - Option 4 : 62.5%
Explanation:
Overall Efficiency (η): It is defined as a ratio of the power output of the pump to the power input to the pump.
The overall efficiency of the pump will be given as,
\({{\rm{\eta }}_{\rm{}}} = \frac{{{\rm{water\;power}}}}{{{\rm{shaft\;power\;}}}} = \frac{{{\rm{\omega QH}}}}{{\rm{P}}}\)
\(P = \frac{{{\bf{\omega QH}}\;}}{{{\eta }}}\)
Calculation:
\(\eta = \frac{{{\bf{\rho g QH}}\;}}{{{P }}} = \frac{{{\bf{1000\times10\times0.04\times25}}\;}}{{{16000}}}=0.625\)
Manometric Efficiency (ηman): It is the ratio of the manometric head to head imparted by the impeller to the water.
\({\eta _{man}} = \frac{{{H_m}}}{{\frac{{{V_{w2}}{u_2}}}{g}}} = \frac{{g{H_m}}}{{{V_{w2}}{u_2}}}\)
Mechanical Efficiency (ηm): It is the ratio of the power available at the impeller to the power at the shaft of the centrifugal pump.
\({\eta _m} = \frac{{{\rm{Power\;at\;the\;impeller}}}}{{{\rm{Power\;at\;the\;shaft}}}} = \frac{{\frac{W}{g}\left( {\frac{{{V_{w2}}{u_2}}}{{1000}}} \right)}}{{{\rm{SP}}}}\)