An engine pumps water from a tank at the rate of 10 kg per second and ejects from a nozzle 7 m above the surface of the tank with a velocity of 20 m/s. What is the output power of the engine?

An engine pumps water from a tank at the rate of 10 kg per second and

1.	An engine pumps water from a tank at the rate of 10 kg per second and ejects from a nozzle 7 m above the surface of the tank with a velocity of 20 m/s. What is the output power of the engine?
Answer» Solution :Let P, and P, be the PRESSURE, w, and v, the VELOCITIES, at the surface of the tank and the nozzle respectively. By Bernoulli.s theorem, `P_1 +H_1 rhog +(1)/(2)v_1^(2) rho = P_2 +H_2rho g +(1)/(2)v_2^(2) rho ` `""P_1 - P_2 = rho g (H_2 -H_1)+(1)/(2)rho ( v_2^(2) -v_1^(2)) ` `H_2 -H_1 =7 m ` `v_1 =0, v_2 = 20 m//s` ` P_1 -P_2 = rho xx 9.8 xx 7 +(1)/(2) rho ( 20^(2) -0) ` ` "" =208.6 rho` Rate of DISCHARGE of water ` =(10)/( rho)` Rate of doing WORK ` = (P_1 -P_2)xx (10)/(rho )` ` ""=208.6 rho xx (10)/(rho)` ` ""=2086 J//s` i.e. , Output power of the engine = 2086 WATT