show work please please A proposed water tank on the sixth floor (roof top) of t

Question

show work please please A proposed water tank on the sixth floor (roof top) of the UT administration building would be used to supply pressurized water for the campus. A pump fills the tank at a rate of 13.5 kg/s. What size motor (hp) is needed to operate the pump given the data below? The motor size (hp) must be 20% greater than the required pump work. Note: Give the motor size as a positive value. The pump includes the riser pipe to the tank. There is no heat transfer from the pump to the surroundings (i.e., adiabatic conditions). Pump Inlet Temperature = 20oC Pump Inlet Pressure = 144 kPa Pump Inlet Diameter = 12 cm Pump Inlet Elevation = 23.1 m Pump Exit Temperature = 20oC Pump Exit Pressure = 271 kPa Pump Exit Diameter = 4.8 cm Pump Exit Elevation = 41 m [Answer Correct Answer: 7.17

Explanation / Answer

now from steam table enthalapy of water at 144 Kpa=532.87 KJ/kg

and at 271 Kpa enthalapy=593.901 KJ/kg

So Pump Power=(change in entalapy+change in kinetic energy+change in Potential energy)2+

(change in entalapy+change in kinetic energy+change in Potential energy)1

=13.5*(593.901+1/2*(13.5/pi*0.5*2.4*10^-2)^2+9.81*41)

+13.5*(532.87+1/2*(13.5/pi*0.5*6*10^-2)^2+9.81*23.1)

=5346.7 W

=5346.7/746

=7.17

for 20 % greater we have

7.17

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