Concept explainers
Water is pumped from a lake to a storage tank 15 m above at a rate of 70 L/s while consuming 15.4 kW of electric power. Disregarding any frictional losses in the pipes and any changes in kinetic energy, determine (a) the overall efficiency of the pump–motor unit and (b) the pressure difference between the inlet and the exit of the pump.
FIGURE P2–69
(a)
The overall efficiency of the pump-motor unit.
Answer to Problem 69P
The overall efficiency of the pump-motor is
Explanation of Solution
Write the mass flow rate of water.
Here, the volumetric flow rate of water is
The potential energy at point 1 is considered as 0
Write the equation of potential energy at point 2.
Here, acceleration due to gravity is g and lake surface at point 2 is
Calculate the rate at which mechanical energy of fluid supplied to the pump.
Here, the mechanical energy of water inlet and outlet are
Calculate the overall efficiency of the combined pump-motor.
Here, and electric power consumption is
Conclusion:
Substitute
Substitute
Substitute 70 kg/s for
Substitute 10.3 kW for
Thus, the overall efficiency of the pump-motor is
(b)
The pressure difference between the inlet and the exit of the pump.
Answer to Problem 69P
The pressure difference between the inlet and the exit of the pump is
Explanation of Solution
Calculate the rate at which mechanical energy of fluid supplied by the pump.
Here, change in the pressure of water is
Conclusion:
Substitute 10.3 kJ/s for
Thus, the pressure difference between the inlet and the exit of the pump is
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