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The pump of a water distribution system is powered by a 15-kW electric motor whose efficiency is 90%. The water flow rate through the pump is 50 L/s. The diameters of the inlet and outlet pipes are the same, and the elevation difference across the pump is negligible. If the absolute pressures at the inlet and outlet of the pump are measured to be 100 kPa and 300 kPa, respectively, determine: (a) the mechanical efficiency of the pump (b) the temperature rise of water as it flows through the pump due to mechanical inefficiencies. 300 kPa Water 50 L/s G 100 kPa W pump motor = 90% Motor 15 kW

The pump of a water distribution system is powered by a 15-kW electric motor whose efficiency is 90%. The water flow rate through the pump is 50 L/s. The diameters of the inlet and outlet pipes are the same, and the elevation difference across the pump is negligible. If the absolute pressures at the inlet and outlet of the pump are measured to be 100 kPa and 300 kPa, respectively, determine: (a) the mechanical efficiency of the pump (b) the temperature rise of water as it flows through the pump due to mechanical inefficiencies. 300 kPa Water 50 L/s G 100 kPa W pump motor = 90% Motor 15 kW

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Water Pump System Analysis #### Problem Statement The pump of a water distribution system is powered by a 15-kW electric motor whose efficiency is 90%. The water flow rate through the pump is 50 L/s. The diameters of the inlet and outlet pipes are the same, and the elevation difference across the pump is negligible. If the absolute pressures at the inlet and outlet of the pump are measured to be 100 kPa and 300 kPa, respectively, determine: (a) the mechanical efficiency of the pump (b) the temperature rise of water as it flows through the pump due to mechanical inefficiencies. #### Diagram Explanation The diagram on the right illustrates a water distribution system. Key components and data are: 1. **Inlet and Outlet:** - Inlet Pressure: 100 kPa - Outlet Pressure: 300 kPa 2. **Water Flow Rate:** - Flow Rate: 50 L/s 3. **Pump Motor:** - Power: 15 kW - Efficiency: 90% 4. **Water Flow Path:** - Water enters the pump at the bottom (inlet, 100 kPa) and is discharged at the top (outlet, 300 kPa). Both inlets and outlets have the same pipe diameter. - The pump is driven by the motor, which transfers power (\(\dot{W}_{pump}\)) to the water. #### Detailed Steps: (a) **Mechanical Efficiency of the Pump:** - Calculate the actual power delivered to the water and compare it to the power supplied by the motor. (b) **Temperature Rise of Water:** - Calculate the energy losses due to mechanical inefficiencies and determine the consequent temperature rise of the water. Use the diagram and given data for precise calculations and step-by-step analysis in determining the pump's efficiency and the temperature rise.
Transcribed Image Text:### Water Pump System Analysis #### Problem Statement The pump of a water distribution system is powered by a 15-kW electric motor whose efficiency is 90%. The water flow rate through the pump is 50 L/s. The diameters of the inlet and outlet pipes are the same, and the elevation difference across the pump is negligible. If the absolute pressures at the inlet and outlet of the pump are measured to be 100 kPa and 300 kPa, respectively, determine: (a) the mechanical efficiency of the pump (b) the temperature rise of water as it flows through the pump due to mechanical inefficiencies. #### Diagram Explanation The diagram on the right illustrates a water distribution system. Key components and data are: 1. **Inlet and Outlet:** - Inlet Pressure: 100 kPa - Outlet Pressure: 300 kPa 2. **Water Flow Rate:** - Flow Rate: 50 L/s 3. **Pump Motor:** - Power: 15 kW - Efficiency: 90% 4. **Water Flow Path:** - Water enters the pump at the bottom (inlet, 100 kPa) and is discharged at the top (outlet, 300 kPa). Both inlets and outlets have the same pipe diameter. - The pump is driven by the motor, which transfers power (\(\dot{W}_{pump}\)) to the water. #### Detailed Steps: (a) **Mechanical Efficiency of the Pump:** - Calculate the actual power delivered to the water and compare it to the power supplied by the motor. (b) **Temperature Rise of Water:** - Calculate the energy losses due to mechanical inefficiencies and determine the consequent temperature rise of the water. Use the diagram and given data for precise calculations and step-by-step analysis in determining the pump's efficiency and the temperature rise.
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