2300_hw_11_sol

2300_hw_11_sol - Homework 11 Solutions #1 2-75 Water is...

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Homework 11 Solutions #1 2-75 Water is pumped from a lake to a storage tank at a specified rate. The overall efficiency of the pump-motor unit and the pressure difference between the inlet and the exit of the pump are to be determined. Assumptions 1 The elevations of the tank and the lake remain constant. 2 Frictional losses in the pipes are negligible. 3 The changes in kinetic energy are negligible. 4 The elevation difference across the pump is negligible. Properties We take the density of water to be r = 1000 kg/m 3 . Analysis ( a ) We take the free surface of the lake to be point 1 and the free surfaces of the storage tank to be point 2. We also take the lake surface as the reference level ( z 1 = 0), and thus the potential energy at points 1 and 2 are pe 1 = 0 and pe 2 = gz 2 . The flow energy at both points is zero since both 1 and 2 are open to the atmosphere ( P 1 = P 2 = P atm ). Further, the kinetic energy at both points is zero (ke 1 = ke 2 = 0) since the water at both locations is essentially stationary. The mass flow rate of water and its potential energy at point 2 are kg/s 70 /s) m 070 . 0 )( kg/m 1000 ( 3 3 = = = V m kJ/kg 196 . 0 /s m 1000 kJ/kg 1 m) 20 )( m/s (9.81 2 2 2 2 2 = ˜ ˆ = = gz pe Then the rate of increase of the mechanical energy of water becomes kW 13.7 kJ/kg) 6 kg/s)(0.19 70 ( ) 0 ( ) ( 2 2 in mech, out mech, fluid mech, = = = - = - = D pe m pe m e e m E The overall efficiency of the combined pump-motor unit is determined from its definition, 67.2% or 0.672 kW 20.4 kW 7 . 13 in elect, fluid mech, motor - pump = = D = W E h ( b ) Now we consider the pump. The change in the mechanical energy of water as it flows through the pump consists of the change in the flow energy only since the elevation difference across the pump and the change in the kinetic energy are negligible. Also, this change must be equal to the useful mechanical energy
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This note was uploaded on 09/04/2009 for the course CHEM 2300 taught by Professor Thermo during the Summer '08 term at Utah.

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2300_hw_11_sol - Homework 11 Solutions #1 2-75 Water is...

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