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Unformatted text preview: Chapter 12 Bernoulli and Energy Equations Energy Equation 1249C It is impossible for the fluid temperature to decrease during steady, incompressible, adiabatic flow since this would require the entropy of an adiabatic system to decrease, which would be a violation of the 2 nd law of thermodynamics. 1250C Yes, the frictional effects are negligible if the fluid temperature remains constant during steady, incompressible flow since any irreversibility such as friction would cause the entropy and thus temperature of the fluid to increase during adiabatic flow. 1251C Head loss is the loss of mechanical energy expressed as an equivalent column height of fluid, i.e., head. It is related to the mechanical energy loss by g m E g e h L loss mech, loss mech, = = . 1252C Pump head is the useful power input to the pump expressed as an equivalent column height of fluid. It is related to the useful pumping power input by g m W g w h u pump, u pump, pump = = 1253C The kinetic energy correction factor is a correction factor to account for the fact that kinetic energy using average velocity is not the same as the actual kinetic energy using the actual velocity profile. Its effect is usually negligible (the square of a sum is not equal to the sum of the squares of its components). 1254C By Bernoulli Equation, the maximum theoretical height to which the water stream could rise is the tank water level, which is 20 meters above the ground. Since the water rises above the tank level, the tank cover must be airtight, containing pressurized air above the water surface. Otherwise, a pump would have to pressurize the water somewhere in the hose. 1234 Chapter 12 Bernoulli and Energy Equations 1255 Underground water is pumped to a pool at a given elevation. The maximum flow rate and the pressures at the inlet and outlet of the pump are to be determined. Assumptions 1 The flow is steady, onedimensional, and incompressible. 2 The elevation difference between the inlet and the outlet of the pump is negligible. 3 We assume the frictional effects to be negligible since the maximum flow rate is to be determined, . loss mech, = E Properties We take the density of water to be 1 kg/L = 1000 kg/m 3 (Table A3). Analysis ( a ) The pumpmotor draws 3kW of power, and is 70% efficient. Then the useful mechanical (shaft) power it delivers to the fluid is kW 1 . 2 kW) 3 )( 70 . ( electric motor pump u pump, = = = W W We take point 1 at the free surface of underground water, which is also taken as the reference level ( z 1 = 0), and point 2 at the free surface of the pool. Also, both 1 and 2 are open to the atmosphere ( P 1 = P 2 = P atm ), the velocities are negligible at both points ( V 1 = V 2 = 0), and frictional losses are disregarded. Then the energy equation for steady incompressible flow through a control volume between these two points that includes the pump and the pipes reduces to loss mech, turbine 2 2 2 2 u pump, 1 2 1 1 2 2 E W gz P m...
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This homework help was uploaded on 04/18/2008 for the course EML 3007 taught by Professor Chung during the Spring '08 term at University of Florida.
 Spring '08
 Chung

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