FTFS Chap12 P001 - Chapter 12 Bernoulli and Energy...

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Chapter 12 Bernoulli and Energy Equations Chapter 12 BERNOULLI AND ENERGY EQUATIONS Mechanical Energy and Pump Efficiency 12-1C The mechanical energy is the form of energy that can be converted to mechanical work completely and directly by a mechanical device such as a propeller . It differs from thermal energy in that thermal energy cannot be converted to work directly and completely. The forms of mechanical energy of a fluid stream are kinetic, potential, and flow energies. 12-2C Mechanical efficiency is defined as the ratio of the mechanical energy output to the mechanical energy input. A mechanical efficiency of 100% for a hydraulic turbine means that the entire mechanical energy of the fluid is converted to mechanical (shaft) work. 12-3C The combined pump-motor efficiency of a pump/motor system is defined as the ratio of the increase in the mechanical energy of the fluid to the electrical power consumption of the motor, in elect, pump in elect, fluid mech, in elect, in mech, out mech, motor pump motor - pump W W W E W E E The combined pump-motor efficiency cannot be greater than either of the pump or motor efficiency since both pump and motor efficiencies are less than 1, and the product of two numbers that are less than one is less than either of the numbers. 12-4C The turbine efficiency, generator efficiency, and combined turbine-generator efficiency are defined as follows: | | fluid the from extracted energy Mechanical output energy Mechanical fluid mech, out shaft, turbine E W in shaft, out elect, generator input power Mechanical output power Electrical W W | | fluid mech, out elect, out mech, in mech, out elect, generaor turbine gen - turbine E W E E W 12-1
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Chapter 12 Bernoulli and Energy Equations 12-5 A river is flowing at a specified velocity, flow rate, and elevation. The total mechanical energy of the river water per unit mass, and the power generation potential of the entire river are to be determined. Assumptions 1 The elevation given is the elevation of the free surface of the river. 2 The velocity given is the average velocity. 3 The mechanical energy of water at the turbine exit is negligible. Properties We take the density of water to be = 1000 kg/m 3 . Analysis Noting that the sum of the flow energy and the potential energy is constant for a given fluid body, we can take the elevation of the entire river water to be the elevation of the free surface, and ignore the flow energy. Then the total mechanical energy of the river water per unit mass becomes kJ/kg 887 . 0 /s m 1000 kJ/kg 1 2 ) m/s 3 ( m) 90 )( m/s (9.81 2 2 2 2 2 2 mech V gh ke pe e The power generation potential of the river water is obtained by multiplying the total mechanical energy by the mass flow rate, kg/s 500,000 /s) m 00 )(5 kg/m 1000 ( 3 3 V m MW 444 kW 000 , 444 kg/s) 87 kg/s)(0.8 000 , 500 (
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