Lecture_09022009_Compatibility_Mode_ - ENGR 301 ENGR 301...

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ENGR 301 Thermodynamics 9/02/2009 Madison 201 MW 12:00 – 1:15 PM ENGR 301
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Energy N . m or J or kg . m 2. s -2 ft lb ft . lb f Total energy in a system E = kinetic energy + macroscopic potential energy + internal energy microscopic flow energy electrical energy ENGR 301
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On a unit mass basis (U) u = U/m (kJ/kg) ENGR 301
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A closed system whose KE and PE remain constant. Pressure of a flowing fluid is associated with a form of mechanical energy. Flow work/mass = P/ ρ Energy content of a flowing fluid/mass flow = e = P/ ρ + v 2 /2 + g Z ENGR 301
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e mech = P/ ρ + v 2 /2 + g Z Energy associated with flowing fluid E = m e ENGR 301
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Known : velocity v = 3 m/s volumetric flow rate = 500 m 3 /s elevation = Z = 90 m To be determined : total mechanical energy/mass in river water power generation potential of river Governing equations : useful mechanical energy of river water = e = v 2 /2 + g Z power potential = m e assuming zero velocity at lake Density of water = 1000 kg/m 3 Solution : e = 4.5 (m/s) 2 + (9.81 m/s 2 )(90 m) = 887.4 m 2 /s 2 or J/kg = 0.887 kJ/kg mass flow rate = (500 m 3 /s)(1000 kg/m 3 ) = 500,000 kg/s Power generation potential = (0 887 kJ/kg)(500 000 kg/s) = 443 700 kJ/s
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