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Unformatted text preview: Energy Conservation (Bernoullis Equation) 2 1 2 1 2 1 = + + gdz VdV dp Integration of Eulers equation Bernoullis equation 2 2 2 2 1 2 1 1 2 2 gz V p gz V p + + = + + Flow work + kinetic energy + potential energy = constant p A x Under the action of the pressure, the fluid element moves a distance x within time t The work done per unit time W/ t (flow power) is rate flow mass unit per done work 1 , = = = = = t W AV p P AV t x A p t x pA t W Energy Conservation (cont.) t) unit weigh per (energy g where , 2 2 2 2 2 2 1 2 1 1 = + + = + + z g V p z g V p It is valid for incompressible fluids, steady flow along a streamline, no energy loss due to friction, no heat transfer. Examples: Determine the velocity and mass flow rate of efflux from the circular hole (0.1 m dia.) at the bottom of the water tank (at this instant). The tank is open to the atmosphere and H=4 m H 1 2 p 1 = p 2 , V 1 =0 ) / ( 5 . 69 ) 85 . 8 ( ) 1 . ( 4 * 1000 ) / ( 85 . 8 4 * 8 . 9 * 2 2 ) ( 2 2 2 1 2 s kg AV m s m gH z z g V = = = = = = = Energy Equation(cont.) Example: If the tank has a crosssectional area of 1 m 2 , estimate the time required to drain the tank to level 2....
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 Fall '08
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 Mechanical Engineering

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