Lecture 10 The Bernoulli Equation

Lecture 10 The Bernoulli Equation - Thermal and Fluids...

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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski Lecture 10 – The Bernoulli Equation and Flow Measurement The Bernoulli Equation The first law for an open system is 22 cv i e cv cv i i i e e e dE QW m h g z mh g z dt ⎛⎞ =−+ + + − + + ⎜⎟ ⎝⎠ ∑∑ ± ± ±± VV Apply this equation to a particular type of flow - steady - one inlet and one exit - adiabatic - isothermal - inviscid (frictionless) - incompressible (constant density) - no work For a steady flow entering at station 1 and exiting at station 2 12 11 2 0 cv cv Q W g z g z ± ± 2 By definition, huP v =+ 1 1 2 2 2 2 0 cv cv QWm uP v g z m v g z ++ + − + + + ± ± For an adiabatic flow with no work Lecture 10 Page 1
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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski 22 12 11 1 1 2 2 2 2 0 uP v g z v g z ⎛⎞ =+++−+++ ⎜⎟ ⎝⎠ VV By definition, 1 v ρ = Using this definition and noting that the flow is incompressible, (density is constant): 2 0 PP ug z u ρρ =++ + −++ + 2 g z We also assume the flow is isothermal and uu = The Bernoulli equation is gz gz ++=++ When is a flow inviscid?
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This note was uploaded on 04/06/2009 for the course ENGR 2250 taught by Professor Borca-tasciuc during the Spring '08 term at Rensselaer Polytechnic Institute.

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Lecture 10 The Bernoulli Equation - Thermal and Fluids...

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