# lecture 10 - Thermal and Fluids Engineering I Lecture 10...

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Thermal and Fluids Engineering I Lecture 10 Page 1 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 Q W m h gz m h gz 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 2 0 cv cv Q W mh g z g z + + + + & & By definition, huP v =+ 1 1 2 2 2 2 0 cv cv mu P v g z mu Pv g z = + + ++ +++ & & For an adiabatic flow with no work

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Thermal and Fluids Engineering I Lecture 10 Page 2 22 12 11 1 1 2 2 2 2 0 uP v g z u P v g z ⎛⎞ =+ + + −+ + + ⎜⎟ ⎝⎠ VV By definition, 1 v ρ = Using this definition and noting that the flow is incompressible, (density is constant): 2 2 2 2 0 PP ug z u g z ρρ = + ++ + We also assume the flow is isothermal and uu = The Bernoulli equation is 2 2 gz gz = When is a flow inviscid?
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## This note was uploaded on 04/08/2008 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 - Thermal and Fluids Engineering I Lecture 10...

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