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macromo_lect_2

# macromo_lect_2 - Macroscopic Momentum Balances Momentum...

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Macroscopic Momentum Balances

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Momentum Which terms can be eliminated? But why? Accumulation = In – Out + {Generation – Consumption} None: Momentum is not necessarily conserved It (momentum) can be generated by forces acting on system It is a vector quantity. Exerted momentum is based on flow direction
Momentum So how is momentum transferred to a system? Bulk Flow Forces on System Shear Stress on Walls Fluid flows easier in center of pipe Friction Gravity

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Momentum Momentum is a vector quantity Must write balances in all three directions
Momentum At Steady State Consumed Generated Output Input - + - = 0 cc c c c Flow Bulk o o o o o o o System on acting Forces

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Momentum Input Output Forces - =
Bulk Flow Momentum Momentum Flow Rate Balance mu M = ( 29 S u u uS 2 ρ ρ = = = u m M a a a b b b a b S u S u M M F 2 2 ρ ρ - = - =

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Why M? Newton’s Law ma F = dt du m = ( 29 dt mu d = dt dM = M F
Forces Acting on Systems Surface Forces Pressure Volume Forces Gravity Force pushing

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