44832_Integral Analysis

44832_Integral Analysis - MASS BALANCE General case: d ∫...

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Unformatted text preview: MASS BALANCE General case: d ∫ ρdV + AoutρvdA − AinρvdA = 0 ∫ ∫ dt CV Incompressible flow: dVC + ∫ vdA − ∫ vdA = 0 dt Aout Ain MOMENTUM BALANCE General case: r r r r r d ∫ ρv dV + Aoutρvv dA − Ainρvv dA = CV ρgdV − AcvnpdA ∫ ∫ ∫ ∫ dt CV To calculate forces in external flows (jets): (FOS…Fluid Over Surface) r r r r r d ρv dV + ∫ ρvv dA − ∫ ρvv dA = ∫ ρgdV − FFOS ∫ dt CV Aout Ain CV To calculate forces in internal flows (bends, y-tubes): r r r r r r r d ρv dV + ∫ ρvv dA − ∫ ρvv dA + ∫ n ( p − p ext )dA + ∫ n ( p − p ext )dA = ∫ ρgdV − FFOS ∫ dt CV Aout Ain Ain Aout CV ( p ext ... pressure acting outside the bend, y-pipe, etc…usually atmospheric pressure) MECHANICAL ENERGY BALANCE d 2 3 3 ∫ ρv dV + Aoutρv dA − Ainρv dA = ∫ ∫ dt CV && ∫ pvdA − ∫ pvdA + ∫ ρφvdA − ∫ ρφvdA + W − E Ain Aout Ain (where φ = −( xg x + yg y + zg z ) ) Aout v ...
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This note was uploaded on 09/06/2011 for the course ASE 13180 taught by Professor Goldstein during the Spring '10 term at University of Texas.

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