Lecture 18.pptx

# Lecture 18.pptx - Lecture 18 CBE 218 Fluid Mechanics March...

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Lecture 18 CBE 218 Fluid Mechanics March 2, 2015

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MOMENTUM BALANCE EQUATION – UNSTEADY FLOW AND STEADY FLOW d(mVx) sys /dt = Vx in in – Vx out out + ∑ Fx unsteady flow 0 = Vx in in – Vx out ṁ + ∑ Fx in = ṁ out steady flow 0 = ṁ (Vx in – Vx out ) + ∑ Fx steady flow 0 = ṁ (Vy in – Vy out ) + ∑ Fy steady flow y- component z- component 0 = ṁ (Vz in – Vz out ) + ∑ Fz steady flow
MOMENTUM BALANCE EQUATION – UNSTEADY FLOW AND STEADY FLOW d(mVx) sys /dt = Vx in in – Vx out out + ∑ Fx unsteady flow 0 = Vx in in – Vx out ṁ + ∑ Fx in = ṁ out steady flow 0 = ṁ (Vx in – Vx out ) + ∑ Fx steady flow 0 = ṁ (Vy in – Vy out ) + ∑ Fy steady flow y- component z- component 0 = ṁ (Vz in – Vz out ) + ∑ Fz steady flow

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MULTIDIMENSIONAL FLOWS –MASS BALANCE Vx Vz Vy y x z 1 2 5 6 3 4 Accumulation rate of mass in system = all mass flow rate in – all mass flow rate out x y z d  dt  y z ( .Vx 1 .Vx 2 ) + x z ( .Vy 3
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