Lecture 17.pptx - Lecture 17 CBE 218 Fluid Mechanics...

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Lecture 17 CBE 218 Fluid Mechanics Feb 25, 2015
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MOMENTUM, VECTORS AND SCALAR COMPONENTS F = m a boldface indicates vector F = F x i + F y j + F z k F x , F y , and F z scalar components of vector F Momentum of a body = (Mass of a body). (velocity of a body) = mV Momentum is vector. I, j and k are called unit vectors in direction of x, y and z. V = V x i + V y j + V z k Chapters 7 and 15
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MOMENTUM BALANCE Flow in Flow out x y z Momentum in – momentum out = V in dm in V out dm out Creation or destruction of momentum, can be written using F = m a = m d V /dt If mass is constant, F .dt = d(m V ) sys
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MOMENTUM BALANCE EQUATION d(m V ) sys = V in dm in V out dm out + ∑ F .dt F = + creation F = - destruction Flow in Flow out x y z Pressure force Gravity force d(m V ) sys /dt = V in dm in /dt – V out dm out /dt + ∑ F d(m V ) sys /dt = V in in V out out + ∑ F
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MOMENTUM BALANCE EQUATION – X, Y AND Z COMPONENTS d(m V ) sys = V in dm in V out dm out + ∑ F .dt d(mVx) sys /dt = Vx in in – Vx out out + ∑ Fx X- component d(mVx) sys = Vx in dm in
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