Steady-State Momentum Force Balance Equation

4 Steady-State Momentum (Force) Balance Equation 

Rate of input of momentum Rate of output of momentum + Rate of generation of momentum Rate of accumulation of momentum 

As momentum is a vector, the steady-state momentum equation above is a vector equation and, in general, needs to be applied in each of the three directions (x, y, z) in which momentum (i.e. velocity) has a 

As the rate of momentum transfer is equal to a force, momentum balances are equivalent to force balances. 

The generation term is equal to ZE. the sum of forces acting on the control volume, which is comprised of the three following terms  

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Shell Momentum Balance for Flow Down an Inclined Plane. Consider the case of a Newtonian fluid in steady-state laminar flow down an inclined plane surface that makes an angle 6 with the horizontal. Using a shell momentum balance, find the equation for the velocity profile within the liquid layer having a thickness L and the maximum velocity of the free surface. Hint The convective momentum terms cancel for fully developed flow and the pressure-force terms also cancel, because of the presence of a free surface. Note that there is a gravity force on the fluid.)... 

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