308-26-28 - NCSU MAE308 26 Identify the physical...

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NCSU MAE308 26. Identify the physical significance of each of the following four terms in the steady two- dimensional form of the Navier-Stokes equations as labelled: 1 2 3 4 ρ u u x + v u y = - P x + μ 2 u x 2 + 2 u y 2 + X { { ρ u v x + v v y = - P y + μ 2 v x 2 + 2 v y 2 + Y { { 1=inertial forces 2=pressure forces 3=viscous forces 4=external body forces 27. Steady, incompressible laminar flow between two-stationary, infinite parallel plates is called Poiseuille flow . The plates are infinite in the x and z directions. Neglect body forces. (a) Write the three-dimensional form of the conservation of mass equation and reduce this equation for the flow considered. (b) Write the three components of the Navier-Stokes equation and reduce these equations for the flow considered. Determine the velocity profile u(y). Note that, unlike Couette flow, fluid motion between the plates is now sustained by a finite pressure gradient.
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