Unformatted text preview: α and the bulk expansion coeﬃcient β for a perfect gas. Problem 8. Reduce the continuity equation for 2D unsteady compressible ﬂow to the one for 2D incompressible ﬂow using the transformation: τ = t, ξ = x, η = Z y ρ ( t,x,y ) d y, (1) and redeﬁning the ycomponent of velocity appropriately. Hint : use the conection operator in your considerations. Problem 9. Consider ﬂuid occupying a halfspace. At its free surface there are a constant pressure p and a constant shear stress T applied. Determine how much time it takes for the velocity at depth z to take its halfvalue of the velocity at the free surface. Calculate the value for water and the depth of 100 m. Give your physical interpretation of the result....
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 Fall '10
 krechet
 Fluid Dynamics, Thermodynamics, τ, 100 m, incompressible viscous ﬂuid, w point

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