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  3. problem 3 consider the steady flow of a viscous incompressible...

Question: problem 3 consider the steady flow of a viscous incompressible...

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Problem 3 Consider the steady flow of a viscous incompressible fluid in an infinitely long two-dimensional stationary channel of height h with negligible body forces - see Fig. 2. This is called Pois- seuille flow. The flow is fully developed such that the fluid velocity has no dependence on x and has a constant viscosity μ. A constant pressure gradient-dp/dz in the axial direction maintains the fluid flow. Figure 2: Poisseuille flow (a) Starting with the full continuity and momentum equations, show that the velocity profile between the two plates is given by: du 1 dp dr =-- (b) Find the velocity and shear stress distribution in the fluid (c) Find an expression for the average velocity in the channel consistent with the mass flux

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