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Problem 6 An incompressible fluid ( density and viscosity ) flows steadily in the annular region between two stationary, concentric cylinders under an applied pressure

Problem 6
An incompressible fluid (density and viscosity ) flows steadily in the annular region between two stationary, concentric cylinders under an applied pressure difference, as shown. The inner cylinder has radius R1 and the outer cylinder has inner radius R2. The concentric cylinders have length L. On the upstream side the pressure is P1 and on the downstream side it is P2. Assume that the flow is laminar and fully developed over the entire length. Neglect gravitational forces.
Cross-section view
a) Sketch the velocity profile, vz(r), and identify important features.
b) Derive an expression for the velocity profile, vz(r), in terms of P1,P2,R1,R2,L,,, and r.
c) Calculate the average flow speed, V, for the case where P1=2kPa,P2=0Pa,R1=3cm,R2=6cm,L=10m,=1000kgm3, and =0.001Pas.
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