Question
2. Blood (incompressible fluid of density p and viscosity μ) is flowing at steady state through a cylindrical vessel of radius R and length L under gravity only (no pressure gradient) as shown in the Figure. Use appropriate equation of continuity and Navier-Stokes equation to (a) Deduce the differential equation for the velocity with respect to radius (r) by stating all the conditions, (b) Find an expression for the velocity as a function of r (in terms of the vessel dimension and relevant blood properties) by solving this differential equation (c) Compute the average velocity of the blood. (d) Repeat the problem (for a, b, and c), when the blood vessel inclined at angle ẞ as shown in the figure. 2R 2R
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