Consider an incompressible fluid, at constant temperature, flowing radially between two porous cylindrical shells with inner and outer radii kR and R.

(a) Show that the equation of continuity leads to V _r = C/r where C/r a constant.

(b) Simplify the components of the equation of motion to obtain the following expressions for the modified pressure distribution:

dp/dr = -pV _r (dV _r /dr), dp/dθ =0, dp/dz = 0

The equation of Change for Isothermal systems

(c) Integrate the expression for dp/ dr above to get.

P(r) - P(R) = 1/2 p(v _r (R) ² [(1- (R/r) ² ]

(d) Write out all the nonzero components of τ for this flow

(e) Repeat the problem for concentric spheres.

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