Consider an incompressible Newtonian fluid, at constant temperature, flowing radially between two porous concentric spheres with inner and outer radii $kR$ and $R.$ The flow is steady and the gravity effect can be neglected. You can assume only $v_r$ exists $(r$ is the radial coordinate$)$ and both $v_{}$ and $v_{}$ are $0.$ Also $v_r$ is a function of $r$ only.

$(1)$ Show that the solution to $v_r$ can be written as $v_r=\frac{c}{r^2},$ where $C$ is a constant.

$(2)$ Simplify the components of the equation of motion to find the equations for del$\frac{p}{d}$elr,del$\frac{p}{d}el$ and del$\frac{p}{d}$elr, where $p$ is the pressure.

$(3)$ Find the pressure distribution for the case that at $r=R$ the pressure is $P_0$ and $V_r=V_0.$