$(16$ pts$)$ Consider the steady state flow of a Newtonian fluid through a porous vertical

cylindrical container shown below. The cylindrical container has a closed bottom. Both the

sides and the bottom of the container are made of a porous material through which the fluid

may flow. The level of liquid is maintained at a constant height, $h,$ above the top of the

container.

Liquid maintained at a

constant level $h$ above

the tod of the container

Porous walls and

$($a$)(4$ pts$)$ List all appropriate assumptions.

$($b$)(2pts)$ Write out the appropriate form of the continuity equation and eliminate all the

terms equal to zero.

$($c$)(10$ pts$)$ Write out the equations of motion for each direction $(z,r,)$ and again eliminate

the terms equal to zero.