For flow of a fluid through a porous medium the equation of continuity is where f is porosity and q is the superficial (Darcy) velocity. The equation of motion is Darcy's law where k is permeability....

For flow of a fluid through a porous medium the equation of continuity is

where f is porosity and q is the superficial (Darcy) velocity.

The equation of motion is Darcy's law

where k is permeability. Define

(gravity in the z-direction).

a. Show by combining the above that the equation of condition for single fluid flow in a porous medium is

b. Show for the flow of an incompressible flow

if k is constant

c. For a compressible liquid

If c_e
is constant and assume gravity is negligible and show

d. For the flow of an ideal gas

Assume gravity is negligible and show