The velocity profile of flow in a pipe in the z−direction (Vz) is given by:
Vz = ΔpR2 4μL
1 −
r2 R2 !
where r is the radial component (in cylindrical coordinates), R in this case is the radius of the pipe, L is the length of the pipe, Δp is considered to be a pressure difference between the entrance and exit of the pipe, and μ is something called the dynamic viscosity. Obtain an expression for the mass flow rate through the pipe.