If represents the pressure-drop between two points at a distance l along x- direction, then Eq. (5.2.14) is expressed as,

(5.2.15)

The average velocity can be calculated as follows;

(5.2.16)

The wall shear stress for this case can also be obtained from the definition of Newtonian fluid;

(5.2.17)

The following silent features may be obtained from the analysis of Couette and Poiseuille flows;

• • The Couette flow is induced by the relative motion between two parallel plates while the Poiseuille flow is a pressure driven flow.

• Both are planner flows and there is a non-zero velocity along x- direction while no velocity in y and z directions.

• The solutions for the both the flows are the exact solutions of Navier-Stokes equation.

• The velocity profile is linear for Couette flow with zero velocity at the lower plate with maximum velocity near to the upper plate.

• The velocity profile is parabolic for Poiseuille flow with zero velocity at the top and bottom plate with maximum velocity in the central line.

• In a Poiseuille flow, the volume flow rate is directly proportional to the pressure gradient and inversely related with the fluid viscosity.

• In a Poiseuille flow, the volume flow rate depends strongly on the cube of gap width.

• In a Poiseuille flow, the maximum velocity is 1.5-times the average velocity.