Combined Couette - Poiseuille Flow between Parallel Plates

Another simple planner flow can be developed by imposing a pressure gradient between a fixed and moving plate as shown in Fig. 5.3.1. Let the upper plate moves with constant velocity and a constant pressure gradient is maintained along the direction of the flow.

Fig. 5.3.1: Schematic representation of a combined Couette-Poiseuille flow.

The Navier-Stokes equation and its solution will be same as that of Poiseuille flow while the boundary conditions will change in this case;

(5.3.1)

The constants can be found with two boundary conditions at the upper plate and lower plate;

(5.3.2)

After substitution of the constants, the general solution for Eq. (5.3.2) can be obtained;

(5.3.3)