Starting from Navier-stokes equation for incompressible fluid and laminar flow, derive the equation for velocity profile for couette flow. State the assumptions made.

Couette flow:

Assumptions:

i) Fluid is incompressible (S=constant)

ii) The flow is one dimensional (in x-direction)

$\therefore u \ne 0, v=w=0$

iii) The flow is steady $\therefore \frac{\partial u}{\partial t}=0$

iv) The flow is independent of variation in z-direction

v) The body force per unit mass are zero.

$\therefore F_x=F_y=F_z=0$ …