We know that the Incompressible Navier Stokes equation is as follows,

$ρ[\frac{∂U}{∂t}+(\bar{U}∙∇U)]=-∇P-ρg+[μ∇^2 \bar{U}+\frac{μ}{3} ∇(∇∙\bar{U})]$

For the Steady State flow,

$\frac{∂U}{∂t}=0and∇∙\bar{U}$=0 (Continuity equation for incompressible flows)

$ρ[(U ̅∙∇U)]=-∇P-ρg+[μ∇^2 U ̅ ]$

Couette flow is a viscous laminar flow of a Newtonian fluid between 2 parallel plates separated by gap, in which …