A viscous, incompressible fluid flows steadily along a flat, horizontal plate due to a constant pressure gradient applied in the x$-$direction. The flow is one$-$dimensional, fully developed, and steady. The velocity of the fluid depends only on the distance from the plate surface, y$,$ and is denoted by v$($y$).$ The fluid density

is $\backslash$rho $,$ and the dynamic viscosity is $\backslash$mu $.$ The governing Navier$-$Stokes equation for

the velocity field v$($y$)$ is:

$$

$2$

$2$

$=$

$$

$($a$)$ After applying the dimensionless variables, derive the dimensionless form of

the Navier$-$Stokes equation: $[=$

$\backslash$infty

$,=$

$$

$($b$)$ Identify any dimensionless parameters that govern the flow.