We consider a flat plate at *y*=0 with a stream with constant speed *U* parallel to the plate. We are interested in the steady state solution. We are not interested in how the flow outside the boundary layer reached the speed *U*. In this case, we need only to consider boundary conditions and the equation (2.18) simplifies since
.
At the plate surface there is no flow across it, which implies that

Due to the viscosity we have the no slip condition at the plate. In other words,

At infinity (outside the boundary layer), away from the plate, we have that

For the flow along a flat plate parallel to the stream velocity

and the appropriate boundary conditions are:

These conditions demand an infinite gradient in speed at the leading edge

If we substitute equations (3.31) and (3.32) into the equation (3.27), we obtain a partial differential equation for , which is given by

and the boundary conditions (3.28) and (3.29) assume the form

The boundary value problem admits a similarity solution. We would like to reduce the partial differential equation (3.33) to an ordinary differential equation. We would like to find a change of variables which allows us to perform the reduction mentioned above.