ON THE IMPULSIVE MOTION OF A FLAT PLATE IN A VISCOUS FLUID

The motion in the boundary layer which arises when a semi-infinite flat plate is impulsively started from rest with velociyt U is investigated. It is found that the velocity field is independent of x, the distance along the plate if Ut<x, and at Ut=x the flow has an essential singularity, thereafter depending on x as well as x as well as t. As t→∞ the influence of t is shown to die out exponentially. Solutions are also obtained using two approximate methods and they both agree in requiring the velocity to be independent of x for a finite time. The same problem is also solved for a compressible fluid. It is found that in this case the outflow is increased and this may lead to the formation of two compression waves.