Consider the case of channel flow where the top plate at \(y=H\) is moving at a velocity of \(U_{1}\) and the bottom plate at \(y=0\) is moving with a velocity of \(U_{0}\). We also impose a pressure gradient in the system. Show that the velocity profile is given by

and that the volumetric flow rate per unit width of the channel, \(Q / W\), is

Transcribed Image Text:

= 11 2 y(H y) + U + (U - U) (6.88)