Fluid fills the space between two parallel plates. The differential equation that describes instantaneous fluid velocity for unsteady flow with the fluid moving parallel to the walls is

rho. ζu/ζx = μ. ζ^2 u/ζy^2

The lower plate is stationary and the upper plate oscillates in the x-direction with a frequency ω and an amplitude in the plate velocity of U. Use the characteristic dimensions to normalize the differential equation and obtain the dimensionless groups that characterize the flow.