Consider fully developed Couette flow—flow between two infinite parallel plates separated by distance h, with thetop plate moving and the bottom plate stationary as illustrated in Fig. P7–56. The flow is steady, incompressible, and two-dimensional in the xy-plane. Use the method of repeating variables to generate a dimensionless relationship for the xcomponent of fluid velocity u as a function of fluid viscosity μ, top plate speed V, distance h, fluid density rho, anddistance γ, Show all your work.

Two microscope slides are placed horizontally, one on top of the other, with a drop of a dishwashing liquid between them. the gap between the slides is 1 mm. a machine pulls the top slide to the right with a velocity of 0.15 millimeters per second while the bottom slide is held stationary. a stress gage indicates that a shearing stress of 0.5 pa is required to pull the top slide with this velocity. if the dishwashing liquid adheres to both slides during this process, what is the viscosity of the liquid? specify whether your answer is dynamic or kinematic viscosity, and use appropriate units.