The velocity profile in a turbulent boundary layer flow with zero pressure gradient (over a flat plate, length L) may be approximated by the 1/6-power profile expression, u/U = (y/delta)^1/6.
The wall shear stress can be expressed as tau_w = 0.0233_p U^2 (v/U delta)^1/4. Using the Karman integral
equation, obtain expression for (a) delta/x, (b) C_f for this velocity profile, (c) drag force on the entire flat plate.

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.