There is fluid film with thickness of h between two flat plates. The upper plate moves to the right at speed of U. The lower plate is stationary.

a. Find the velocity profile for flow between flat plates. Use Navier-Stokes equations. Provide a detailed solution. Specify all simplifying assumptions that you make, and clarify how each assumption simplifies the problem.
b. Draw the velocity profile for dp/dx = -5 Pa/m
c. Draw the velocity profile for dp/dx = +5 Pa/m

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Water at 55c flows across a flat plate whose surface temperature is held constant at 95c. if the temperature gradient at the plate's surface for a given value of x is 18 c/mm, find a) local heat transfer coefficient. b) heat flux

Prove the equivalence between the two statements of the 2nd law of thermodynamics (i.e., a violation of one statement leads to the violatio the other statement)