Consider the fluid flow between two large plates at a distance L from each other. While the top plate is motionless and insulated from these plates, the bottom plate moves with a constant velocity V. It moves and is kept at temperature T0. General continuity, momentum and energy equations, simplifying these equations and solving for each separately Obtain a relation for the temperature of the fluid. In addition, the maximum Find where the temperature is formed and find its value

4) A constriction in a pipe will cause the velocity to rise and the pressure to fall at section 2 in the throat. The pressure difference is a measure of the flow rate through the pipe. The smoothly necked-down system shown in Figure is called a venturi tube. Find an expression for the mass flux in the tube as a function of the pressure change. (1) HGL 4²² (2)

A Newtonian fluid is flowing in the narrow gap between two infinite parallel horizontal plates due to the movement of the top plate (see the figure below). The top plate is moving at a speed U from left to right, and the bottom plate is stationary. Consider the flow is steady, incompressible, and laminar. The distance between two plate is H, and the gravity acts in negative z-direction (which is perpendicular into the page). There is an applied constant pressure gradient of apJəx in the x-direction. Calculate the velocity and pressure fields. Plot typical velocity profiles in dimensionless form for a pressure gradient value of 0 and -15. In your solution show the conceptual diagram of the problem; write all relevant assumptions and boundary conditions; show the detailed steps of the problem solutions including equations and detailed processing of those equations. Moving plate Fluid: p.H Fixed plate P2-P1

g Figure 3: Fluid flows between two infinite plates A viscous, incompressible steady fluid flows between two infinite, vertical, parallel plates distance h apart, as shown in Figure 3. Use the given coordinates system and assume that the flow is laminar, fully developed (30), and planar (w = 0,0). Assume that pressure and gravity are not negligible. (a) Simplify the contnuity equation and show that v = 0. (b) Using the y-momentum equation show that pressure is a function of a only. (c) Find the velocity distribution u(y) in terms of u, g, h, p and d (d) Find the wall shear stress of the flow.

For a flow in the xy plane, the x component of the velocity is u=3x2y-y3is given. Determine the y component for steady state and incompressible flow. Does this result also apply to unstable, incompressible flow? Why is that? How many possible y components are there? Discuss.

THREE DIMENSIONAL ( NEED NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE).