The distance between the two stationary parallel plates of a fluid is h. Both plates have width W and length L. The fluid between the plates has a density of ρ and viscosity of μ. Suddenly a force Fy is applied to the upper plate and it moves in the y-direction with a constant velocity of ?௛. Derive the velocity profile equation that indicates velocity is a function of vertical distance z.

Transport Phenomena Question

4. Consider two-dimensional, laminar, unidirectional flow between parallel (spacing: 2h), vertical plates. One plate, to the left, is moving downward with constant velocity vi; the other is moving upward at a constant velocity v2. If we consider the fluid Newtonian, solve for the velocity profile using our newly defined Navier-Stokes Eqns.

Please state clearly the answer for a

consider the fully developed laminar flow of a newtonian fluid at steady state in the annulus between two concentric horizontal pipes. derive an equation for the velocity profile if the outer pipe has a radius of r2 and inner pipe r1. derive an equation for vmax

please solve b and shows the steps

Consider an incompressible 2D flow with stream function Y = xy + y³. Determine (a) the velocity at point (3,5). (b) the flow rate per depth for a curved segment y + x² = 4 in the second quadrant.

Consider the following system where the fluid is moving upward in an annulus of height L using cylindrical coordinates

1. An incompressible fluid of kinematic viscosity v = μ/p= 10-4 m²/s flows steadily through a circular pipe of diameter d = 10 cm. The pipe flow is fully developed. Friction Factor If the average velocity V is 2 m/s, is the flow laminar or turbulent? What is the value of the friction factor, f? If the pipe is perfectly smooth on its internal surface and V is 20 m/s, the pipe flow is turbulent (double check yourself). Evaluate its friction factor using the Moody chart below. Repeat (c) by numerically solving the Colebrook formula (using, for example, Matlab). Attach the source code you used. Suppose that the pipe internal surface is rough. Also suppose that increasing V up to 200 m/s yields no change in the value of f found in (a). Determine the relative roughness, e/d, using the Colebrook formula. 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.015 0.01 Laminar Flow 64 Material Concrete, coarse Concrete, new smooth Drawn tubing Glass, Plastic Perspex Iron, cast Sewers, old Steel, mortar…

A Newtonian fluid with constant density flows in a parallel-plate apparatus that separated by a distance d and length L as shown in Figure 1. The top plate is moving in z-direction with a velocity uw. Derive the velocity distribution of the fluid, vz as a function of y using equation of motion in Appendix 1. List the postulates and you may neglect the gravity force.