An incompressible fluid is flowing at steady state in the annular region (i.e., torus or ring between two concentric cylinders). The coaxial cylinders have an outside radius of R and inner radius of &R. Find: (a) Shear stress profile (b) Velocity profile (c) Maximum and average velocities

5. Consider the problem of laminar, unidirectional flow in a pipe of radius a. Using the Navier- Stokes Equations: Solve for the velocity profile, u(r), in the pipe Calculate the maximum and bulk velocity (umax, ub) for this flow

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

a) (i) What are a Newtonian fluid and a -Newtonian fluid? Classify pendent non-Newtonian fluids and illustrate - flow time- behaviours in a diagram g. shear stress vs. shear (ii) across a flat plate and the s with the aid of a schematic diagram. Explain boundary concept for a flow

A horizontal 10-cm-diameter jet of water strikes a vertical plate. Determine the velocity issuing from the jet if a force of 1000N is needed to:  (1) Hold the plate stationary (2) Move the plate away from the jet at 10 m/s (3) Move the plate into the jet at 10 m/s

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.

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