Consider the laminar flow of an incompressible fluid over a flat plate at y-0.

Asap write correct solution

4. Consider fully developed laminar flow in the annular space formed by two concentric cylinders with a pressure gradient, op/ax, and the inner cylinder stationary. Let r = Rand r = kR. Assuming that the velocity profile is given by u: [¹-( 7 )² + +(ma 1 R R² ap 4μ &x 1-k² In- In(1/k) R a) Obtain an expression for the location of the maximum velocity as a function of k. b) Compare the limiting case, k→ 0,with the corresponding expression for flow in a circular pipe. c) Determine the volume flow rate. d) Find an expression for the average velocity. e) Compare the limiting cases for the volume flow rate and average velocity, k →0, with the corresponding expression for flow in a circular pipe.

An incompressible fluid flows steadily in the entrance region of a two dimensional channel of height 2h. Density of the fluid is 1.24 kg/m3. The uniform velocity at the channel entrance is U1=6.1m/s. The velocity distribution at a section downstream is: