Air at 15°C flows at 10 m/s over a flat plate of length 3 m. Using one-seventh power law of the turbulent flow, what is the ratio of local skin friction coefficient for the turbulent and laminar flow cases? (The kinematic viscosity of air is 1.470 × 10−5 m2/s.) (a) 4.25 (b) 5.72 (c) 6.31 (d ) 7.29 (e) 8.54

Please write down a related Average Nusselt number equation for each case. (Do not calculate) Laminar flow SCHEMATIC: Air 4∞ = 2 m/s Top = 25°C p = 1 atm w= 0.2 m L=25 AL 0.25 m T = 500 °C ASSUMPTIONS: (1) Top surface is smooth, (2) Bottom surface is adiabatic, (3) Critical Reynolds number is 5 × 105, (4) Negligible radiation.

Evaluate the boundary-layer shape factor, H.

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.

8- Air (p = 1.21 kg/m') flows over a thin flat plate 1 m long and 0.3 m wide. The flow is uniform at the leading edge of the plate. Assume the velocity profile in the boundary layer is linear, and the free stream velocity is 2.7 m/s. Using control volume (abcd) shown in figure, compute the mass flow rate across surface (ab). Determine the magnitude and direction of the x- component of the force required to hold plate stationary. [3.9×10 kg/s ; -3.5x10 N]