2. Air at 40 °C moves over a long flat plate with a uniform free stream velocity of U = 900 m/s. Assume the boundary layer formed above the surface of the plate starts at the tip of the leading edge and the velocity profile inside the boundary layer has power-law form as Re, <107 {8 10’ < Re, < 10* 9 10* < Re, <10° 7 ,for u Sx

Question 2 a) A laminar boundary layer profile may be assumed to be approximately of the form u/Ue = f (n)=f(y/8) i) Use an integral analysis with the following two-segment velocity profile, ƒ (n)=(n/6)(10–3n−n³), for 0≤n≤0.293 and ƒ (n) = sin(лn/2) for 0.293≤ŋ≤1, to find expressions for the displacement thickness &*, the momentum thickness 0, the shape factor H, the skin-friction coefficient of, and the drag coefficient CD. ii) Derive an expression for the velocity normal to the stream wise direction given that, u/U₂ = f(n). iii) Hence obtain the velocity normal to the stream wise direction for the above two- segment velocity profile.

(b) A smooth thin plate 10 m long and 1 m wide is placed in an air stream at 3 m/s with its length parallel with the flow. Determine the total drag force acting on the plate if the air temperature is 30°C. (c) Based on question Q4(b), determine the total drag force acting on the thin plate if the length of the plate is 3 m long and the air stream velocity is 1 m/s.

Air at 20⁰c and 1 ATM flows over a flat plate, v= 35 m/s. The plate is 75 cm long and guarded at 60⁰c. Suppose the depth of one Units on Z, count the transfer of Calor from that plate.

A ship 200 f t long with a wetted area of 5000 ft2 moves at 25 ft/s. Find the friction drag, assuming that the ship surface may be modeled as a flat plate, and ρ = 1.94 slugs/ft3 and ν = 1.2 × 10−5 ft2/s. What is the minimum power required to move the ship at this speed?  

The shock waves on a vehicle in supersonic flight cause a component ofdrag called supersonic wave drag Dw. Define the wave-drag coefficient asCD,w = Dw/q∞S, where S is a suitable reference area for the body. Insupersonic flight, the flow is governed in part by its thermodynamicproperties, given by the specific heats at constant pressure cp and atconstant volume cv. Define the ratio cp/cv ≡ γ . Using Buckingham’spi theorem, show that CD,w = f (M∞, γ ). Neglect the influence of friction.