a) Estimate the drag force on the plate. You may use the expression ?? = ∫ τ?d? b) When the flow becomes turbulent, we can approximate the velocity gradient at the wall as constant, ∂? ∂? = ?. If the total drag force is 300 N, find ?. c) When the fluid is heated to 90oC, the density drops slightly and the viscosity decreases a lot, and engineers observe that the equation, τ? = 0.0644??∞ 2 δ ? , becomes less accurate. Explain why this might occur (1-2 sentences)

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.

Q2: A) Assuming linear variation of velocity in the boundary layer i.e. (u/u) =(y/6), up to y= 8 and then u = u, determine using the integral momentum equation, the boundary layer thickness. B) The temperature ratio: [T,-T)/(T, -T)] = sin (zy/0.015) in flow over a flat plate. If k = 0.03 W/m.K, determine the value of convective heat transfer coefficient.