A flat plate with sharp leading edge is placed in the test section of a low-speed wind tunnel. The working section of the wind tunnel has been designed to produce a region of constant free stream velocity (i.e., for x < 1.0 m, U, = 27.0 m/s), followed by a region of decelerating flow (i.e., for x 2 1.0, U. = A'(1 – m/s, Figure Q1. %3D Wind Tunnel Wal yU. = 27.0.for zS 10m U. m/s, for x2 1.0 m For 1.0m Flat Plate Figure Q1 U, is the freestream air velocity, x is the streamwise position in meter, L,ref is a reference length equal to 10 m and x = 0 corresponds to the leading edge of the flat plate. 1- Determine the constant A and its dimension.

2. The table below shows experimental data for the shape and pressure distribution on the upper and lower surface of an airfoil at zero angle of attack. X 0 0.25 0.5 0.75 1 Yu 0 0.0952 0.0922 0.0588 0 Fx = dYu dx 5 Y₁ 0 -0.0254 -0.0144 -0.0052 0 PL Pd) d: dx Y = Yu (x) Calculate the drag and lift force on the airfoil by numerically evaluating the integrals = S₁² ( P₂₁ = ['(P₁ - F (P₁ - Pu)dx 0 y = Y₂ (x) Pu 1.000 -1.640 -0.786 -0.212 0 Fy x Pi 1.000 0.589 0.426 0.322 0 Use finite difference approximations of the derivatives and the composite Simpson's rule to evaluate the integrals. Hint: Use central differences to estimate the derivatives wherever possible since they are more accurate than forward or backward differences.

A ship 50 m long, with a wetted area of 800 m2, has the hullshape tested in Fig. There are no bow or stern bulbs.The total propulsive power available is 1 MW. For seawaterat 20°C, plot the ship’s velocity V kn versus power Pfor 0 < P <1 MW. What is the most efficient setting?

A simple parallel flow with constant velocity shear σ is given byu = σy v = w = 0 Evaluate the five components of motion (e.g. translation, divergence, vorticity,shearing and stretching deformation.)