GIVEN A thin rectangular plate having a width w and a height h is located so that it is normal to a moving stream of fluid as shown in Fig. E7.1. Assume the drag, D, that the fluid exerts on the plate is a function of w and h, the fluid viscosity and density, u and p, respectively, and the velocity V of the fluid approaching the plate. V7.2 Flow past a flat plate V P.H IFIGURE E7.1 FIND Determine a suitable set of pi terms to study this prob- lem experimentally. 18

D

Some engineers want a good estimate of drag and boundary-layerthickness at the trailing edge of a miniature wing. The chord and span ofthe wing are 6 mm and 30 mm, respectively and a typical flight speed is5 m/s in air (kinematic viscosity = 15 × 10−6 m2/s; density = 1.2kg/m3). An engineer may decide to make a superseding model withchord and span of 150 mm and 750 mm, respectively. Measurements onthe model in a water channel flowing at 0.5 m/s (kinematic viscosity = 1× 10−6 m2/s, density = 1000 kg/m3) give a drag of 0.19 N and aboundary-layer thickness of 3 mm. Estimate the corresponding values forthe prototype

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.

Air flows across a thin airfoil at a velocity of 90 m/s. For the same Reynolds number based on the actual chord length, L = 1.40 m, what velocity of water is required for a 1/2 scale model test? Assume a temperature of 15°C for both fluids. air U = 90 m/s L = 1.40 m