The results of Example 4.4 showed that the aerodynamic force on a body is proportional to the square of the free-stream velocity. This is strictly true, however, only when the aerodynamic force is due to the pressure exerted on the surface and when the flow is incompressible. When the aerodynamic force is also due to the distribution of frictional shear stress over the surface and or the flow is compressible, the “velocity squared” law does not strictly hold. The purpose of this problem is to examine how the friction drag on a body varies with free-stream velocity for an incompressible flow.
Consider a square flat plate at zero incidence angle to a low-speed incompressible flow. The length of each side is 4 m. Assume that the transition Reynolds number is 5 × 105 and that the free-stream properties are those at standard sea level. Calculate the friction drag on the flat plate when the free-stream velocity is (a) 20 m/s and when it is (b) 40 m/s. (c) Assuming that the friction drag, Df, varies with velocity as Vn∞, calculate the value of the exponent n based on the answers from (a) and (b). How close does n come to 2? That is, how close is the friction drag to obeying the velocity squared law?
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