For a laminar boundary layer on a flat plate, evaluate the kinetic energy lost between the free stream and any point in the boundary layer. Assume that the boundary layer is linear (see Problem 9.8) and use a control volume so that the flow rate for the oncoming flow and boundary layer are equal. How may this loss of kinetic energy be accounted for?

Data From Problem 9.8

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9.8 Velocity profiles in laminar boundary layers often are approxi- mated by the equations Linear: y 916 Sinusoidal: sin U Parabolic: -2- Compare the shapes of these velocity profiles by plotting y/8 (on the ordinate) versus u/U (on the abscissa).