The fluid moving along a flat plate gradually slows, as shown in Example 9.3-1. That deceleration creates a positive v_y at the outer edge of the boundary layer. It is desired to compare the average value of that normal velocity (V) with the approach or free-stream velocity (U). The control volume that is suggested is shown by the dashed rectangle in Fig. P9.11, in which h > δ(x).

It is found from the similarity solution that (Jones and Watson, 1963, p. 224)

Use this to evaluate V⁄U and plot the result as a function of Re for 10² ≤ Re ≤ 10⁶. Your results should confirm that V⁄U is quite small when Re is large enough for there to be a boundary layer.

Transcribed Image Text:

U - tv 8(x) y=h y=0 X=0 X=L Figure P9.11 Control volume for calculating V, the average velocity normal to a flat plate of length L with free-stream velocity U. The height h exceeds the boundary layer thickness 8(x).