Integral_flat_plate - Control Volume Example: Flat Plate...

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Control Volume Example: Flat Plate Boundary Layer Author: John M. Cimbala, Penn State University Latest revision: 20 September 2007 Given : Consider flow over a two-dimensional flat plate. The freestream flow upstream of the plate is steady, uniform, and incompressible, with pressure p and velocity U in the x -direction as shown. A boundary layer of thickness δ grows along the top and bottom sides of the plate. (Only the top boundary layer is shown in the sketch.) The boundary layer velocity profile is shown at some x -location along the plate. x x = boundary layer thickness U , p U , p y To do : Calculate the drag per unit depth, D ( x )/ b , on one side of the plate (for a plate of length x and depth b ). Solution : First pick a control volume. There are several choices - let’s pick the simplest one, as sketched below. There are 6 surfaces which define the closed control surface. Namely, surface I is a vertical plane just upstream of the leading edge of the plate. Surface II is a vertical plane at location x .
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