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 δgrows 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 xand 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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