## Tzz

Red flow

Hypothetical flow m

Figure 2.10: Displacement thickness in boundary layer

The motivation for using displacement thickness is to permit the use of a displaced body in place of the actual body, such that the frictionless mass flow around the displaced body is the same as the actual mass flow around the real body. Use is made of the displacement thickness in the design of wind tunnels, air intakes for airplane jet engine.

As the boundary layer thickness growth, the fluid is pushed away from the plate, which means that the velocity has also a component in the y direction , vy. we would expect that vy ^ vx because the boundary layer thickness is small compared to any significant body dimension. The boundary layer thickness, that is the value of y for which vx = 0.99v^, can be obtained as following:

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