Question

Using Von Karman momentum integral equation, find the boundary layer thickness, the displacement thickness, the momentum thickness the wall shear stress, the friction coefficient, and the drag coefficient for a flat plate with zero pressure gradient in a laminar flow. Assume a third-order polynomial for the velocity profile. What happens is we add a constant positive pressure gradient?

Answer 1

Kindly check Explanation section.

Step-by-step explanation:

NB: please check the attachment for the solution to: the boundary layer thickness, the displacement thickness, the momentum thickness the wall shear stress, the friction coefficient, and the drag coefficient for a flat plate with zero pressure gradient in a laminar flow.

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So,for the solution the second part of the question that asked us to state;

What happens if we add a constant positive pressure gradient?

SOLUTION: Whenever we have dp/dx > 0 that is a positive pressure gradient then, we are going to have what is known as a divergent flow which makes pressure to increase in the direction of flow. The pressure will be minimum around the centre. Also, as the velocity decreases(velocity gradient becomes negative), the area of flow increases.