Question

: derive an expression for momentum transfer equation for flow over flat plate

Answer 1

Consider the 2D continuity equation and integrate over the height of the boundary layer

(25.1)

(25.2)

Note that the velocity at the wall is zero and at the edge of the boundary layer is the free stream

value

Momentum Equation-Derivation-2

Now, consider the momentum equation.

(25.3)

Integrate this over the thickness of the boundary layer

(25.4)

Momentum Equation-Derivation-3

Perform the integration for equn (25.4):

(25.5)

Simplify equn (25.5) using equn (25.2), velocity is zero at wall and the velocity gradient is zero

for free stream at y = δ and replace pressure gradient with free stream velocity gradient.

Momentum Equation-Derivation-4

The equn (25.5) therefore becomes: