Let us consider a fully developed channel flow, without loss of generality

Assumption: All derivatives with respect to x are zero except

Mean velocity field

The averaged NS equations give

	(18.1)
	(18.2)

Integrating 2 between 0 and y , with no-slip boundary condition, we get

(18.3)

Thus

(18.4)

also,

From (18.1) and (18.4)

(18.5)

Integrating (18.5) between 0 and y , we get

	(18.6)
Set

Where, is the friction velocity. The equation (18.6) becomes

(18.7)

At y =h , at the center of the channel, due to symmetry,

Thus from (18.7), we get

Equation (18.7) becomes

(18.8)

put

Now equation (18.8) reads as

(18.9)

Where