In order to correlate the data for variety of boundary layers under different conditions, a dimensionless profile shape factor is often defined as the ratio of displacement thickness to momentum thickness. For a flat plate laminar boundary layer,

(5.9.19)

Skin friction coefficient : Analogous to friction factor in a duct/pipe flows, a non-dimensional parameter is defined for boundary layer flow as the skin-friction coefficient (Fig. 5.9.4). It relates the shear stress at the wall to the free stream dynamic pressure.

(5.9.20)

From Eqs (5.9.18 & 5.9.20), it is observed that the non-dimensional momentum thickness is identical to the skin friction coefficient. Further, the wall shear stress can be estimated from Eq. 5.9.20.

(5.9.21)

It may be noted here that shear stress decreases with increase in the value of x because of the increase in the boundary layer thickness and decrease in velocity gradient at the wall along the direction of x . Also, varies directly with not as U which is the case for a fully-developed laminar pipe flow.

Fig. 5.9.4: Decay of wall shear stress due to decrease in slope at the wall.