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Table 1.6 Values of laminar boundary‐layer thicknesses for laminar flow over a flat plate.

      Source: Olson and Wright [8].

η	0.0	0.6	1.2	1.8	2.4	3.0	3.6	4.2	4.8	5.4	6.0
δ	0.000	0.200	0.394	0.575	0.729	0.846	0.924	0.967	0.988	0.996	0.999

Table 1.7 Momentum equations for laminar boundary layer.

      Source: Olson and Wright [8].

Velocity profile	δ/x	C f	δ * /x
u/us = y/δ
u/us = 2(y/δ) − (y/δ)2
u/us = 1.5(y/δ) − 0.5(y/δ)3
u/us = sin πy/2δ
Blasius exact solution

Table 1.8 Momentum equations for a turbulent boundary layer for flat plate flow and for pipe flow.

      Source: Olson and Wright [8].

ReD	F	u/us	V/us	C f	Rex
<105		(y/R)1/7	49/60		5 × 105 − 107
104 − 106		(y/R)1/8	128/153		1.8 × 105 − 4.5 × 107
105 − 107		(y/R)1/10	200/231		2.9 × 106 − 5 × 108

Table 1.8 presents additional momentum equations for a boundary turbulent layer along a flat plate, including additional pipe flow velocity profiles, and summarizes the following for a turbulent boundary layer on a flat plate:

       The boundary‐layer thickness increases as the 4/5 power of the distance from the leading edge, as compared with x1/2 for a laminar boundary layer.

       The local and average skin‐friction coefficients vary inversely as the fifth root of both x and us, as compared with the square root for a laminar boundary layer.

       The total drag varies as , and x4/5 as compared with values of corresponding parameters for a laminar boundary layer.

      Initially, as the boundary layer develops, it will be laminar in form. The boundary layer will become turbulent, based on the ratio of inertial and viscous forces acting on the fluid, referring to the value of the Reynolds number. For example, in pipe flow, for the values of Re < 2300 the flow is laminar. If the Reynolds number increases,

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