For a developed turbulent flow, in the near wall region, inertial effects are insignificant and we can write eqn. (9.2) as

(9.3)

which may be integrated as

constant

(9.4)

As we know, the fluctuating components do not exist near the wall, the shear stress on the wall is purely viscous.

It follows

(9.5)

The wall shear stress is estimated as in Couette flow by

(9.6)

where is the fluid velocity at the edge of sublayer. A friction velocity or viscous velocity is defined as

(9.7)

It has been confirmed experimentally that the turbulent intensity distributions are scaled with . For example, maximum value of is always about 8 . The relationship between and can be determined from (9.6) and (9.7) as

(9.7)

Let us assume . We can now write

where is a proportionality constant

or,

(9.8)

A non-dimensional coordinate may be defined as

(9.8)

• The thickness of laminar sublayer, 5
• Turbulent effect starts in the zone, 5
• Laminar and turbulent motions co exist, 5 < 70
• Turbulent core, 70