Reynolds show that the exchange of transverse momentum due to velocity fluctuation causes a tangential force between the adjacent layers. He developed an expression for turbulent shear stress between than adjacent layer, is given by


Where u’ and v’ = fluctuating component of velocity in x and y direction due to turbulence

The shear stress will be vary as the fluctuating component of velocity are vary. Hence usually the time average value of shear stress is stress is considered. Bt taking time average on both sides of the equation. The equation becomes as,

-      _____
τ  =  ρ u' v'

The shear stress by turbulence given by equation is called as Reynold’s stress.

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