Answer :

Solution :

Reynolds Expression for Turbulent Shear stress :

Reynold's through his experiment developed an expression between two layers of a fluid at a small distance apart, which is given as :

${\tau }_t=\rho u^{\prime }{v}^{\prime }$

where u', v' = fluctuating component of velocity in the direction of x and y respectively.

u' and v' are both varying and hence τ will also vary. To calculate τ, time average is done on both sides of the equation.

${\tau }_t=\overline{\rho }{\overline{u}}^{\prime }{\overline{v}}^{\prime }$