Before we proceed further, we require to find the governing equations for free shear flows.

In the fully developed turbulent flow, the y-momentum equation may be written as

(19.5)

Integration across the shear layer yields

(19.6)

where is the pressure in the outer flow. The result is similar to the channel flow described in Letuure-18. Differentiating (19.6) with respect to x gives

(19.7)

Substituting (19.7) into the steady (time-averaged) mean x-momentum equation, yields

(19.8)

Now if we apply the scaling analysis and ignore the viscous stresses in the presence of much higher turbulent stresses, the equation (19.8) reduces to

(19.9)

While deriving Eqn. (19.9) the turbulence has been considered as isotropic .

Eqn. (19.9) is the governing equation for all free shear flows. Turbulent jet is a class of free shear flows.