The integral method can also be applied to turbulent flow conditions if experimental data for the wall shear stress are available. In one of the earliest attempts to analyze turbulent flow over a flat plate, Ludwig Prandtl proposed in 1921 the following relations for the dimensionless velocity and temperature distributions

From experimental data, an empirical relation relating the shear stress at the wall with boundary layer thickness is

Following the approach outlined in Section 4.9.1 for laminar conditions, substitute the above relations in the boundary layer momentum and energy integral equations and derive equations for: (a) The boundary layer thickness(b) The local friction coefficient, and(c) The local Nusselt number.Assume δ = δt and discuss the limitations of your results.GIVENTurbulent flow over a flat plateVelocity and temperature distributions as given aboveShear stress at the wall as given aboveASSUMPTIONSSteady state conditionsThe hydrodynamic and thermal boundary layer thicknesses areequal

(T- T) (T, - T.) (T,> T>T)