The velocity profile for turbulent flow in circular pipes is often approximated by the 1/7thpower law: vz = vmax(1 − r/R) 1/7 Find an expression for the cross-sectionally averaged velocity

The velocity profile for turbulent flow in circular pipes is often approximated by the 1/7thpower law: vz = vmax(1 − r/R) 1/7 Find an expression for the cross-sectionally averaged velocity. A more general expression for the velocity profile is vz = vmax(1 − r/R) 1/n where n is an index that is fitted as a function of the Reynolds number. The value of n increases with Re, indicating that the profiles becomes steeper at large values of Re. Find an expression for the average velocity for this general profile. Answer: 2n2/[(n+1)(2n+1)] for the ratio of average to maximum velocity. Use the above velocity profile and the Prandlt equation for the eddy viscosity and plot the eddy viscosity as a function of the radial location.