In a turbulent pipe flow that is fully developed, the axial velocity profile is, [ u=u_{c}left[1-left(frac{r}{R} ight) ight]^{1 / 7} ] as is illustrated in

In a turbulent pipe flow that is fully developed, the axial velocity profile is,

\[ u=u_{c}\left[1-\left(\frac{r}{R}\right)\right]^{1 / 7} \]

as is illustrated in Fig. P5.68. Compare the axial direction momentum flowrate calculated with the average velocity, \(\bar{u}\), with the axial direction momentum flowrate calculated with the nonuniform velocity distribution taken into account.

Figure P5.68

R -