Average flow velocity in turbulent tube flow. 

(a) For the turbulent flow in smooth circular tubes, the function 1 is sometimes useful for curve-fitting purposes: near Re = 4 x 10³, n = 6; near Re = 1.1 x 10⁵, n = 7; and near Re = 3.2 x 10⁶, n = 10. Show that the ratio of average to maximum velocity is and verify the result in Eq. 5.1-5. 

(b) Sketch the logarithmic profile in Eq. 5.3-4 as a function of r when applied to a circular tube of radius R. Then show how this function may be integrated over the tube cross section to get Eq. 5.5-1. List all the assumptions that have been made to get this result.

Part (a) 1/1 Uz,max Part (b) 2n? (;) ) (n + 1)(2n + 1) Vz,max