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.