Average flow velocity in turbulent tube flow. (a) For the turbulent flow in smooth circular tubes, the function 1 vz,maxvz=(1Rr)1 is sometimes useful for curve-fitting purposes: near Re=4103,n=6; near Re=1.1105, n=7; and near Re=3.2106,n=10. Show that the ratio of average to maximum velocity is vz,maxvz=(n+1)(2n+1)2n2 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. vvz=2.5ln(Rv)+1.75 Average flow velocity in turbulent tube flow. (a) For the turbulent flow in smooth circular tubes, the function 1 vz,maxvz=(1Rr)1 is sometimes useful for curve-fitting purposes: near Re=4103,n=6; near Re=1.1105, n=7; and near Re=3.2106,n=10. Show that the ratio of average to maximum velocity is vz,maxvz=(n+1)(2n+1)2n2 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. vvz=2.5ln(Rv)+1.75