For turbulent flow in a smooth, circular tube with a radius R, the velocity profile varies according to the following expression at a Reynolds number of 105: = 56.(1 − ⁄)A/C, where r is the radial distance from the center and 56. the maximum velocity at the center. Show that, for an incompressible fluid, the average velocity 68 is related to 56. through: 68 = (49⁄60)56.. If the fluid is water at 25 ℃ flowing through a 30 cm-diameter steel pipe, calculate: (i) 56., (ii) the mass velocity, (iii) the volumetric flow rate, and (iv) the mass flow rate.