Water flows vertically upward in a circular cross-sectional pipe as shown in Fig. P5.12R...

Water flows vertically upward in a circular cross-sectional pipe as shown in Fig. P5.12R. At section (1), the velocity profile over the cross-sectional area is uniform. At section (2), the velocity profile is

where v =local velocity vector,wc = centerline velocity in the axial direction, R = pipe radius, and r = radius and from pipe axis. Develop an expression for the fluid pressure drop that occurs between sections (1) and (2).