GATE Civil Engineering (CE) 2021 Shift 1 Solved Paper

A fluid flowing steadily in a circular pipe of radius R has a velocity that is everywhere parallel to the axis (centerline) of the pipe. The velocity distribution along the radial direction is ${\mathit{V}}_{\mathit{r}}=\mathit{U}\left(1-\frac{{\mathit{r}}^2}{{\mathit{R}}^2}\right)$, where r is the radial distance as measured from the pipe axis and U is the maximum velocity at r = 0. The average velocity of the fluid in the pipe is