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 \({{{V_r}}} = U\left( {1 - \frac{{{r^2}}}{{{R^2}}}} \right)\), 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

• A. \((\frac{5}{6})U\)
• B. \(\frac{U}{4}\)
• C. \(\frac{U}{3}\)
• D. \(\frac{U}{2}\)