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

  1. $\frac{U}{2}$
  2. $\frac{U}{3}$
  3. $\frac{U}{4}$
  4. $\left(\frac{5}{6}\right)U$
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