Multiple choice

The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by the expression u(r) = -$\frac{R^2}{4 \mu} \Big(\frac{dp}{dx}\Big) \Big(1-\frac{r^2}{R^2}\Big)$, where $\frac{dp}{dx}$ is a constant. The average velocity of fluid in the pipe is

  1. -$\frac{R^2}{8 \mu} \Big(\frac{dp}{dx}\Big)$
  2. -$\frac{R^2}{4 \mu} \Big(\frac{dp}{dx}\Big)$
  3. -$\frac{R^2}{2 \mu} \Big(\frac{dp}{dx}\Big)$
  4. -$\frac{R^2}{\mu} \Big(\frac{dp}{dx}\Big)$
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