Question

In fully developed laminar flow in a circular pipe the velocity at R/2 (mid-way between the wall surface and the centerline) is measured to be 13 m/s. Determinethe velocity at the center of the pipe.

Answer 1

Answer:

$u_{max} = 17.334\,\frac{m}{s}$

Explanation:

Let consider that velocity profile inside the circular pipe is:

$u(r) = 2\cdot U_{avg} \cdot \left(1 - \frac{r^{2}}{R^{2}} \right)$

The average speed at $r = \frac{1}{2} \cdot R$ is:

$U_{avg} = \frac{13\,\frac{m}{s} }{2\cdot \left(1-\frac{1}{4} \right)}$

$U_{avg} = 8.667\,\frac{m}{s}$

The velocity at the center of the pipe is:

$u_{max} = 2\cdot U_{avg}$

$u_{max} = 17.334\,\frac{m}{s}$

Answer 2

Answer:

17.3m/s

Explanation:

Detailed explanation and calculation is shown in the image