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

17.3m/s

Step-by-step explanation:

Detailed explanation and calculation is shown in the image

Answer 2

`u_(max) = 17.334\,(m)/(s)`

Step-by-step explanation:

Let consider that velocity profile inside the circular pipe is:

`u(r) = 2\cdot U_(avg) \cdot \left(1 - (r^(2))/(R^(2)) \right)`

The average speed at
`r = (1)/(2) \cdot R` is:

`U_(avg) = (13\,(m)/(s) )/(2\cdot \left(1-(1)/(4) \right))`

`U_(avg) = 8.667\,(m)/(s)`

The velocity at the center of the pipe is:

`u_(max) = 2\cdot U_(avg)`

`u_(max) = 17.334\,(m)/(s)`