Mass flow rate calculation from velocity contour in pipe

[ca2n]

Hello all,

Looking for ideas on how to calculate mass flow rate from a velocity contour plot. The cross-sectional area is circular. An example of the velocity contour plot is shown in the figure below:

In most of the cases (as exemplified above) the flow is non-axisymmetric. Any suggestions welcomed. Thank you in advance.

 

[Chestermiller]

Why is it non-symmetric?

 

[boneh3ad]

Why is it non-symmetric?

As a follow-up, why doesn't the velocity go to zero at the walls?