How to impose "full developed flow" condition?

[HYB777]

Hi, I want to impose the full developed flow condition on the inlet boundary, which means the average inlet velocity is given. The condition is formulated as follow:

$\frac{1}{-|{\mathrm{\Gamma }}_{\text{inlet}}|}{\int }_{{\mathrm{\Gamma }}_{\text{inlet}}}\mathbf{u}\cdot \mathbf{n}ds=u_{\text{avg}}$.

For my case, the domain is $[0,1]\times [0,1]$, and the inlet boundary is at $y=1$.

How should I do for this?

[francesco-ballarin]

Please do not duplicate questions here and on FEniCS discourse. It is the second time you do that in the last few days.