How to calculate the average velocity over a surface through time using paraview?

My problem is a little more complex, but here is a simplified similar model.

Let us consider a fire source inside a box and the hot gases (burnt or unburnt) from the combustion are going out of the exhaust (white surface) at a certain velocity. We have the velocity field of the entire domain and can be visualized using ParaView. We also have density and temperature fields among others.

Now, using ParaView I would like to calculate the average velocity of the gases coming out of this surface (white) over time (unsteady regime).

Note: The individual boundaries are not loaded in ParaView. That is outlet as a separate surface, the domain as a separate surface. The entire volume is treated as a single entity with specified boundary conditions.

Any help to calculate this is appreciated.