finding a specified flow rate in a '3D cut plane'

Hello,

I'm trying to do some postprocessing in a 3D fluid channel flow over a fractured hole.
The channel is filled with water and is laminar.
Here's what I'm trying to do:

1. cut the surface at an arbitrary channel location (i used the 'cut plane')
2. within that surface, I would like to start from one edge and integrate the velocity profile in a prescribed area.
eg) if the surface slice is a 2mmx2mm rectangle, i want to make another rectangle that is 1mmx1mm within that original 'cut plane' and measure the surface integrated velocity value (flow rate).

I was able to cut the surface where I wanted it, but I cannot find a way to resolve what I said in 2.

Any ideas?

Thanks!

TJ