Surface Integral

I'm supposed to find the flow rate per width over a surface x + y = 1. How do I parametrize and cross product this without a z dimension?

Lol, well, if z dimension is basically depth in RL, you would measure length and angle of z in whatever form of measurement you're going to use as a standard throughout the test. If the flow moves either right or left when traveling along z it is varying along x axis, if still traveling along z and it moves from top to bottom it is varying along y axis.
The best way I've found is to use graph-lined-acetate and measure the blocks, and document the speed, angle, distance and also the mass of flow matter and don't forget about the mass of the acetate if you use acetate. The resistance should be noted for whatever material you are flowing on or through. If this doesn't help, ask your prof to delineate some of your unknown testing parameters. That's the best I can give ya. Good luck! :3