The static pressure pickup "sees" the same air condition changes as the differential pressure so the Cd of your sharp edge orifice plate does not change. If you see a change flowing the opposite way you have a problem with your plate or bench design.
Plenum design and quality of flow to your orifice plate will play into this. This has been extensively discussed in great details on various forms of flowbench design on my
flowbench forum. I welcome anyone who is thinking of building a bench to take the time to read all they can before settling on a flowbench design.