When a fluid enters in a pipe at a particular flow rate and suddenly if the pipe contracts to a orifice diameter all the fluid cannot enter into the orifice. This generates a increase in pressure at the larger diameter side. If i know only the flow rate , Pipe bigger diameter and smaller diameter is it possible to find out the pressure difference. This question is specific to the flow control valve where this difference in pressure compress the spring and allow more fluid.
There are a lot of options for valve trim, which controls the amount of flow going through a valve for a given valve position. Talk to the appropriate valve vendor, and give him information regarding the valve size, type of valve, valve trim, upstream and downstream pressure, etc. The vendor should be able to provide a plot (or chart) of valve position vs. flow rate, and flow rate vs. pressure drop across the valve.