When the needle valve is completely closed, pressure rises at the relief valve inlet, increasing the ___________ across the relief spool.

• A. volume
• B. spring force
• C. pressure differential
• D. time

Answer: (C)

The main idea is that the valve spool responds to the difference in pressure across it, not to absolute pressure alone or to time. When the needle valve is completely closed, flow to the relief path stops and the pressure on the inlet side rises while the outlet side stays lower. This increases the pressure difference across the relief spool (P_in minus P_out). As this differential pressure grows, it overcomes the spring force and moves the spool to open the relief path, keeping the system pressure from climbing further. So the term that increases across the spool is the pressure differential. Volume and time aren’t what drive the spool movement, and while spring force matters, the situation described specifically enhances the differential pressure.