What position in cm do you expect the water column to be on the y-axis in order to open the valve?

Question

Relief valves keep the pressure of a vessel from exceeding some threshold by opening to release fluid. You are designing a pressure relief valve with a 1,816 N/m spring pushing a 5 cm diameter disk against the open end of a pipe of the same diameter. The spring is compressed by 1 cm from its natural length. To test the valve you attach it to a static column of water.

Answer 1

A good way to consider water pressure due to a column of water (like a standpipe in a fire suppression system) is that every 10 meters ≈ 1 atm ≈ 100 kPa ≈ 1E5 N/m² . P = ρgh

Pressure = Force / Area, P = F/A, and Force = (spring constant) x displacement, F= kx

You can use this relationship and the formulas for Area (A = π r² , the question gives you the diameter!)

Solve for h, the height of the water column.

WATCH YOUR UNITS!

BTW, from a significant figures (SF) perspective, the data for the diameter and displacement is limited to 1 SF, but you could assume that the data in cm might be good to 2 SF.

The spring constant, k, is given to 4 SF!

Measuring the diameter of the disc and its displacement to 10 μm is a little silly.

¯\_(ツ)_/¯