What is the gauge pressure at the bottom of the cylinder?

Question

Oil = 0.88m
Poil = 790kg
Brine = 1.11m
Pbrine = 1,025 kg

Answer 1

To find the gauge pressure at the bottom of the cylinder, we need to calculate the pressure at that point.

1. Convert the heights of the oil and brine to meters:
Oil = 0.88 m
Brine = 1.11 m

2. Calculate the pressures at the bottom of the oil and brine columns:
Poil = 790 kg/m^3
Pbrine = 1025 kg/m^3

Pressure at the bottom of the oil column = Poil * g * height_oil
= 790 kg/m^3 * 9.8 m/s^2 * 0.88 m
= 6665.44 Pa

Pressure at the bottom of the brine column = Pbrine * g * height_brine
= 1025 kg/m^3 * 9.8 m/s^2 * 1.11 m
= 10977.45 Pa

3. Add the pressures of the oil and brine columns to find the total pressure at the bottom of the cylinder:
Total pressure = Pressure at the bottom of the oil column + Pressure at the bottom of the brine column
= 6665.44 Pa + 10977.45 Pa
= 17642.89 Pa

Therefore, the gauge pressure at the bottom of the cylinder is 17,642.89 Pa.