What is the gauge pressure at the bottom of the cylinder?
oil= 0.88m
brine= 1.11m
p oil= 790 kg/m^3
p brine= 1025 kg/m^3
To find the gauge pressure at the bottom of the cylinder, we need to calculate the pressure exerted by both the oil and brine columns.
The gauge pressure at a certain depth is given by the formula:
P = ρgh
Where:
P is the pressure
ρ is the density of the fluid
g is the acceleration due to gravity
h is the depth
For the oil:
P_oil = ρ_oil * g * h_oil
= 790 kg/m^3 * 9.8 m/s^2 * 0.88 m
= 6787.44 Pa
For the brine:
P_brine = ρ_brine * g * h_brine
= 1025 kg/m^3 * 9.8 m/s^2 * 1.11 m
= 11298.15 Pa
The total pressure at the bottom is the sum of the pressures from the oil and brine:
P_total = P_oil + P_brine
= 6787.44 Pa + 11298.15 Pa
= 18085.59 Pa
Therefore, the gauge pressure at the bottom of the cylinder is 18085.59 Pa.