What is the gauge pressure at the bottom of the cylinder?
oil= 0.88 m p oil = 790 kg/m^3
brine= 1.11m 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 the brine separately, and then add them together.
First, let's calculate the pressure exerted by the oil at the bottom of the cylinder. The gauge pressure is given by the formula:
P = p*g*h
where P is the pressure, p is the density of the fluid, g is the acceleration due to gravity, and h is the height. Plugging in the values:
P_oil = 790 kg/m^3 * 9.8 m/s^2 * 0.88 m
P_oil ≈ 6781.44 Pa
Now, let's calculate the pressure exerted by the brine at the bottom of the cylinder:
P_brine = 1025 kg/m^3 * 9.8 m/s^2 * 1.11 m
P_brine ≈ 11160.15 Pa
Finally, we can add these two pressures together to find the total gauge pressure at the bottom of the cylinder:
Total gauge pressure = P_oil + P_brine
Total gauge pressure ≈ 17941.59 Pa
Therefore, the gauge pressure at the bottom of the cylinder is approximately 17941.59 Pa.