Question 9.5: Oil and Water GOAL Calculate pressures created by layers of ...
Oil and Water
GOAL Calculate pressures created by layers of different fluids.
PROBLEM In a huge oil tanker, salt water has flooded an oil tank to a depth of h_2 = 5.00 m. On top of the water is a layer of oil h_1 = 8.00 m deep, as in the cross-sectional view of the tank in Figure 9.14. The oil has a density of 0.700 g/cm³. Find the pressure at the bottom of the tank. (Take 1 025 kg/m³ as the density of salt water.)
STRATEGY Equation 9.11 must be used twice. First, use it to calculate the pressure P_1 at the bottom of the oil layer. Then use this pressure in place of P_0 in Equation 9.11 and calculate the pressure P_{bot} at the bottom of the water layer.
P=P_{0}+\rho g h [9.11]
Use Equation 9.11 to calculate the pressure at the bottom of the oil layer:
\text { (1) } P_1=P_0+\rho g h_1
=1.01 \times 10^5 Pa
+\left(7.00 \times 10^2 kg / m ^3\right)\left(9.80 m / s ^2\right)(8.00 m )
P_1=1.56 \times 10^5 Pa
Now adapt Equation 9.11 to the new starting pressure, and use it to calculate the pressure at the bottom of the water layer:
\text { (2) } \quad P_{\text {bot }}=P_1+\rho g h_2
=1.56 \times 10^5 Pa
+\left(1.025 \times 10^3 kg / m ^3\right)\left(9.80 m / s ^2\right)(5.00 m )
P_{\text {bot }}=2.06 \times 10^5 Pa
REMARKS The weight of the atmosphere results in P_0 at the surface of the oil layer. Then the weight of the oil and the weight of the water combine to create the pressure at the bottom.