In a huge oil tanker, salt water has flooded an oil tank to a depth of h2 = 4.50 m. On top of the water is a layer of oil h1 = 7.55 m deep, as in the cross-sectional view of the tank as shown in the figure. 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.)
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To find the pressure at the bottom of the tank, we can use the concept of hydrostatic pressure.
The hydrostatic pressure is given by the formula:
P = ρ * g * h
Where:
P is the pressure
ρ is the density of the fluid
g is the acceleration due to gravity
h is the height or depth of the fluid
To solve for the pressure at the bottom of the tank, we need to consider the pressure due to the salt water and the pressure due to the oil.
Step 1: Calculate the pressure due to the salt water.
Given:
Density of salt water, ρ(sw) = 1,025 kg/m^3
Height or depth of salt water, h(sw) = 4.50 m
Using the formula for hydrostatic pressure:
P(sw) = ρ(sw) * g * h(sw)
Substituting the given values:
P(sw) = 1,025 kg/m^3 * 9.8 m/s^2 * 4.50 m
Step 2: Calculate the pressure due to the oil.
Given:
Density of oil, ρ(oil) = 0.700 g/cm^3 = 700 kg/m^3
Height or depth of oil, h(oil) = 7.55 m
Using the formula for hydrostatic pressure:
P(oil) = ρ(oil) * g * h(oil)
Substituting the given values:
P(oil) = 700 kg/m^3 * 9.8 m/s^2 * 7.55 m
Step 3: Calculate the total pressure at the bottom of the tank.
The total pressure at the bottom of the tank is the sum of the pressures due to the salt water and the oil:
P(total) = P(sw) + P(oil)
Substituting the calculated values from steps 1 and 2 into this equation will give us the final answer for the total pressure at the bottom of the tank.
To find the pressure at the bottom of the tank, we can use the equation for pressure:
Pressure (P) = density (ρ) × gravitational acceleration (g) × height (h)
First, we need to find the densities of the oil and salt water in SI units.
Density of oil (ρ_oil) = 0.700 g/cm^3 = 0.700 × 1000 kg/m^3 = 700 kg/m^3
Density of salt water (ρ_water) = 1025 kg/m^3
Now, we can calculate the pressure at the bottom of the tank.
Pressure at the bottom of the tank = Pressure due to oil + Pressure due to salt water
Pressure due to oil = ρ_oil × g × h1 (where h1 is the depth of the oil)
Pressure due to salt water = ρ_water × g × h2 (where h2 is the depth of the salt water)
Substituting the given values:
Pressure due to oil = 700 kg/m^3 × 9.8 m/s^2 × 7.55 m
Pressure due to salt water = 1025 kg/m^3 × 9.8 m/s^2 × 4.50 m
Now, we add the two pressures to find the total pressure at the bottom of the tank:
Pressure at the bottom of the tank = Pressure due to oil + Pressure due to salt water
= (700 kg/m^3 × 9.8 m/s^2 × 7.55 m) + (1025 kg/m^3 × 9.8 m/s^2 × 4.50 m)
Simplifying the equation will give you the final answer for the pressure at the bottom of the tank.