Suppose you pour water into a container until it reaches a depth of 12 cm. Next, you pour in a 25-cm-thick layer of oil so that it floats on top of the water. The density of the oil is 0.92 g/cm3 and that of water is 1.00 g/cm3. What is the pressure at the bottom of the container?
To find the pressure at the bottom of the container, we need to consider the pressure due to the water and the pressure due to the oil separately.
First, let's calculate the pressure due to the water. The pressure at a certain depth in a fluid is given by the equation:
Pressure = density × gravitational acceleration × depth
The density of water is 1.00 g/cm3, and the depth of the water is 12 cm. The gravitational acceleration is approximately 9.8 m/s2.
Converting the density to kg/m3:
Density of water = 1.00 g/cm3 = 1000 kg/m3
Now, let's calculate the pressure due to the water:
Pressure_water = Density_water × g × depth
= 1000 kg/m3 × 9.8 m/s2 × 0.12 m
Next, let's calculate the pressure due to the oil. The density of oil is 0.92 g/cm3, and the depth of the oil is 25 cm.
Converting the density to kg/m3:
Density of oil = 0.92 g/cm3 = 920 kg/m3
Now, let's calculate the pressure due to the oil:
Pressure_oil = Density_oil × g × depth
= 920 kg/m3 × 9.8 m/s2 × 0.25 m
Finally, to find the total pressure at the bottom of the container, we need to add the pressure due to the water and the pressure due to the oil:
Total pressure = Pressure_water + Pressure_oil
Now you can plug in the values to calculate the total pressure at the bottom of the container.