A container is filled to a depth of 15.0 cm with water. On top of the water floats a 27.0 cm thick layer of oil with specific gravity 0.800. What is the absolute pressure at the bottom of the container.
(water density)*g*[0.15 + (0.8*0.27]
= 1000 kg/m^3*(9.8m/s^2)*0.366 m = ____ N/m^2 + Patm
Patm is atmospheric pressure, which must be added to the pressure caused by the weight of the two liquids.
To find the absolute pressure at the bottom of the container, we need to consider the pressure due to the weight of both the water and the oil.
The pressure due to the weight of water can be calculated using the formula:
Pwater = ρwater * g * h
Where:
Pwater is the pressure due to the weight of water,
ρwater is the density of water (1000 kg/m³),
g is the acceleration due to gravity (9.8 m/s²),
and h is the height of the water column (15.0 cm = 0.15 m).
Plugging in the values, we get:
Pwater = 1000 kg/m³ * 9.8 m/s² * 0.15 m = 1470 Pa
The pressure due to the weight of oil can be calculated using the formula:
Poil = ρoil * g * h
Where:
Poil is the pressure due to the weight of oil,
ρoil is the density of oil (which can be calculated by multiplying the specific gravity by the density of water, since the specific gravity is the ratio of the density of the oil to the density of water),
g is the acceleration due to gravity,
and h is the height of the oil column.
ρoil = specific gravity * ρwater
= 0.800 * 1000 kg/m³
= 800 kg/m³
Plugging in the values, we get:
Poil = 800 kg/m³ * 9.8 m/s² * 0.27 m = 2112 Pa
Finally, to find the absolute pressure at the bottom of the container, we sum the pressures due to water and oil:
Pabsolute = Pwater + Poil
= 1470 Pa + 2112 Pa
= 3582 Pa
Therefore, the absolute pressure at the bottom of the container is 3582 Pa.
To find the absolute pressure at the bottom of the container, we need to consider the pressure contributions from both the water and the oil layers.
The pressure at a certain depth in a fluid is given by the formula:
P = P0 + ρgh
Where:
P is the pressure at the desired depth
P0 is the atmospheric pressure (which we will assume to be 1 atm)
ρ is the density of the fluid
g is the acceleration due to gravity
h is the height or depth of the fluid column
First, let's calculate the pressure contribution from the water:
The density of water, ρ_water, is approximately 1000 kg/m^3.
The height of the water column, h_water, is 15.0 cm = 0.15 m.
Using the formula:
P_water = P0 + ρ_water * g * h_water
P_water = 1 atm + (1000 kg/m^3) * (9.8 m/s^2) * (0.15 m)
P_water = 1 atm + 1470 Pa
P_water = 1 atm + 0.0147 atm
P_water ≈ 1.0147 atm
Next, let's calculate the pressure contribution from the oil:
The specific gravity of the oil, SG_oil, is given as 0.800. Specific gravity is defined as the ratio of the density of a substance to the density of water.
So, the density of the oil, ρ_oil, is:
ρ_oil = SG_oil * ρ_water
ρ_oil = 0.800 * 1000 kg/m^3
ρ_oil = 800 kg/m^3
The height of the oil column, h_oil, is given as 27.0 cm = 0.27 m.
Using the same formula as before:
P_oil = P0 + ρ_oil * g * h_oil
P_oil = 1 atm + (800 kg/m^3) * (9.8 m/s^2) * (0.27 m)
P_oil = 1 atm + 2104.8 Pa
P_oil = 1 atm + 0.0209 atm
P_oil ≈ 1.0209 atm
Finally, to find the absolute pressure at the bottom of the container, we need to combine the pressures from the water and the oil:
P_total = P_water + P_oil
P_total ≈ 1.0147 atm + 1.0209 atm
P_total ≈ 2.0356 atm
Therefore, the absolute pressure at the bottom of the container is approximately 2.0356 atmospheres.