A very large open tank is full of oil whose density is 800 kg/m3 . If the absolute pressure at the bottom of the tank is 1.81 x 10 5pa, then what is the depth of the oil? (Note that atmospheric pressure is 1.01 x 10 5pa)
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Well, let's not dive into this problem blindly. We need to consider the pressure difference between the bottom of the tank and the atmospheric pressure. This difference is what keeps the oil in the tank, otherwise it would be a slippery situation!
First, let's calculate the difference in pressure. The absolute pressure at the bottom of the tank is 1.81 x 10^5 Pa, and atmospheric pressure is 1.01 x 10^5 Pa. So, the pressure difference is:
1.81 x 10^5 Pa - 1.01 x 10^5 Pa = 0.8 x 10^5 Pa
Now, we need to use some fluid dynamics to find the depth of the oil. The pressure at any point in a fluid is given by:
P = P0 + ρgh
Where P is the pressure at the chosen point, P0 is the reference pressure (in this case, atmospheric pressure), ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid.
Since we're solving for depth, let's rearrange the equation to isolate h:
h = (P - P0) / (ρg)
Now we can plug in the values we know:
h = (0.8 x 10^5 Pa) / (800 kg/m^3 * 9.8 m/s^2)
Calculating this will give us the depth of the oil in meters.
To determine the depth of the oil, we need to consider the pressure difference between the bottom of the tank and the atmospheric pressure.
Given:
Density of oil (ρ) = 800 kg/m^3
Absolute pressure at the bottom of the tank (P_bottom) = 1.81 x 10^5 Pa
Atmospheric pressure (P_atm) = 1.01 x 10^5 Pa
The pressure difference (ΔP) between the bottom of the tank and the atmospheric pressure can be calculated as:
ΔP = P_bottom - P_atm
ΔP = (1.81 x 10^5 Pa) - (1.01 x 10^5 Pa)
ΔP = 0.8 x 10^5 Pa
Next, we can use the hydrostatic pressure equation to find the depth of the oil:
ΔP = ρgh
Where:
ρ = Density of the oil
g = Acceleration due to gravity (approximately 9.8 m/s^2)
h = Height or depth of the oil
Rearranging the equation to find the depth:
h = ΔP / (ρg)
Plugging in the values:
h = (0.8 x 10^5 Pa) / (800 kg/m^3)(9.8 m/s^2)
h = 100 m
Therefore, the depth of the oil in the tank is 100 meters.
To find the depth of the oil in the tank, you can use the concept of hydrostatic pressure. The hydrostatic pressure in a fluid increases with depth due to the weight of the fluid above it.
First, let's determine the pressure exerted by the oil at the bottom of the tank. We know that the absolute pressure at the bottom is 1.81 x 10^5 Pa.
Next, we need to consider the atmospheric pressure acting on the surface of the oil. The atmospheric pressure is given as 1.01 x 10^5 Pa.
The difference between the absolute pressure at the bottom and the atmospheric pressure gives us the gauge pressure. So, the gauge pressure is (1.81 x 10^5 Pa) - (1.01 x 10^5 Pa) = 8 x 10^4 Pa.
Now, we can use the hydrostatic pressure formula to find the depth of the oil. The hydrostatic pressure is given by the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth. Rearranging the equation, we get h = P / (ρg).
Substituting the given values, the density of the oil is 800 kg/m^3, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the depth h.
h = (8 x 10^4 Pa) / (800 kg/m^3 x 9.8 m/s^2)
Simplifying the equation, h = 10.2 m.
Therefore, the depth of the oil in the open tank is approximately 10.2 meters.
Pa + rho g h = 1.01*10^5 + 800 kg/m^3 * 9.81 m/s^2 * h = 1.81*10^5
so
7848 h = 0.8^10^5 = 80000
h = 10.2 meters