What is the absolute pressure at the bottom of a storage tank of oil 18-m deep that is open to the atmosphere? Take the density of oil to be 800 kg/m3.
p=p₀+ρgh= 1.013•10⁵ + 800•9.8•18 =
=2.42•10⁵ Pa
Well, if we're talking about a storage tank of oil, then it's safe to say that we're deep in "liquid assets." Now, to determine the absolute pressure at the bottom of the tank that's open to the atmosphere, we need to take a dive into some physics.
First things first, let's calculate the pressure due to the weight of the oil column. We can use the formula P = ρgh, where P is the pressure, ρ is the density of the oil, g is the acceleration due to gravity, and h is the height of the oil column.
Given that the density of oil is 800 kg/m³ and the height is 18 m, we can plug in the values and calculate the pressure. But before we do that, let me just say that this oil is dense enough to make any rock oil-ed, or rather, "oiled" with envy!
So, P = (800 kg/m³) * (9.8 m/s²) * (18 m) = 141,120 Pa.
Now, since the tank is open to the atmosphere, the pressure at the bottom will also be affected by atmospheric pressure. Atmospheric pressure is approximately 101,325 Pa. So, we need to add that to the pressure calculated above.
Adding these pressures together, we get:
Total Pressure = 141,120 Pa + 101,325 Pa = 242,445 Pa.
Voila! The absolute pressure at the bottom of the storage tank of oil, open to the atmosphere, is approximately 242,445 Pa. That's a lot of pressure, but luckily, clowns like me handle pressure every day!
To find the absolute pressure at the bottom of the storage tank, we can use the concept of hydrostatic pressure.
Step 1: Determine the pressure at the surface of the oil.
Since the surface of the oil is open to the atmosphere, the pressure at the surface is the atmospheric pressure. The standard atmospheric pressure is approximately 101,325 Pascals (Pa).
Step 2: Calculate the hydrostatic pressure due to the height of the oil.
The hydrostatic pressure is given by the formula: P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the depth.
Given:
Density of oil (ρ) = 800 kg/m3
Depth (h) = 18 m
Acceleration due to gravity (g) = 9.8 m/s2
Substituting the values into the formula, we get:
P = (800 kg/m3) * (9.8 m/s2) * (18 m)
P = 141,120 Pa
Step 3: Add the hydrostatic pressure to the atmospheric pressure.
The absolute pressure at the bottom of the tank is obtained by adding the hydrostatic pressure to the atmospheric pressure.
Absolute Pressure = Atmospheric Pressure + Hydrostatic Pressure
Absolute Pressure = 101,325 Pa + 141,120 Pa
Absolute Pressure = 242,445 Pa.
Therefore, the absolute pressure at the bottom of the storage tank is 242,445 Pascals.
To determine the absolute pressure at the bottom of the storage tank, we need to consider the pressure due to the weight of the oil column above it.
The formula for pressure is given by the equation:
Pressure = Density x Gravity x Height
In this case, the height is the depth of the oil column, which is 18 meters, the density of the oil is 800 kg/m^3, and the acceleration due to gravity is approximately 9.8 m/s^2.
Plugging these values into the equation, we can calculate the pressure at the bottom of the tank:
Pressure = 800 kg/m^3 x 9.8 m/s^2 x 18 m
= 141,120 Pascal
Therefore, the absolute pressure at the bottom of the storage tank is approximately 141,120 Pascal.