A full 500,000 gallon crude oil tank with a circular diameter of 50 ft is burning, how long will the fire burn without intervention assuming the tank maintains containment. Assume a crude oil density of 850 kg/m3. Round answer to the nearest hour.
In order to determine how long the fire will burn, we first need to calculate the volume of oil in the tank.
We are given the diameter of the tank is 50 ft. To convert this to meters, we can use the conversion factor: 1 ft = 0.3048 m.
So, the diameter of the tank in meters is 50 * 0.3048 = 15.24 m.
Now, we need to find the radius of the tank, which is half of the diameter:
Radius = Diameter / 2
Radius = 15.24 m / 2 = 7.62 m
We are also given the volume of the tank in gallons. We can convert this to cubic meters using the conversion factor: 1 gallon = 0.00378541 m^3.
So, the volume of the tank in cubic meters is 500,000 * 0.00378541 = 1892.705 m^3.
Now that we have the volume of the tank and the radius, we can find the height of the tank using the formula for the volume of a cylinder:
Volume = π * (Radius^2) * Height
Rearranging the formula to solve for the height:
Height = Volume / (π * (Radius^2))
Height = 1892.705 m^3 / (π * (7.62 m^2))
Height ≈ 10.83 m
Now, we need to find the mass of the crude oil in the tank. We can do this by multiplying its density by its volume:
Mass = Density * Volume
Mass = 850 kg/m^3 * 1892.705 m^3
Mass ≈ 1,608,799 kg
Now, we need to find the energy released by the burning crude oil. The energy content of crude oil is approximately 45 MJ/kg.
So, the total energy released by 1,608,799 kg of crude oil is:
Energy = Mass * Energy content
Energy = 1,608,799 kg * 45 MJ/kg
Energy = 72,395,955 MJ
Now, we can calculate how long the fire will burn without intervention.
We need to know the rate at which the oil burns, but we do not have enough information to accurately calculate this. However, we can estimate a constant burn rate using the following assumption: it takes around 1.4 hours to burn through 1 ft of oil. Since we know there are 10.83 m (about 35.53 ft) of oil in the tank (height), we can now calculate the time it will take to burn through all the oil:
Time = (1 h/ft) * Number of feet of oil in the tank.
Time = 1.4 h/ft * 35.53 ft
Time ≈ 49.74 h
So, the fire will burn for approximately 50 hours without intervention, assuming the tank maintains containment.
To calculate the time it will take for the fire to burn a full 500,000-gallon crude oil tank, we need to consider the following steps:
Step 1: Calculate the volume of the crude oil tank.
The volume of a cylindrical tank can be calculated using the formula: V = π * r^2 * h, where V is the volume, π is a mathematical constant (approximately 3.14159), r is the radius of the tank, and h is the height of the tank.
Given that the tank has a circular diameter of 50 ft, the radius can be calculated as r = d/2 = 50/2 = 25 ft.
Let's convert this radius to meters since the density of crude oil is given in kg/m^3. Since 1 ft = 0.3048 m, the radius in meters is 25 ft * 0.3048 m/ft = 7.62 m.
Assuming the height of the tank is the same as the diameter, the height is also 50 ft = 15.24 m.
Now, we can calculate the volume in cubic meters:
V = π * (7.62 m)^2 * 15.24 m
≈ 3.14159 * 58.1764 m^2 * 15.24 m
≈ 8767.70631 m^3
Step 2: Calculate the mass of the crude oil in the tank.
Given the crude oil density of 850 kg/m^3, we can multiply the density by the volume to find the mass:
Mass = Density * Volume
= 850 kg/m^3 * 8767.70631 m^3
≈ 7,446,550.36 kg
Step 3: Calculate the energy required to burn the crude oil.
The energy required to burn crude oil can vary depending on many factors, such as the specific composition of the oil and the conditions of the fire. However, for an estimate, we can use the energy content of crude oil, which is approximately 45 MJ/kg.
Energy = Mass * Energy per unit mass
= 7,446,550.36 kg * 45 MJ/kg
≈ 335,095,263 MJ
Step 4: Calculate the burn rate.
The burn rate represents the rate at which the energy is released by the burning oil. It can also vary depending on the specific circumstances of the fire. However, for an estimate, we can use an average burn rate of 1300 MJ per hour.
Burn rate = Energy / Burn rate per hour
= 335,095,263 MJ / 1300 MJ per hour
≈ 258,534.05 hours
Step 5: Round the answer.
Rounding the burn rate to the nearest hour gives us the final answer.
The fire will burn for approximately 258,534 hours, rounded to the nearest hour.