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.

Answer 1

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.