11. Suppose 3,500 gallons of gasoline spill into a banked up area that measures circular area that is 10ft in diameter. If the fuel’s vertical burning rate is 6 in/hour, how long will the fire last if it is left unattended?
1 gallon = 231 in^3.
The fuel depth in the spill is volume/area:
3500*231/2500π = 102.94 in
so, at 6 in/hr, it will burn for
102.94/6 = 17.157 hours
To find out how long the fire will last, we need to determine the volume of gasoline and then calculate the time it takes for the fire to consume that volume.
1. Calculate the volume of gasoline:
- Since the area is circular and the diameter is given, we can find the radius by dividing the diameter by 2.
Radius = 10 ft / 2 = 5 ft
- The formula to calculate the volume of a cylinder is V = π * r^2 * h, where π is approximately 3.14, r is the radius, and h is the height (burning rate in this case).
- In this scenario, the height represents the burning rate in inches per hour. To make sure all units are consistent, convert the radius from feet to inches, as 1 foot is equal to 12 inches.
Radius = 5 ft * 12 in/ft = 60 in
- The volume of the gasoline is then:
V = π * 60 in^2 * 6 in/hour
V ≈ 3.14 * 3600 in^3/hour
V ≈ 11,304 in^3/hour
2. Calculate the time it takes for the fire to consume the volume of gasoline spilled:
- Divide the total volume of gasoline spilled (3,500 gallons) by the volume consumed in one hour (11,304 in^3/hour).
Time = 3,500 gallons / 11,304 in^3/hour
Time ≈ 309.3 hours
Therefore, if the fire is left unattended, it will last approximately 309.3 hours.