Math Equations

Instructions

Complete the required math calculations to determine heat release rates (HRR) and fuel packages. All math calculations, and, if necessary, the proper conversions, must be shown. Upload your document to Blackboard and place your name, student ID, and full course number in the header of the document. If you need to put pen or pencil to paper in order to show your math work, you can scan in your paper, and then again use the File Upload in Blackboard to submit your paper.

Determining Heat Release Rates

1. Assume that a slab of polymethyl methacrylate (PMMA) (0.15 m2) is burning and is weighed as it burns. The average mass loss flux is 40 g/m2s. The complete heat of combustion for PMMA has been listed as 25 kJ/g. Assume that the combustion efficiency is 40%, and estimate the resulting energy release rate.
2. Assume that a slab of polymethyl methacrylate (PMMA) (0.5 m2) is burning and is weighed as it burns. The average mass loss flux is 15 g/m2s. The complete heat of combustion for PMMA has been listed as 25 kJ/g. Assume that the combustion efficiency is 30%, and estimate the resulting energy release rate.
3. Assume that a slab of polymethyl methacrylate (PMMA) (0.20 m2) is burning and is weighed as it burns. The average mass loss flux is 50 g/m2s. The complete heat of combustion for PMMA has been listed as 25 kJ/g. Assume that the combustion efficiency is 60%, and estimate the resulting energy release rate.

Fire Growth Curves

Firesciencetools.com (2012, December 11). T-squared heat release rate (HRR) example [Video file]. Retrieved from https://www.youtube.com/watch_popup?v=TZEXWbv8Iw0

Please click here to access the video transcript.

1. Estimate the HRR for a sofa fire after 45 seconds. Ignore any effective ignition time. You will need to identify fast for the fire growth based on Table 7.5 located on page 132 of your textbook.
2. Estimate the HRR for an overstuffed chair fire after 30 seconds. Ignore any effective ignition time. You will need to identify fast for fire growth based on Table 7.5 located on page 132 of your textbook.
3. Estimate the HRR for a Christmas tree fire after 25 seconds. Ignore any effective ignition time. You will need to identify ultrafast for fire growth based on Table 7.5 located on page 132 of your textbook.
4. Estimate the HRR for a dresser fire after 60 seconds. Ignore any effective ignition time. You will need to identify fast for fire growth based on Table 7.5 located on page 132 of your textbook.

Calculating Fuel Packages

Part 1: Calculate the base fuel package.

Part 2: Calculate the heat release rate of the base fuel package.

Part 3: Check the base fuel package.

1. The fuel load in a large room consists of the polyurethane foam-filled sofas and chairs shown in the picture. The ceiling is sufficiently high and there are no fire suppression systems. The peak HRR of the sofas is 2,960 BTUs (3,120 kW). The peak HRR of the chairs is 2,010 BTUs (2,120 kW). The combustion efficiency is 0.3 for these furniture items. Note: r1 = r2 = 3.6 ft (1.1 m)



Use 20kW/m2 for radiant mass flux non-piloted. Your base fuel package is 3,750 kW.

Calculate the base fuel package of the room, HRR of the fuel package, and check your fuel package to answer the following questions:

1. How many sofas and chairs make up the base fuel package, and what is the HRR of the base fuel package?
2. Based on the HRR, will ignition of the base fuel package occur and which items will probably be ignited?
3. Based on base fuel package, will ignition occur to the remaining sofas and chair?

You will need to show all of your work and complete all three parts.

1. The fuel load in a large room consists of the polyurethane foam-filled sofas and chairs shown in the picture. The ceiling is sufficiently high, and there are no fire suppression systems. The peak HRR of the sofas is 2,650 BTUs (2,796 kW). The peak HRR of the chairs is 1,910 BTUs (2,015 kW). The combustion efficiency is 0.3 for these furniture items. Note: r1 = r2 = 2.6 ft (0.8 m)



Use 20kW/m2 for radiant mass flux non-piloted. Your base fuel package is 3,600 kW.

Calculate the base fuel package of the room, HRR of the fuel package, and check your fuel package to answer the following questions:

1. How many sofas and chairs make up the base fuel package, and what is the HRR of the base fuel package?
2. Based on the heat release rate, will ignition of the base fuel package occur, and which items will probably be ignited?
3. Based on the base fuel package, will ignition occur to the remaining sofas and chair?

You will need to show all of your work and complete all three parts.

1. The fuel load in a large room consists of the polyurethane foam-filled sofas and chairs shown in the picture. The ceiling is sufficiently high, and there are no fire suppression systems. The peak HRR of the sofas is 2,900 BTUs (3,059 kW). The peak HRR of the chairs is 2,000 BTUs (2,110 kW). The combustion efficiency is 0.3 for these furniture items. Note: r1 = r2 = 5.5 ft (1.7 m)



Use 20kW/m2 for radiant mass flux non-piloted. Your base fuel package is 3,800 kW.

Calculate the base fuel package of the room, HRR of the fuel package, and check your fuel package to answer the following questions:

1. How many sofas and chairs make up the base fuel package, and what is the HRR of the base fuel package?
2. Based on the heat release rate, will ignition of the base fuel package occur, and which items will probably be ignited?
3. Based on the base fuel package, will ignition occur to the remaining sofas and chair?

You will need to show all of your work and complete all three parts.

1. The fuel load in a large room consists of the polyurethane foam-filled sofas and chairs shown in the picture. The ceiling is sufficiently high, and there are no fire suppression systems. The peak HRR of the sofas is 3,033 BTUs (3,200 kW). The peak HRR of the chairs is 1,800 BTUs (1,900 kW). The combustion efficiency is 0.4 for these furniture items. How many sofas and chairs make up the base fuel package, and what is the HRR of the base fuel package? You will need to show all of your work and complete all three parts. Note: r1 = r2 = 4.0 ft (1.2 m)



Use 20kW/m2 for radiant mass flux non-piloted. Your base fuel package is 3,500 kW.

Calculate the base fuel package of the room, HRR of the fuel package, and check your fuel package to answer the following questions:

1. How many sofas and chairs make up the base fuel package, and what is the HRR of the base fuel package?
2. Based on the heat release rate, will ignition of the base fuel package occur, and which items will probably be ignited?
3. Based on base fuel package, will ignition occur to the remaining sofas and chair?

You will need to show all of your work and complete all three parts.

1. The fuel load in a large room consists of the polyurethane foam-filled sofas and chairs shown in the picture. The ceiling is sufficiently high, and there are no fire suppression systems. The peak HRR of the sofas is 2,825 BTUs (2,980 kW). The peak HRR of the chairs is 2,010 BTUs (2,120 kW). The combustion efficiency is 0.3 for these furniture items. Note: r1 = r2 = 2.5 ft (0.8 m)



Use 20kW/m2 for radiant mass flux non-piloted. Your base fuel package is 4,200 kW.

Calculate the base fuel package of the room, HRR of the fuel package, and check your fuel package to answer the following questions:

1. How many sofas and chairs make up the base fuel package, and what is the HRR of the base fuel package?
2. Based on the heat release rate, will ignition of the base fuel package occur, and which items will probably be ignited?
3. Based on base fuel package, will ignition occur to the remaining sofas and chair?

You will need to show all of your work and complete all three parts.

Calculating Flame Height

1. A truck carrying kerosene was 40 meters away from a warehouse wall when it collided with a utility pole and caused a kerosene spill. The kerosene spread horizontally and resulted in a pool approximately 7.5 meters in diameter. The air temperature is at 68oF. The fire’s HRR was calculated as 40,009 kW. What is the flame height for the pool fire? Show all of your calculations.
2. A truck carrying gasoline crashed on the highway 18 meters from a school and spilled the gas. The gasoline spread horizontally and resulted in a pool approximately 20 meters in diameter. The air temperature is at 68oF. What is the flame height for the pool fire? Show all of your calculations.
3. A truck carrying JP-4 fuel crashed on the highway 100 meters from the airport and spilled the fuel. The fuel spread horizontally and resulted in a pool approximately 15 meters in diameter. The air temperature is at 68oF. What is the flame height for the pool fire? Show all of your calculations.