Understanding Fire Demand Estimation

Estimating the necessary water quantity for firefighting, known as fire demand, is a crucial aspect of water supply engineering, especially for urban areas. The required fire demand depends on various factors like the size and type of buildings in the area, their construction materials, and the population density. Several empirical formulas have been developed over time to estimate this fire demand for different scenarios.

The Freeman Formula for Fire Demand

One of the formulas used for estimating fire demand, particularly for high-value districts or congested areas, is the Freeman formula. This formula helps engineers determine the approximate water flow rate required in litres per minute (lpm) based on the population served by the water supply system.

The question asks for the Freeman formula for estimating fire demand (Q) in litres per minute. The correct representation of the Freeman formula is given by:

\( Q = 1136 \left( \frac{P}{5} + 10 \right) \)

Where:

• \( Q \) represents the fire demand in litres per minute (lpm).
• \( P \) represents the population of the city or the area in thousands.

Let's look at the provided options and compare them to the correct Freeman formula.

Analyzing the Options

The question provides four potential formulas for estimating fire demand (Q).

1. \( Q = 5663 \sqrt{P} \)
2. \( Q = 2500 \left( \frac{P}{5} + 10 \right) \)
3. \( Q = 1136 \left( \frac{P}{5} + 10 \right) \)
4. \( Q = 3182 \sqrt{P} \)

Comparing these options with the standard Freeman formula, \( Q = 1136 \left( \frac{P}{5} + 10 \right) \), we can see which option matches the correct formula.

• Option 1: \( Q = 5663 \sqrt{P} \) is the Kuichling's formula, not the Freeman formula.
• Option 2: \( Q = 2500 \left( \frac{P}{5} + 10 \right) \) uses a different constant (2500) instead of 1136.
• Option 3: \( Q = 1136 \left( \frac{P}{5} + 10 \right) \) exactly matches the standard Freeman formula where Q is in lpm and P is in thousands of population.
• Option 4: \( Q = 3182 \sqrt{P} \) is related to the National Board of Fire Underwriters (NBFU) formula (often given in gallons per minute and population in thousands, which needs conversion), not the Freeman formula structure. The NBFU formula is commonly \( Q = 1020 \sqrt{P} (1 - 0.01\sqrt{P}) \) or a simplified \( Q = 1020 \sqrt{P} \) for certain ranges (Q in US gpm, P in thousands). The constant 3182 is approximately 1020 gpm converted to lpm ($1020 \times 3.785 \approx 3861$, so 3182 might be based on slightly different factors or units, but it's clearly not the Freeman formula structure).

Based on this comparison, the formula \( Q = 1136 \left( \frac{P}{5} + 10 \right) \) correctly represents the Freeman formula for estimating fire demand in litres per minute when the population P is in thousands.

Confirmation of the Freeman Formula

The Freeman formula is a well-established empirical formula used in water supply system design for fire protection. It provides a conservative estimate suitable for high-density or high-value areas. The constants in the formula, 1136 and 5 and 10, are derived based on historical fire data and requirements.

As seen in the table, the third option provided, \( Q = 1136 \left( \frac{P}{5} + 10 \right) \), is indeed the correct representation of the Freeman formula when Q is in litres per minute and P is in thousands.

Revision Table: Fire Demand Formulas

Additional Information on Fire Demand Calculation

While empirical formulas like the Freeman formula provide quick estimates, the actual required fire flow can be influenced by many other factors. Water supply system designers also consider:

• Type of Construction: Buildings made of fire-resistant materials require less water than those made of wood.
• Building Size and Height: Larger and taller buildings pose greater firefighting challenges and require more water.
• Building Occupancy: Industrial buildings or areas storing hazardous materials might require higher fire flows than residential areas.
• Spacing between Buildings: Closely spaced buildings increase the risk of fire spreading, requiring more water for exposure protection.
• Firefighting Equipment and Tactics: The availability of modern firefighting equipment and trained personnel can affect the required flow rate.

Engineers use these formulas as starting points and then adjust the estimated fire demand based on specific local conditions and standards set by authorities like the National Board of Fire Underwriters (NBFU) or local fire departments.