4.2 Friction Loss Calculations (FL = C * (Q/100)^2 * (L/100))

4.2 Friction Loss Calculations (FL = C * (Q/100)^2 * (L/100))

Quick Answer: Friction loss (FL) is the loss of pressure energy caused by water rubbing against the interior lining of fire hose, internal couplings, valves, and water molecules colliding during flow. Driver/operators calculate friction loss using the standard fire service formula $FL = C \times (Q/100)^2 \times (L/100)$, where $C$ is the hose diameter coefficient, $Q$ is flow rate in gallons per minute (gpm), and $L$ is total hose length in feet.

When water moves through a fire hose, energy is converted into heat due to resistance between liquid molecules and the interior hose walls. This pressure drop is termed friction loss (FL). Driver/operators must accurately calculate friction loss to determine how much pressure the pump must generate to overcome hose line resistance and deliver proper pressure to the nozzle. Under-calculating friction loss leads to weak, ineffective fire streams that jeopardize interior attack crews; over-calculating causes excessive nozzle reaction, line stiffness, and potential hose failure.

Four Fundamental Laws of Friction Loss

Friction loss in fire hose lines follows four established hydraulic principles:

1. First Law: Friction loss varies directly with the length of the hose line. If hose length is doubled while diameter and flow rate remain constant, friction loss doubles ($FL \propto L$).
2. Second Law: When hose lines are the same size, friction loss varies approximately as the square of the velocity (or flow rate). If flow rate is doubled ($2\times$), friction loss increases four times ($2^2 = 4\times$). If flow rate is tripled ($3\times$), friction loss increases nine times ($3^2 = 9\times$).
3. Third Law: For the same velocity, friction loss decreases dramatically as the diameter of the hose increases. Larger diameter hoses present a smaller surface-area-to-volume ratio, significantly reducing molecular resistance.
4. Fourth Law: For a given flow rate, friction loss varies inversely as the fifth power of the hose diameter ($FL \propto 1/d^5$). Replacing a 2.5-inch hose with a 3-inch hose at identical flow rates reduces friction loss by more than 50%.

Fire Hose Coefficients ($C$)

The friction loss coefficient ($C$) is an empirically derived numerical constant representing interior roughness and fluid resistance for specific hose diameters. Standard NFPA hydraulic coefficients used nationwide are outlined below:

The Standard Friction Loss Formula

The universal mathematical formula for calculating total friction loss in a single hose line is:

$FL = C \times \left(\frac{Q}{100}\right)^2 \times \left(\frac{L}{100}\right)$

Where:

• $FL$ = Total friction loss in pounds per square inch (psi)
• $C$ = Friction loss coefficient for hose diameter
• $Q$ = Total volumetric flow rate in gallons per minute (gpm)
• $L$ = Total length of hose lay in feet

Step-by-Step Single Line Worked Examples

Worked Example 1: 1.75-Inch Preconnected Handline

Calculate friction loss for a 200-foot lay of 1.75-inch attack hose ($C = 15.5$) flowing 150 gpm.

1. Step 1: Calculate Flow Factor $(Q/100)^2$ $\frac{Q}{100} = \frac{150}{100} = 1.5 \implies (1.5)^2 = 2.25$
2. Step 2: Calculate Length Factor $(L/100)$ $\frac{L}{100} = \frac{200}{100} = 2.0$
3. Step 3: Multiply Terms with Coefficient $FL = 15.5 \times 2.25 \times 2.0 = 69.75\text{ psi}$ Operational Result: Total friction loss in the line is 69.75 psi (rounded to 70 psi).

Worked Example 2: 2.5-Inch Attack Handline

Calculate friction loss for 300 feet of 2.5-inch hose ($C = 2.0$) supplying a smooth bore nozzle flowing 250 gpm.

1. Step 1: Flow Factor $\frac{Q}{100} = \frac{250}{100} = 2.5 \implies (2.5)^2 = 6.25$
2. Step 2: Length Factor $\frac{L}{100} = \frac{300}{100} = 3.0$
3. Step 3: Calculate Friction Loss $FL = 2.0 \times 6.25 \times 3.0 = 37.5\text{ psi}$

Parallel and Siamesed Hose Line Calculations

When high flow rates are required, driver/operators frequently lay parallel hose lines (two or more lines of equal length and diameter connected together) to reduce overall friction loss.

To calculate friction loss in parallel lines of equal length and diameter:

1. Divide total gpm ($Q_{total}$) equally between the parallel lines to find flow per line ($Q_{line} = Q_{total} / n$, where $n$ is number of lines).
2. Calculate friction loss for one of the individual lines using $Q_{line}$. That single calculation represents total friction loss for the parallel system.

Worked Example 3: Parallel 2.5-Inch Supply Lines

An engine lays two parallel 400-foot lines of 2.5-inch hose ($C = 2.0$) to supply a portable master stream flowing 500 gpm total. Calculate system friction loss.

1. Step 1: Determine Flow Per Line $Q_{line} = \frac{500\text{ gpm}}{2\text{ lines}} = 250\text{ gpm}$
2. Step 2: Calculate Friction Loss for One 250 gpm Line $\left(\frac{250}{100}\right)^2 = 6.25, \quad \frac{L}{100} = \frac{400}{100} = 4.0$ $FL = 2.0 \times 6.25 \times 4.0 = 50.0\text{ psi}$

The Hydraulics Advantage of Parallel Lines

Comparing Example 3 to a single 2.5-inch line carrying the full 500 gpm over 400 feet reveals why parallel lines are vital: $\text{Single Line } FL = 2.0 \times \left(\frac{500}{100}\right)^2 \times 4.0 = 2.0 \times 25 \times 4.0 = 200.0\text{ psi}$ Splitting flow into parallel lines drops friction loss from 200 psi down to 50 psi—a massive 75% reduction in friction loss, saving engine horsepower and fuel while remaining well within safe pump operating limits.