**BY PAUL SPURGEON**

The pump operator has a distinct responsibility to keep the crews at the end of the fire hose safe. He/she has to do this without usually ever seeing the seat of the fire. It is the pump operator’s responsibility to produce a proper fire stream while standing at the pump panel, which sometimes can be a distance away from the fire. This can only be done by knowing how to calculate a correct discharge pressure, which, in turn, delivers the proper flow rates your crews need.

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To calculate the discharge pressure, figure the following formula:

**DP = NP + FL + APP + ELEV**

** **Where DP = Discharge Pressure

NP = Nozzle Pressure

FL = Friction Loss

APP = Appliance FL

ELEV = Elevation

Nozzle pressure (NP) is a number usually assigned by the nozzle manufacture or by trial and error. There are some traditional nozzle pressures, but more and more nozzles are being introduced for which the manufacturers recommend different pressures. The nozzle pressure is needed to calculate other formulas such as flow rates, nozzle reaction, and friction loss. The nozzle pressure is usually needed as a starting point in making further calculations.

Friction Loss (FL) is the loss in pressure in the hoselines caused by friction between the water and the lining of the hose, the couplings, and even itself. Numerous factors affect friction loss; it would take too long to cover them in this article. The important thing to know is that friction loss can be precisely calculated. This loss can be determined using any number of formulas.

The first and oldest is the Underwriters Formula”

FL = 2Q^{2 }+ Q

Q = Gallons per Minute (gpm)/100

For flows under 100 gpm, replace the + Q with ½Q (2Q^{2} + ½Q).

Newer versions of this formula simply leave off the + Q or ½Q.

This formula is designed for 2½-inch hoselines. If you are using a different size hoseline, multiply or divide your answer by a conversion factor.

**Conversion Factor**

1½ inch 12.99 or **13**

1¾-inch 5.98 or **6**

2-inch 3.05 or **3**

3-inch 2.49 or **2.5 (divide)**

This is the old, tried and true method for calculating friction loss. When you finally get a finished number, you then need to multiply that number by the number of 100 foot lengths of hose in the hoseline. This is not a very quick method to use on the fireground.

Another method of calculating friction loss is using the Coefficient Formula.

**CQ ^{2}L**

C = Coefficient

Q = Gpm / 100

L = Length in 100 feet

A coefficient is simply a number used for different hose sizes. The following table shows the coefficients for different hose sizes.

1¾-inch **15.5**

2½-inch **2.0**

3-inch **.80**

4-inch **.20**

** **5-inch **.08**

This formula is slightly easier because all you need do is to plug the numbers in the formula.

C = coefficient

Q^{2} = GPM/100

L = 100 feet length of hose

The only true way of figuring the friction loss is to test the hose itself. Place a pressure gauge at the beginning of the hoseline and another at the end, and subtract the difference. A department can test all of its hose and come up with an average. There are so many variables that can affect friction loss that this may be the only way to accurately figure your friction loss.

Friction loss is the most complicated calculation to make when developing a proper fire stream. Whatever method you or your department chooses, get proficient with it. It gets easier with practice.

Appliance Friction Loss (APP) is the loss of pressure when the water runs through the appliance. All of the same causes of friction loss in hoses are applicable to appliances. Appliances are designed to work in conjunction with hoses to help deliver the water. Appliances can be used to combine or divide hoselines or to help deliver the water to where it needs to go. Every water appliance used in the fire service, from a wye to a ladderpipe, has friction loss. Just as with hoselines, every time water changes direction, more friction loss is created. As the water is split, combined, or as it moves through the appliance, it will change direction, which causes friction loss. Just as with hoses, the friction loss can be measured using pressure gauges or using the number the appliance manufacturer assigns based on various flow rates. Pump operators should know what appliances are on their apparatus and their friction losses.

Elevation is the last calculation we need to finish the equation. Many times, the elevation change is minimal, but the pump operator needs to be aware of it at all times. Although the pressure caused by elevation may be minimal, it can be a factor to the crews at the nozzle.

The downward pressure of a liquid is directly proportional to its depth. This is a law of nature based on gravity. A 1- by 1-inch column of water standing 1 foot tall will have a pressure at its base of 0 .434 pounds. The pressure will increase by 0.434 pound for every foot added to the height. Pump operators need to adjust for this pressure. The amount of pressure created by gravity depends on the height of the level of the water in comparison to where it is being used. For example, a column of water 50 feet tall will create a pressure of 21.7 pounds at its base (0.434 × 50). The pump operator needs to determine the height at which the nozzle is working and multiply it by 0.434.

On the fireground, our calculations don’t need to be so precise. To make calculations quickly, round 0.434 to 0.50 or ½ pound per foot. If you are taking a written test, use 0.434 pounds. On the fireground, we can make things easier and use ½ pound per foot. To make things even easier, figure the height, and divide in half.

Now we have a simplified explanation of fire service hydraulics. Every time a hoseline is placed in action, this formula needs to be figured. Some calculations can be simple; others can be complex, using multiple figures for each portion. For example, a single handline laid on flat ground needs only NP + FL. On the opposite end, laying multiple lines into an elevated master stream device can have a nozzle pressure, multiple friction loss figures, multiple appliances, and elevation. Practice these calculations over and over until they become second nature.

**BIO**

**PAUL SPURGEON**, a 22-year veteran of the fire service, began his career with the Denver (CO) Fire Department in 1991. In 1998, he was promoted to the rank of engineer and assigned to Engine 7 in northwest Denver. He received his AAS degree in fire science technology from Red Rocks Community College. He is the author of *Fire Service Hydraulics and Pump* *Operations* (2012).

* Originally ran December 2, 2014.*