Proficiency in the mental arithmetic of hydraulics will pay dividends on the foreground and in the boardroom. Third in a series.

Nozzle reaction, the force pushing a nozzle in the direction opposite the flow of water, operates on the same principle as the recoil of a gun and the thrust of a rocket engine—Newton’s Third Law of Motion, “Every action has an equal and opposite reaction.” Anyone who has held a fire hoseline has felt nozzle reaction.

To darken fires the flow rate must be maximized to whatever nozzle reaction the nozzleman can safely transmit to the surface he is standing on. This requires an understanding of nozzle reaction.

In Fire Service Hydraulics (Fire Engineering Books, 1970) the formula for nozzle reaction R in pounds given is R = 2 x P X A, where P — pressure at the nozzle tip in pounds per square inch (psi) and A = area of nozzle discharge opening in square inches. Since a modern firefighter should know the nozzle’s flow rate in gallons per minute (gpm ), it is convenient to rework the equation by substituting the Freeman equation for flow rate through an orifice (the nozzle). The Freeman equation is gpm = 37.83 X Cd X A X /P, where Cd = discharge coefficient, which is assumed to be 1, and P means “the square root of P.” Solving for A in the Freeman equation and substituting it in equation R = 2 X P X A gives R = 2 x gpm x /P/37.83. This is approximately equal to R = gpm X JP/20.

Fog nozzles. For most fog nozzles the tip pressure is taken to be 100 psi. Since the square root of 100 is 10, the nozzle reaction for a fog nozzle is R = gpm x 10/20 – gpm/2. That is, the nozzle reaction is half of the flow rate in gpm, which is easy to calculate in your head.

Smooth-bore nozzles. For a smooth-bore nozzle, which can be assumed to operate at a tip pressure of SO psi, the nozzle reaction is R = gpm X 50/20 gpm X 7/20 = 0.35 X gpm. This reaction force is equal approximately to one-third of the flow rate in gpm.

Note that smooth-bore nozzle reaction is only 2 (or 1/1.4 or 0.7) of a fog nozzle’s reaction —that is, 0.7 x gpm/2. Comparing the two nozzle types reveals an advantage of the smooth-bore nozzle in that, for the same flow, the reaction is 70 percent of that of a fog nozzle set for straight stream. For example, the traditional 2*/2-inch hoseline with a 250-gpm fog nozzle has a nozzle reaction of 250/2 = 125 pounds at 100 psi. The equivalent 1 ⅛-inch smooth-bore tip flowing about 250 gpm at 50 psi has a nozzle reaction of only 125 x 0.7 = 100 x 0.7 + 25 X 0.7 = 70 + 17.5 = 87.5 pounds.

Before you rush out to buy smoothbore tips there are a few more factors to consider, such as reach, which will be discussed in a subsequent article. Also, when a fog nozzle is used in a spray pattern, the nozzle reaction is reduced. In a 90-degree (wide) pattern it would be reduced to 1 2 or 70 percent of the straight stream reaction. This brings the reaction down to that of a smooth-bore tip.

Low-pressure fog nozzles. A lowpressure fog nozzle (see “Taking the Pressure Off,” Fire Engineering, December 1990, p. 58) operating at 75 psi will have a theoretical reaction of R = gpm X P/20 = gpm x /75/20 = gpm x 0.43 or 86 percent of the reaction of a fog nozzle operated at 100 psi and flowing the same gpm. You can estimate this in your head by remembering that 75 psi is halfway between the 100 psi standard fog nozzle pressure and the 50 psi standard smooth-bore pressure, so the 75 psi nozzle reaction will be roughly halfway between the 100 psi fog nozzle reaction (gpm/2) and the smoothbore reaction (gpm/3) —that is, R = gpm/2.5 = 4 x gpm/10. It is easy to estimate this by doubling the gpm twice and then dividing it by 10.

For example, a fog nozzle flowing 250 gpm at 75 psi will have a reaction of roughly 2 x 2 x 250/10 = 100 pounds. The actual value is 108 pounds. Compare this with a fog nozzle flowing 250 gpm at 100 psi, which has a reaction of 125 pounds, and to a smooth-bore flowing 250 gpm at 50 psi, which has a reaction of 87 pounds. For the same flow rates, a low-pressure fog nozzle operated at 75 psi therefore has a reaction roughly halfway between that of a fog nozzle at 100 psi and a smooth-bore operated at 50 psi, as expected.

Constant gallonage nozzles. If a constant-gallonage nozzle is operated at 75 psi, the nozzleman should feel only 75 percent of the reaction at 100 psi, which looks at first like a great advantage. Let’s look more closely. As explained in the previous articles in this series, because of lowered tip pressure the flow will be reduced by the familiar square root of the pressure ratios to 86 percent (0.75). At 75 psi, a 250 gpm fog nozzle will flow only 217 gpm, reducing the size of the fire that can be knocked down. Also, the reach will be decreased and the droplet size will be increased—this may not be advantageous.

To darken the same size fire, the flow must be kept constant at 250 gpm. This means that the nozzle baffle must be opened, requiring internal adjustment. If the nozzle is set to flow 250 gpm at 75 psi, the reaction will be 108 pounds, which is not a big improvement over 125 pounds.

Note: Constant gallonage only means that at a constant tip pressure, the flow rate in gpm will be the same for any pattern.

Another important consideration applies to the modern practice of maximizing the gpm for attack by using 1 ¾-inch or 2-inch hose with a high engine pressure of 200 psi or above. For example, 200 feet of 1 ¼inch hose with a fog nozzle will flow 200 gpm with an engine pressure of 200 psi. This will give a reaction of 100 pounds. When the nozzle is first opened, the initial pressure at the nozzle tip can be as high as 200 psi. This will increase the flow by 1.4 times to 280 gpm at a pressure of 200 psi (see “The Smooth-Bore Nozzle,” Fire Engineering, October 1990) The reaction will be R = gpm X , P/ 20 = 280 X 200/20 = 280 X 2/2 = 140 X 1.4 = 140 X (1 + 0.4) = 140 + 56 = 196 pounds. This is why a nozzle should be opened slowly!

A zealous volunteer discovered the power of initial nozzle reaction when, contrary to procedure, he suddenly fully opened his nozzle in straight stream while running toward a fire. The force with which the nozzle broke the siding of an adjacent building confirmed both a nozzle’s power as a forcible entry tool and the importance of taming that power.

When a hoseline is straight behind the nozzle, the reaction is transmitted along the hose. In practice, a hoseline never is perfectly straight, but correct stance can be used to transmit the maximum reaction along it and subsequently to the ground, minimizing the force that the nozzleman must resist. Having a backup man straighten the hose behind the nozzleman and hold it down also makes it very easy to handle.

I have seen four or five men struggling to control a 250-gpm line. One person, using a suitable technique, can easily control a 350-gpm line. Being able to calculate nozzle reaction in your head is the first step toward taming the power of the fire nozzle.

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