Random thoughts concerning fire sprinklers and the water that passes through them

By Thomas W. Gardner P.E., FSFPE, LEED AP, Alex Munguia P.E., April M. Musser P.E.

Before hydraulic calculations, fire sprinkler systems were designed by the pipe schedule method, which limits the number of sprinklers supplied by piping of a specific diameter. In 1903, after studying recorded friction loss measurements produced by dozens of experimenters, Allen Hazen and Gardner Williams published an empirical formula now known as the Hazen-Williams friction loss formula. Until the early 1970s, using this friction loss formula was tedious, requiring the use of logarithms and slide rules.
Hydraulic calculations were first introduced into NFPA 13 Standard for the Installation of Sprinkler Systems in the 1966 edition. In 1972, the concept of sizing system piping and water supplies based on density and area of expected sprinkler operation was introduced. Between 1966 and 1978, the standard was revised four times to include successively expanded hydraulic design criteria, such as area/density curves for different hazard severities. The advent of electronic calculators and personal computers made application of the Hazen-Williams formula routine and, as a result, hydraulically designed systems eventually became the norm.

This article reviews and discusses selected water supply and hydraulic issues concerning fire sprinkler systems.

Significant digits

The significant digits of a number are those digits that carry meaning contributing to its precision. For example, 1.4136 carries more significant digits and precision than say 1.2. The number of significant digits in an answer to a calculation will depend on the number of significant digits in the data used to derive the answer. Common significant digit mistakes in calculations include reporting more digits in an answer than justified by the number of digits in the data or rounding off to a smaller number of digits in an intermediate calculation and then reporting even more digits in the final answer (e.g., rounding off to two digits in friction loss in each pipe, then adding up the friction loss of several pipes and stating a three-digit total).

Much of the work required by fire protection professionals performing sprinkler system design is based on testing/measuring available water supplies (i.e., hydrant flow test and fire pump tests). Anyone who has ever held a pitot tube in a stream of water discharging from a fire hydrant knows the difficulty of trying to keep the pitot in the correct position and read the velocity pressure from the gauge as the needle “bounces” around, while wiping water off the face of the gauge and out of your eyes. Even if you have never performed such a test, it is obvious that the resulting data will have a significant margin of error. (1)

Unfortunately, many take that test data as gospel (instead of an approximation) and prepare hydraulic calculations without regard to its accuracy. A hydrant water flow measurement of 890.2937 gpm implies a high level of measurement accuracy, which is usually not the case.

Another area where fire protection professionals must be cognizant of significant digits is in the calculation of the sprinkler piping network. As mentioned above, the Hazen-Williams formula is an empirical formula and therefore not an exact derivation of mathematical and physical conservation equations. Therefore, the Hazen-Williams equation has certain limitations, such as not being applicable to turbulent water flow. More accurate fluid flow formulas account for turbulence and the variation of fluid densities and viscosities over a range of temperatures. NFPA 13 requires the Hazen-Williams formula for water-only systems because the density and viscosity of water do not significantly change over the range of temperature where water is used for fire protection and the effect of turbulence is extremely minor. (2)

The good news is that the successful performance of sprinkler systems designed with the Hazen-Williams formula demonstrates an acceptable degree of accuracy. The bad news is that fire protection professionals utilize calculators or computers and therefore report required flows and pressures of two (or more) decimal places. The calculations simply don’t support the reported significant digits. In the book Sprinkler Hydraulics, Harold S. Wass makes this very point and suggests ignoring everything to the right of the decimal point. We suggest something similar: Round demand pressures/flows up to the next whole number and round supply pressures/flows down to the next whole number.

Calculation safety factors

There are a number of unknowns concerning sprinkler system hydraulics, including the following:

• Accuracy of the water supply test data
• Changes (degradation) in the water supply over time
• Corrosion of internal piping surfaces over time
• Building configuration changes that may be detrimental to successful application of sprinkler spray
• Human error

To account for and protect from these unknowns, many authorities having jurisdiction (AHJ) require a safety factor be applied to the hydraulic calculations. Many AHJs require safety factors that are a delta between the required pressure and the available pressure. Sometimes this is specified as a minimum fixed difference, as a percent of the total available pressure (at the demand flow) or as some combination thereof. Although well intended, an arbitrary safety factor irrespective of the slope of the water supply curve may not actually provide much “safety.” This is best illustrated in Figure 1, where a 5 psi difference provides a good safety factor compared to Supply Curve B (280 gpm) but an almost insignificant safety factor compared to Supply curve A (40 gpm).

Some question whether a safety factor should be an amount of pressure or an amount of flow between the sprinkler system demand and the water supply curve. Since system flow and pressure are interrelated, the authors suggest that the safety factor should be the length of the line between the sprinkler system demand point and the point where the demand curve intersects the supply curve (see Figure 2). Equation 1 can be used to calculate the intersection of these two lines on a N1.85 logarithmic graph. Using this approach, a safety factor can be specified as a pressure or flow and will have meaning because it is measured as the pressure or flow component of the sloped line between demand and supply curves.

Inherent sprinkler system safety factors

Fire sprinkler systems have enjoyed an enviable track record since the first sprinkler was invented in 1874. Beyond regulation, good engineering, and inspection/testing/maintenance, sprinklers systems have been successful due to “built in” safety factors including the following (3):

1. Initial densities are higher due to the descending supply curve.
2. Calculations are started with the design density requirement at the end sprinkler and inherently the average density in the system will be higher.
3. The hydraulically most remote areas are calculated; any other configuration of sprinkler operation will produce higher delivered densities.
4. Calculations are developed on a rectangular pattern, which is the most severe condition.
5. The friction coefficient for wet-pip systems will probably average higher than the calculated C=120 resulting in higher delivered densities.
6. The hose stream demand included in the total water supply is available to sprinklers in the early stages of a fire, further increasing the delivered density of the sprinklers.

Safety factor No. 4 is illustrated in Figure 3. Safety factor No. 2 is best illustrated by the following analysis conducted by the authors on a light hazard wet-pipe sprinkler system in an academic building designed to deliver 0.1 gpm/sq.ft. over the most remote 1,500 sq.ft. The hydraulically most remote area contained 17 sprinklers. Successive sprinkler calculations were prepared that modeled the most remote sprinkler operating (Node 601), followed by the two most remote sprinklers operating (Nodes 601 and 602) and so on until all 17 sprinklers were flowing. The results are presented in Table 1.

This analysis indicates that the first sprinkler to operate provides 260 percent of the minimum design density. As more and more sprinklers operate, the density provided by each sprinkler naturally decreases, but, even with all 17 sprinklers operating, the most remote sprinkler still provides 110 percent of the design density. Not until the fourth sprinkler operates does any sprinkler deliver less than 0.2 gpm/sq.ft. With the entire density area flowing, the average density is 0.21 gpm/sq.ft., with the maximum density at Node 604 of 0.32 gpm/sq.ft.

Accounting for hose stream allowances

Sprinkler hydraulic calculations are required to account for the water used by the fire department to manually suppress a fire. This is referred to as a hose stream allowance. Typically this is shown on a hydraulic graph as a line of a length equal to the allowance (in gpm) and extending horizontally from the maximum sprinkler demand. The problem with this depiction of the total system demand versus the supply is that the hose streams are not flowing at the maximum pressure demand of the sprinklers and not just at flows higher than the maximum sprinkler demand.

In reality, the fire department is “taking this amount of water away” from the available supply and the sprinkler system is “left” with a degraded water supply curve. This concept has been developed and promoted by J. Michael (Mike) Thompson, P.E.; a founding partner of the Protection Engineering Group. Mike has developed software providing a number of hydraulic tools, one of which plots supply vs demand curves in this fashion.

Density

Concerning sprinkler system design, fire protection professionals speak in terms of density; the rate of water application per unit area at the floor level. For example, an office space would typically be protected by a sprinkler system designed to deliver 0.10 gpm/sq.ft. This doesn’t sound like much water, but that conclusion is usually a result of never witnessing an actual sprinkler system discharge. Fire protection professionals should not only know what NFPA 13 requires for various hazards but they should also have a “feel” for the numbers if they are to truly understand how these systems can/will perform.

Participating in an actual sprinkler discharge demonstration or experiment is best to truly understand these designs, but short of that consider the following scenario: An Ordinary Hazard, Group 2 sprinkler system in a room that measures 10 feet wide x 10 feet long x 8 feet high operates and delivers 0.20 gpm/sq.ft. over the entire room’s floor area. Assume the room is watertight. After 10 minutes of discharge, the room would contain 200 gallons of water. That would be 3.2 inches deep across the entire room and weigh 1,670 pounds.

Such a feel for the density gives the fire protection professional a better understanding of the sprinkler system’s power, which is important when solving unusual problems or justifying a performance-based design.

Conclusion

The above examines five random topics concerning fire sprinklers system hydraulics. These and other issues must be well understood by fire protection professionals as part of designing a system that will not only comply with the requirements of NFPA 13 but also will provide the protection intended by the design professional.

Thomas W. Gardner, P.E., FSFPE, LEED AP, Alex Munguia, P.E. and April M. Musser, P.E. are from The Protection Engineering Group Inc. For more information, visit www.pegroup-inc.com.