Often times in designing our sprinkler systems, we need to use formulas to arrive at a value that is useful to us and our work. In these formulas there are variables and constants that we may or may not understand but we mindlessly plug them into equations anyway because we know them by heart. The Hazen-Williams formula is the formula we will most often use when calculating our sprinkler system. In Hazen-Williams we need to input the inside diameter of the pipe be used, the flow in gallons per minute, and the C Factor of the pipe to derive the friction loss for 1′-0″ of pipe. From memory we can probably recite the C values, 150 for CPVC, 120 for black pipe used in a wet system, and 100 for black pipe used in a dry system, etc, etc. Perhaps in the course of our experience we learned that the C Factor represents the roughness on inside of the pipe, which is true. But what does the number actually represent and how does it actually affect our calculations?
As stated before, the C Factor is a representation of the roughness of pipe. To find out the reason why we need to measure or represent the roughness of the pipe, we must first learn a little about how water likes to flow. Water likes a nice, smooth, easy, and straight path to flow in, this is called a laminar flow. In laminar flow conditions, there are few obstructions disturbing the flow path of water which results in very little friction loss. It should be fairly obvious that obstructions to the flow path of water causes friction loss through the pipe meaning it takes more pressure for a given amount of water to flow through a section of pipe with many obstructions then it would have it there were fewer obstructions.
Too many obstructions and the laminar flow will change into what is called turbulent flow. Turbulent flow is when the water makes contact with the obstruction and changes its direction. We have all seen swirls and eddies in a river formed by water constantly changing directions…this is turbulent, not the nice and smooth path water likes to flow in. Again, the more obstructions to the flow path, the more turbulent the water. The more turbulent the water, the more friction loss through the pipe. So what are obstructions in a pipe? Inside walls of a pipe (represented by our C Factor), fittings, turns in the pipe, grooves from roll grooved pipes, and even the water itself.
Over time, the inside surface of most pipe may corrode or scale. Corrosion will “pit” the pipe’s inside surface creating valleys or holes. Scaling of pipe is the undesirable build up of material that attaches itself to the inside surface of the pipe creating little bumps. These valleys, holes, and bumps obstruct and change the direction of the water. Have you ever looked into a new steel piece of pipe? Pretty smooth right. How about a new piece of CPVC pipe? It looks similar to the steel pipe. Why do the two pipes not have the same C Factor? This is because the C Factor tries to account for the corrosion and scaling of pipe over the useful life of the system. When we input the C Factor into our equation, we are not using the C Factor to represent the new pipe we are installing. Instead we input a C Factor that represents what the pipe’s inside conditions could be like in 20, 30 or 40 years down the road. A side note, this is why CPVC pipe has a 150 C Factor, it does not corrode and scaling rarely occurs. The inside of the CPVC pipe should be same today as it is years from now.
So how does the C Factor affect our calculations? First, we need to look at the C Factor values given in NFPA 13, they range from 100 to 150. The rougher the inside surface of the pipe, the lower C Factor value of the pipe (think black steel pipe in a dry system). The smoother the inside surface of the pipe, the higher C Factor value of the pipe (think CPVC pipe). Second, we need to look at where in the Hazen-Williams formula the C Factor is used, which is the denominator. We remember from elementary school math that the larger the denominator, the smaller the fraction. The smaller the denominator, the larger the fraction. Since the C Factor resides in the denominator, a large value for C helps contribute to a smaller result of the Hazen-Willams formula. Remember, the Hazen-Williams formula measures friction loss through 1′-0″ of pipe. The smaller the result of the Hazen-Williams, the less friction loss. The higher the result of Hazen-Williams, the higher the friction loss. So when our pipe has a larger C Factor, it helps contribute to a smaller friction loss through that section of pipe.
I hope this post helps clarify what the C Factor represents and that the next time you are calculating a system, you are confident in knowing the effects of this value in your calculations.
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