# Sprinkler flow calculations (head flow +  friction)



## Coolcat (Aug 26, 2022)

I'm an engineer who started a new job assisting with project management and the like, and one of the things was the check the sprinkler design that was proposed for one of our buildings, not sign off, but just to get an understanding. It doesn't need sprinkler yet, but more levels may come, so owner/engineer wants to be ready.

I found this website where they go through a sample calculation and it seems straight forward enough:





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						Fire Fighting Hydraulic Calculations
					

Fire Fighting Hydraulic Calculations




					www.kamal-mech-engr.com
				




Basically start at farthest sprinkler, assume a flow or pressure per the minimums, then calculate the sprinkler flow/pressure via discharge formula, then work backwards using Hazel-Williams friction losses. Easy enough.

They did an example, and they ended up with this:






They started at 1, assuming 15 gpm/7psi, worked back to 2, solved for a new pressure/flow then junction 2A to get a pressure of 11.544 psi, and this is where I get lost. How can they assume that tiny branch to 3 will see the same pressure drop as the 10x longer branch to 1? They can't. Which means the pressure/flow is going to be considerably higher than 15gpm at 3, as the pressure will not drop from 11.544 psi to 7psi. More like 11 psi at best, resulting in a flow of something like 18.6gpm.

This in turn means that the flow rate from 3A to 2A will not be 45.6 gpm, but 49.2 gpm, which in turns means the friction will be higher, which in turn will result in lower pressure at junction 2A, which in turn lowers flow to sprinkler 3, which in turn decreases friction and it goes on back and forth until in more or less stabilizes numerically. This is possible to do in excel, just put in circular references and have it run until the values stabilize, and is most likely how various numerical CFD systems work to evaluate fire suppression flow.

The further problems in that the author just copies Branch 1-2 into 5-6 and 10-11. Essentially every sprinkler aside from 1 is going to see pressures and flow higher than 7psi/15gpm (unless you incorporate specific throttling valves etc), could all these increased flows (and associated pressure drops) not leave you with a system somewhat under powered?

Am I missing something? Or just vastly over thinking it.


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## steveray (Aug 29, 2022)

Impressive first post....Welcome to the forum!...Hopefully one of the fire guys jumps on this as that is not my specialty....


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## IJHumberson (Aug 30, 2022)

Welcome, Coolcat! You are absolutely correct - in a "tree" system such as you've shown, there will only be one sprinkler flowing the minimum flow, and that will be the 'hydraulically remote' sprinkler. All the other sprinklers will be of a higher flow due to the pressure required to drive the minimum flow to the hydraulically remote sprinkler, with the flows becoming higher and higher as you work the calculation toward the water source. If the system were laid out to be better balanced/similar on both sides of the feed main, then the flow would be better balanced on the last branch lines to each side the the main, but each of the subsequent branch lines working toward the source will still have higher flows. The methodology in the example will significantly underestimate the required sprinkler flow. 

Additionally, they're only calculating the _minimum _required pressure (7 psi) at the hydraulically remote sprinkler, which, for the typical commercial sprinkler (1/2-inch orifice, K=5.6) will only flow 14.8 gpm (they've rounded it 15). With a maximum design of 14.8 gpm at the remote sprinkler, it would limit the sprinkler spacing to 148 sq.ft. per sprinkler for Light Hazard Occupancy (which requires 0.1 gpm/sq.ft.). This is going to require a LOT more sprinklers and pipe than would be required if the system were designed to the maximum allowable 225 sq.ft. per sprinkler for Light Hazard Occupancy. Moreover, the design shown will limit any Ordinary Hazard areas to a maximum of 99 sq.ft. per sprinkler (and only 74 sq.ft. per sprinkler in Ordinary Hazard Group 2 areas). IMHO, not a very smart way to estimate sprinkler demand for a new system.

I would suggest you check out Meyer Fire website (www.meyerfire.com) - they have a great Forum, and a lot of excellent resources (some of which are subscription based).

Good luck!


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