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# Sprinkler flow calculations (head flow + friction)

## Sprinkler flow calculations (head flow + friction)

(OP)
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:

Hydraulic Calculations

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. Additionally I was told that really only the last 3/5 heads need to be evaluated, as all heads won't be likely to go off at the same time, so is that just enough of a safety factor there to account for the potential lack of pressure or flow?

### RE: Sprinkler flow calculations (head flow + friction)

You put the cart before the horse

First

What is the available water supply? Static, Residual and GPM? How far is the flow test from the site? When was the test done and who did it? Do you need a new test? If the water supply is not adequate you may need a new water main, or fire pump or a pump and tank. Do not assume the water supply is no big deal! Big  if you do.

Second

What is the occupancy and the required sprinkler design based on the code in place? What does the property insurance carrier require? Warehouse look out they can change a simple thing ie plan on pallet and someone decides racks are the way to go!

Get this wrong and no one will approve or sign off on the plan review. When I reviewed sprinkler plans from an insurance point of view they got this wrong! Fold the plans up, yea old guy here, they were paper back then, and write a rejection letter!

Fun!

### RE: Sprinkler flow calculations (head flow + friction)

#### Quote (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.)

Correct, Q3 will not equal Q1. Instead, you should calculate the friction loss between Q3 and node 02A, then solve for its K factor and balance the flow to the pressure arrived at by the opposite branch line which is about 11.3 psi. Everything after node 02A is wrong. You are also correct, there can be only one pressure at a point. So the flow and pressure between both branch pipes must balance at the node 02A. One could copy the branch pipes in the calculations but they would have to use the K factor of the branch line to balance the flow of the to the pressure in the main.

All of the sprinklers on the end of the lines are the same pressures and flows, which is not possible as it violates Bernoulli's theorem (unless they all have unique K factors).

Your last comment is also wrong. Typically a designer will calculate all the sprinklers in a given area such as 1,500 sqft or calculate a number of sprinklers like 12 for ESFR storage sprinklers. The only time one would calculate so few as 3-5 sprinklers would be a house or apartment.

LCREP is correct, whatever the demand of the fire sprinkler system, the water supply has to be greater. If the water supply cannot meet the sprinkler demand, a pump and/or tank must be provided.

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