What this calculator does
A sprinkler system is sized on the hydraulically most remote head, and then it has to satisfy every other head on the way back to the riser. The two requirements fight each other: the remote head sets the pipe sizes, but the heads nearest the riser are the ones that over-pressure and discharge more than their K-factor predicts. Most of the judgement in a sprinkler layout is about that balance, and it is invisible in a single flow calculation.
How to use it
- Enter the supply pressure at the riser and the design flow for the branch.
- Add the pipe runs in order, outward from the riser, with each run's length, diameter and C factor. The order matters: the loss accumulates along the branch.
- Add each sprinkler head type with its K-factor and how many of them are on the branch. K-factors are not interchangeable between types and ratings, so yours are the ones that count.
- Read the residual at both ends of the branch against the band you entered. The riser end is the over-pressure risk and the remote end is the under-pressure risk.
Governing method
h_f = 10.67 · L · Q<sup>1.852</sup> / (C<sup>1.852</sup> · d<sup>4.87</sup>) → Q = K · √P Where:
-
= Run length, metres -
= Flow, m³/s -
= Hazen-Williams factor for the pipe -
= Internal diameter, metres -
= Sprinkler discharge coefficient
Derived Equations:
residual = supply − Σ h_f imbalance = nearest − remote Assumptions & limitations
- Supply pressure, design flow, pipe sizes, lengths, C factors, K-factors and both pressure limits are your inputs. This tool holds no pipe schedule, no sprinkler catalogue, no friction-factor table and no code, and looks nothing up.
- This is a static balance at design flow. Surge on system start, the flow pattern of a partially flowing system, and the consequences of an obstruction are not modelled.
- The whole design flow is assumed to pass every run, which is correct for the hydraulically most remote branch and conservative for nearer ones. A full branch-line tree is not calculated.
- A pipe too small for the flow is refused rather than reported, because Hazen-Williams will faithfully return an enormous loss for an absurd velocity and that reads like a result rather than a sizing error.
- A pass here is not a fire-code approval. Occupancy classification, sprinkler spacing and coverage, allowable limits, hose allowance, fire pump sizing and the required residual at the most remote head are all outside this tool.
Worked example — 13 L/s on 65 mm and 50 mm pipe
| Supply pressure | 4 bar |
|---|---|
| Riser to tee | 6 m of 65 mm, C = 120 |
| Branch | 12 m of 50 mm, C = 120 |
| Heads | 8 × K80 pendants |
| Residual band | 3.5 to 12 bar |
13 L/s through 32 mm would be 16 m/s, which is why a 50 mm branch is needed and not something smaller. The friction loss across both runs leaves the remote head below the supply pressure while the heads at the riser see the full supply — and that difference is the imbalance this tool exists to make visible.