Type a line (K 80 at 2 bar 12 nozzles) or fill in the fields: the line and the fields stay in step.
Enter the K-factor of a sprinkler or nozzle and the pressure at the nozzle, and the calculator gives the flow of one nozzle, and with a number of nozzles the total at the same pressure. It works the other way round too: the pressure for a given flow, and K from a measured flow and its pressure. It suits sprinklers, water spray and water mist nozzles and fire hose nozzles whose K is known. It shows the working with your numbers, draws the flow against the pressure for your K, and gives a line you can copy or add to a request.
K comes from the nozzle data sheet or its marking. A K in l/min/bar^0.5 and a K in gpm/psi^0.5 are different figures: the calculator converts them from the definitions of the US gallon and the psi, and shows how. It gives no design densities, minimum pressures or system rules: design figures come from the approved system documents.
Q = K x P^0.5: the flow rises with the square root of the pressure, not in step with it. A sprinkler of K 80 l/min/bar^0.5 at 2 bar gives 80 x 1.41421 = 113.1 l/min; at 8 bar, four times the pressure, it gives twice the flow, 226.3 l/min. Twelve of them at 2 bar give 1358 l/min.
The pressure for a flow: P = (Q / K)^2, for 120 l/min with K 57 that is 4.43 bar at the nozzle. K from a test: K = Q / P^0.5, for 95 l/min at 3.5 bar that is 50.78 l/min/bar^0.5. The pressure is at the nozzle inlet: the loss in the pipe up to it comes on top.
A K in l/min/bar^0.5 and a K in gpm/psi^0.5 are different figures for one nozzle. From the unit definitions, 1 gpm/psi^0.5 = 3.785411784 / 0.0689475729^0.5 = 14.416 l/min/bar^0.5, so K 5.6 is 80.7. References round the factor a little differently, so the data sheet figure, where it gives both units, is the one to use.
| Quantity | Relation | Note |
|---|---|---|
| Flow | Q = K x P^0.5 | flow per nozzle; P the gauge pressure at the nozzle |
| Pressure for a flow | P = (Q / K)^2 | the pressure at the nozzle inlet, before any pipe loss |
| K from a test | K = Q / P^0.5 | flow and pressure measured at the same time |
| N nozzles | Q total = N x Q | every nozzle at the same pressure |
| K: US to metric | 1 gpm/psi^0.5 = 3.785411784 / 0.0689475729^0.5 | = 14.4163 l/min/bar^0.5 |
| K: kPa and bar | K (l/min/kPa^0.5) x 10 | = K (l/min/bar^0.5), as 1 bar = 100 kPa |
| Units | 1 US gallon = 3.785411784 l; 1 psi = 0.0689476 bar | 1 m3/h = 16.667 l/min; 1 l/s = 60 l/min |
The pressure is the gauge pressure at the nozzle inlet. The flow is per nozzle; the total for N nozzles takes them all at one pressure, while in a system the pressure differs from nozzle to nozzle, and the real flow of the system comes from its approved hydraulic calculation.
The relation Q = K x P^0.5 and its two inverted forms, with K in l/min/bar^0.5 or gpm/psi^0.5 and the pressure at the nozzle, are given in the hydraulic calculation references and study guides for fire protection systems, for sprinklers and for water mist and deluge nozzles; the same square-root relation is used for fire hose nozzles in fire service hydraulics. That K is given on the nozzle data sheet and in its marking is stated in the same references. The K conversion is worked out here from the definitions of the US gallon (3.785411784 l) and the psi (6.894757 kPa) in the national unit conversion tables; the rounded factors published differ a little.
Q = K x P^0.5: the flow per nozzle is K times the square root of the gauge pressure at the nozzle inlet. K comes from the nozzle data sheet or its marking. A nozzle of K 80 l/min/bar^0.5 at 2 bar: 2^0.5 = 1.41421, Q = 80 x 1.41421 = 113.1 l/min. In US units, K 5.6 gpm/psi^0.5 at 20 psi: 20^0.5 = 4.47214, Q = 25.04 gpm. The units go together: l/min with bar for a metric K, gpm with psi for a US K.
P = (Q / K)^2, the same relation turned round. For 120 l/min from a nozzle of K 57: 120 / 57 = 2.10526, and P = 2.10526^2 = 4.43 bar at the nozzle. That is the pressure at the nozzle inlet: the pressure lost in the pipe and fittings up to the nozzle comes on top of it.
K = Q / P^0.5. A nozzle that passes 95 l/min at 3.5 bar: 3.5^0.5 = 1.87083, K = 95 / 1.87083 = 50.78 l/min/bar^0.5, or 3.522 gpm/psi^0.5. The flow and the pressure have to be measured at the same time, with the pressure at the nozzle; compare the result with the K on the data sheet or the marking.
From the unit definitions: 1 US gallon = 3.785411784 l and 1 psi = 0.0689475729 bar, so 1 gpm/psi^0.5 = 3.785411784 / 0.0689475729^0.5 = 14.416 l/min/bar^0.5. K 5.6 gpm/psi^0.5 is 80.7 l/min/bar^0.5. References round the factor a little differently, and the nominal classes are rounded too: K 5.6 is usually called K 80 in metric. Where the data sheet gives K in both units, use its figure. A K in l/min/kPa^0.5 is one tenth of the l/min/bar^0.5 figure.
N x Q with every nozzle at the same pressure: 12 nozzles of K 80 at 2 bar give 12 x 113.1 = 1358 l/min. In a real system the pressure differs from nozzle to nozzle, higher near the supply and lower at the far end, so the flow of the system comes from its approved hydraulic calculation, not from this sum.
None. It gives no design densities, no minimum pressures and no system rules: design figures come from the approved system documents. It works out the flow, the pressure or the K for the nozzle and the figures entered, with each step shown.
The calculator gives the flow, the pressure and the K of a nozzle. When sprinklers, nozzles or fire hose nozzles are needed, send the line from the calculator with the marking or the data sheet and a photograph, and Vessel Core checks the details before an offer goes back.
