Sprinkler Flow (K-Factor)
Calculate the flow of an automatic sprinkler, Q = K × √P, from the head's K-factor and the pressure at the sprinkler P. The result, in L/min, is the water discharged by the sprinkler at a given pressure — the basis of the hydraulic design of sprinkler systems, which must ensure enough flow and application density over the most unfavourable operating area. The K-factor characterizes the orifice (the larger it is, the more flow at the same pressure). Mind the units of K and P, which must be consistent. Enter the K-factor and the pressure.
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Sprinkler flow (K-factor)
An automatic sprinkler is, hydraulically, a calibrated orifice: water leaves it at a flow that depends on the available pressure and the nozzle size. That relationship is the K-factor formula: Q = K × √P, where K is the nozzle's discharge coefficient (it characterizes the orifice) and P is the pressure at the sprinkler head. Flow grows with the square root of pressure — to double the flow, the pressure must quadruple. This behavior is the heart of the hydraulic design of sprinkler networks, which must guarantee, simultaneously, that the most remote sprinkler (the farthest and highest relative to the pump) still receives enough pressure to deliver the minimum flow, and that the set of sprinklers operating over the design application area produces the density (L/min/m²) required by the hazard class. Larger-K nozzles (big orifices, ESFR) deliver plenty of water at low pressure, ideal for high hazards; smaller-K nozzles serve light hazards. Mind the units: K is tabulated differently depending on whether P is in bar or kPa — use consistent values. Enter the K factor and the pressure.
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Required Fire Flow
Calculate the water flow required for a firefighting system, Q = area × application rate, multiplying the operating area (m²) by the required application density (L/min per m²). The result, in L/min, is the minimum flow the sprinkler or spray system must deliver over the most unfavourable area to control the fire. The application rate depends on the occupancy's hazard class — the higher the fire load and combustibility, the higher the density required by codes (NBR/NFPA). It is the basis of hydraulic design and water reserve. Enter the area and the application rate.
Hydraulic Retention Time (HRT)
Calculate the hydraulic retention time (HRT) of a reactor or tank, HRT = volume ÷ flow, dividing the working volume (m³) by the influent flow (m³/h). The result, in hours, is the average time the liquid stays in the unit and is decisive in designing clarifiers, anaerobic reactors, lagoons and aeration tanks: short times prevent reactions or settling from completing, while long times raise cost and footprint. Enter the working volume and the inlet flow.
Smoke Plume Mass Flow
Calculate the mass flow of a fire's smoke plume by the Heskestad correlation, ṁ = 0.071·Q̇_c^(1/3)·z^(5/3), from the convective part of the heat release rate Q̇_c (kW) and the height above the fire base z (m). The result, in kg/s, is the amount of hot gases and smoke rising and accumulating, governing the design of smoke control and exhaust systems (mechanical or natural) that keep a smoke-free layer for safe evacuation. The flow grows strongly with height. Enter the convective heat fraction and the height.
Number of Sprinklers
Calculate the number of automatic sprinklers needed, N = area ÷ coverage area per head, dividing the total area to protect (m²) by the maximum coverage area of each sprinkler (m²). The result is the minimum number of heads to cover the space, spaced within code limits (coverage per head depends on hazard class and sprinkler type). In practice, always round up and adjust to the piping and beam layout. It is an initial quantity calculation in sprinkler system design. Enter the area to protect and the coverage area per head.
Spillway Discharge (Creager/Ogee)
Calculate the discharge over a Creager/ogee dam spillway, Q = C·L·H^1.5, from the discharge coefficient C (typically 2.0-2.2 in SI for well-designed ogee profiles), the crest length L (m) and the head over the crest H (m). The spillway is a dam's most critical safety structure: it releases floods safely, preventing overtopping — the leading cause of dam failure. The ogee profile follows the shape of the underside of a free nappe, maximizing discharge while keeping crest pressure near atmospheric (avoiding cavitation). The coefficient C absorbs gravity and approach effects, exceeding that of a sharp-crested weir. Spillway design starts from the design flood (often the 10,000-year flood or the PMF) and sets the required crest length. Enter the discharge coefficient, crest length and head.
Fire Water Reserve (RTI)
Calculate the fire water reserve volume, V = flow × time ÷ 1000, multiplying the system's required flow (L/min) by the required autonomy time (min) and converting to cubic metres. The result, in m³, is the water volume the tank must keep reserved exclusively for firefighting — sized to feed hydrants and/or sprinklers for the minimum time set by codes (typically 30 to 60 min, depending on risk). It is a central calculation in building firefighting installation design. Enter the flow and the autonomy time.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.