| Cubic feet per hour (ft³/h) | Cubic millimeters per second (mm³/s) |
|---|---|
| 1 Cubic foot per hour | 7865.79071944 mm³/s |
| 2 Cubic feet per hour | 15731.5814389 mm³/s |
| 3 Cubic feet per hour | 23597.3721583 mm³/s |
| 4 Cubic feet per hour | 31463.1628778 mm³/s |
| 5 Cubic feet per hour | 39328.9535972 mm³/s |
| 10 Cubic feet per hour | 78657.9071944 mm³/s |
| 20 Cubic feet per hour | 157315.814389 mm³/s |
| 25 Cubic feet per hour | 196644.767986 mm³/s |
| 50 Cubic feet per hour | 393289.535972 mm³/s |
| 100 Cubic feet per hour | 786579.071944 mm³/s |
| Reference | Cubic feet per hour (ft³/h) | Cubic millimeters per second (mm³/s) |
|---|---|---|
| A domestic shower | 19.0699 ft³/h | 150000 mm³/s |
| A kitchen tap | 21.1888 ft³/h | 166667 mm³/s |
| A garden hose | 31.7832 ft³/h | 250000 mm³/s |
| The Amazon river | 2.65708 × 1010 ft³/h | 2.09 × 1014 mm³/s |
The cubic foot per hour is a unit of volumetric flow rate equal to one cubic foot passing a point every hour. Its symbol is ft³/h, and in the gas trades it is abbreviated CFH. It is the unit of fuel gas supply throughout North America, where every appliance and every pipe is sized by it.
Natural gas is billed and metered in cubic feet, so the hourly rate is what a gas fitter works with. A domestic furnace consumes 80 to 150 cubic feet per hour, a water heater 40, a cooking range 65, and a whole house at design conditions perhaps 250. A residential meter is rated at 250 CFH and the service pipe at rather more.
Pipe sizing tables are built entirely around this unit. Given a length of pipe, a diameter and an allowable pressure drop, the table returns a capacity in cubic feet per hour, and the fitter compares it against the sum of the appliance ratings on that branch. Undersize the pipe and the burners starve when everything runs at once; oversize it and the material cost rises for no benefit.
The unit converts easily into heat. Natural gas carries roughly 1,000 British thermal units per cubic foot, so a rate in cubic feet per hour is very nearly the same number in thousands of British thermal units per hour. An appliance rated 100,000 British thermal units per hour therefore burns about 100 cubic feet per hour, which is why the two figures appear together on every rating plate.
Propane behaves differently and is worth stating separately. It carries about 2,500 British thermal units per cubic foot, so the same appliance needs less than half the volumetric flow, and a pipe sized for natural gas is generously large for propane. Confusing the two is a classic and dangerous error in the trade.
Beyond fuel gas, the unit describes slow air and gas flows in imperial practice: purge lines, instrument air, small blowers and laboratory gas supplies. Sixty cubic feet per hour is one cubic foot per minute, and 35.31 cubic feet per hour is one cubic metre per hour.
One cubic foot per hour equals about 0.02832 cubic metres per hour, about 28.32 litres per hour, or about 0.01667 cubic feet per minute.
The cubic millimetre per second is a unit of volumetric flow rate equal to one cubic millimetre passing a point every second. Its symbol is mm³/s. A cubic millimetre is the volume of a grain of coarse salt, so this unit describes flows small enough that a full second delivers something barely visible.
Additive manufacturing made it a working number. A fused-filament printer's extruder is limited by how fast it can melt plastic, and that limit is expressed as a volumetric rate: a standard hot end manages 8 to 12 cubic millimetres per second, a high-flow one 25 to 40. Slicing software converts it into a print speed by dividing by the cross-section of the extruded line, which is why the same printer runs faster with a thin layer than a thick one.
Inkjet printing works at a far smaller scale still. A single droplet is a few picolitres, and a print head firing thousands of droplets per second from hundreds of nozzles adds up to only a few cubic millimetres per second in total. The unit is convenient here because it sits between the droplet and the ink cartridge without needing scientific notation.
Machining uses it for the material-removal rate of fine work. Wire electrical-discharge machining removes 20 to 100 cubic millimetres per minute, which is under two per second, and micro-milling with a tool a fraction of a millimetre across is slower again. Since removal rate governs both time and tool wear, it is the number a process engineer optimises.
Medical and laboratory devices are specified here when the volumes are tiny. Microfluidic chips, capillary electrophoresis and some infusion applications move flows of this order, and a cubic millimetre per second is exactly one microlitre per second, which is why the same rate appears under two names in different catalogues.
The unit's relation to the litre is worth holding: a million cubic millimetres make a litre, so a thousand cubic millimetres per second is one litre per second. A flow of ten cubic millimetres per second, typical of a 3D printer, would take about twenty-eight hours to fill a one-litre bottle.
One cubic millimetre per second equals 0.001 millilitres per second, 0.06 millilitres per minute, or one microlitre per second.