| Cubic meters per hour (m³/h) | Cubic millimeters per second (mm³/s) |
|---|---|
| 1 Cubic meter per hour | 277777.777778 mm³/s |
| 2 Cubic meters per hour | 555555.555556 mm³/s |
| 3 Cubic meters per hour | 833333.333333 mm³/s |
| 4 Cubic meters per hour | 1111111.11111 mm³/s |
| 5 Cubic meters per hour | 1388888.88889 mm³/s |
| 10 Cubic meters per hour | 2777777.77778 mm³/s |
| 20 Cubic meters per hour | 5555555.55556 mm³/s |
| 25 Cubic meters per hour | 6944444.44444 mm³/s |
| 50 Cubic meters per hour | 13888888.8889 mm³/s |
| 100 Cubic meters per hour | 27777777.7778 mm³/s |
| Reference | Cubic meters per hour (m³/h) | Cubic millimeters per second (mm³/s) |
|---|---|---|
| A domestic shower | 0.54 m³/h | 150000 mm³/s |
| A kitchen tap | 0.6 m³/h | 166667 mm³/s |
| A garden hose | 0.9 m³/h | 250000 mm³/s |
| The Amazon river | 752400000 m³/h | 2.09 × 1014 mm³/s |
The cubic metre per hour is a unit of volumetric flow rate equal to one cubic metre passing a point every hour. Its symbol is m³/h. It is the commercial unit of flow: the one that appears on water bills, gas meters, pump curves and ventilation schedules, because a cubic metre per hour multiplied by the hours of operation gives the volume that is actually paid for.
Domestic water and gas meters read in cubic metres, and the meter's rating is a flow in cubic metres per hour — typically 1.5 or 2.5 for a house, meaning the maximum continuous flow it can measure accurately. A gas meter marked G4 passes 6 cubic metres per hour, which at the calorific value of natural gas is roughly 63 kilowatts, comfortably more than a domestic boiler needs.
Pumps are sold by their curve, and the curve's horizontal axis is almost always cubic metres per hour. A domestic booster pump delivers 2 to 5, a swimming-pool pump 10 to 20, an irrigation pump 50 to 200, and a large water-supply pump thousands. Reading the curve at the required flow gives the head the pump can produce and the power it will draw.
Ventilation is scheduled in the same unit across much of Europe. A dwelling requires roughly 0.5 air changes an hour, so a 250 cubic metre flat needs about 125 cubic metres per hour of fresh air; a restaurant kitchen hood may need 3,000, and a laboratory fume cupboard around 1,000 each. Since the room volume is in cubic metres, using the hour as the time base makes the arithmetic immediate.
Industrial process flows are quoted here whether the fluid is liquid or gas. Cooling towers, boiler feedwater, effluent treatment and compressed-air dryers all carry ratings in cubic metres per hour, and district heating substations are sized from the flow needed to carry the heat at a given temperature difference.
Its relation to the SI unit is a division by 3,600. One cubic metre per second is 3,600 cubic metres per hour, which is why river flows look enormous in this unit and why hydrologists avoid it. The hour is the right base for equipment that runs continuously and is billed monthly.
One cubic metre per hour equals about 0.000278 cubic metres per second, 1,000 litres per hour, or about 4.403 US gallons 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.