| Cubic millimeters per hour (mm³/hour) | Cubic meters per second (m³/s) |
|---|---|
| 1 Cubic millimeter per hour | 2.77777777778 × 10-13 m³/s |
| 2 Cubic millimeters per hour | 5.55555555556 × 10-13 m³/s |
| 3 Cubic millimeters per hour | 8.33333333333 × 10-13 m³/s |
| 4 Cubic millimeters per hour | 1.11111111111 × 10-12 m³/s |
| 5 Cubic millimeters per hour | 1.38888888889 × 10-12 m³/s |
| 10 Cubic millimeters per hour | 2.77777777778 × 10-12 m³/s |
| 20 Cubic millimeters per hour | 5.55555555556 × 10-12 m³/s |
| 25 Cubic millimeters per hour | 6.94444444444 × 10-12 m³/s |
| 50 Cubic millimeters per hour | 1.38888888889 × 10-11 m³/s |
| 100 Cubic millimeters per hour | 2.77777777778 × 10-11 m³/s |
| Reference | Cubic millimeters per hour (mm³/hour) | Cubic meters per second (m³/s) |
|---|---|---|
| A domestic shower | 540000000 mm³/hour | 0.00015 m³/s |
| A kitchen tap | 600000000 mm³/hour | 0.000166667 m³/s |
| A garden hose | 900000000 mm³/hour | 0.00025 m³/s |
| The Amazon river | 7.524 × 1017 mm³/hour | 209000 m³/s |
The cubic millimetre per hour is a unit of volumetric flow rate equal to one cubic millimetre passing a point every hour. Its symbol is mm³/h. It is one of the smallest flow rates in ordinary use: a full hour delivers a volume the size of a grain of coarse salt, so it belongs to processes measured in days rather than minutes.
Corrosion is described in these terms whenever the loss is treated as a volume rather than a depth. A steel surface corroding at 0.1 millimetres a year loses, over a square centimetre, roughly one cubic millimetre a year — and the hourly rate that produces it is a ten-thousandth of that. Cathodic-protection engineers work with such numbers because the whole point of the discipline is to make a rate small enough to ignore for decades.
Permeation and leakage testing lives here too. A sealed package, a fuel line or a medical device is tested for how much fluid crosses its wall, and the answer is often a few cubic millimetres per hour or less. A leak too small to see over a working day becomes, at this rate, a measurable volume after a month in a heated test chamber.
Slow drug delivery uses the unit directly. An implanted osmotic pump may release a few cubic millimetres of solution per hour for weeks, and an intrathecal pump can be programmed in fractions of one. Because the reservoir holds only a few millilitres, the hourly rate determines how long the implant lasts before it must be refilled.
Botany borrows it for sap and exudates. Xylem flow in a single small vessel, latex from a tapped rubber tree between collections, and phloem exudate sampled from an aphid stylet are all of this order, and researchers report them per hour because the sampling period is measured in hours.
The scale is worth stating plainly. A litre is a million cubic millimetres, so a flow of one cubic millimetre per hour would take about a hundred and fourteen years to fill a one-litre bottle. That is why the unit almost never describes a bulk transfer — it describes a process one hopes will stay slow.
One cubic millimetre per hour equals 0.001 millilitres per hour, about 0.01667 cubic millimetres per minute, or one microlitre per hour.
The cubic metre per second is the SI unit of volumetric flow rate, equal to one cubic metre passing a point every second. Its symbol is m³/s, and hydrologists call it the cumec. As the coherent SI unit it needs no conversion factor: a velocity in metres per second multiplied by an area in square metres gives a flow directly in cubic metres per second.
Rivers are its natural subject. A small stream runs at a fraction of a cumec, the Thames at Kingston averages about 65, the Rhine at the Dutch border around 2,200, and the Amazon roughly 209,000 — a fifth of all the fresh water reaching the world's oceans. Flood warnings, abstraction licences and reservoir operating rules are all written in these numbers.
Hydroelectric power follows from the same figure. The power available is the flow multiplied by the head, by the density of water and by gravity, so 10 cubic metres per second falling 50 metres yields about 4.9 megawatts before losses. A turbine's rating and a river's flow-duration curve together determine how much of the year a station can run at full output.
Large ventilation and process equipment is rated here too. A road-tunnel fan moves tens of cubic metres per second, a power-station cooling-water pump tens more, and a blast furnace draws hundreds of cubic metres of air per second. Once the numbers reach this scale the cubic metre per second is more readable than any smaller unit.
The unit is also convenient because a cubic metre of water is a tonne. One cubic metre per second is therefore one tonne of water per second, which turns a flow into a force and a mass loading without further arithmetic — useful when sizing a spillway, a screen or a bridge pier.
Building services and hydrology sit awkwardly on either side of it. Ventilation engineers work in litres per second because their flows are a thousandth of a cumec, while river engineers would need six digits to express theirs in litres. The factor of a thousand between the two units is what keeps both trades in comfortable numbers.
One cubic metre per second equals 1,000 litres per second, 60 cubic metres per minute, or about 35.31 cubic feet per second.