| Cubic millimeters per hour (mm³/hour) | Cubic feet per second (ft³/s) |
|---|---|
| 1 Cubic millimeter per hour | 9.80962964555 × 10-12 ft³/s |
| 2 Cubic millimeters per hour | 1.96192592911 × 10-11 ft³/s |
| 3 Cubic millimeters per hour | 2.94288889367 × 10-11 ft³/s |
| 4 Cubic millimeters per hour | 3.92385185822 × 10-11 ft³/s |
| 5 Cubic millimeters per hour | 4.90481482278 × 10-11 ft³/s |
| 10 Cubic millimeters per hour | 9.80962964555 × 10-11 ft³/s |
| 20 Cubic millimeters per hour | 1.96192592911 × 10-10 ft³/s |
| 25 Cubic millimeters per hour | 2.45240741139 × 10-10 ft³/s |
| 50 Cubic millimeters per hour | 4.90481482278 × 10-10 ft³/s |
| 100 Cubic millimeters per hour | 9.80962964555 × 10-10 ft³/s |
| Reference | Cubic millimeters per hour (mm³/hour) | Cubic feet per second (ft³/s) |
|---|---|---|
| A domestic shower | 540000000 mm³/hour | 0.0052972 ft³/s |
| A kitchen tap | 600000000 mm³/hour | 0.00588578 ft³/s |
| A garden hose | 900000000 mm³/hour | 0.00882867 ft³/s |
| The Amazon river | 7.524 × 1017 mm³/hour | 7380765 ft³/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 foot per second is a unit of volumetric flow rate equal to one cubic foot passing a point every second. Its symbol is ft³/s, and in hydrology it has a name of its own: the cusec. One cusec is about 28.32 litres per second, roughly the flow of a vigorous garden hose or a small brook.
American river gauging is entirely built on it. The United States Geological Survey publishes stream flow in cubic feet per second at thousands of gauges, water rights in the western states are granted in cusecs, and the Colorado's allocations between states rest on figures first written in this unit a century ago. The Mississippi at its mouth averages about 600,000 cubic feet per second.
Irrigation districts inherited it from the same tradition. A miner's inch, an older western measure, is defined in most states as a fixed fraction of a cusec, and a canal headgate is set to deliver a farmer's entitlement in cubic feet per second for a stated number of hours. The product of the two is the acre-foot, the volume unit that follows naturally from the cusec.
An easy approximation makes the unit memorable: one cubic foot per second flowing for twenty-four hours delivers almost exactly two acre-feet — 1.983, to be precise. Irrigation engineers use the round figure daily, since it converts a rate into a seasonal water budget in a single step.
Flood hydrology is written in it too. A design storm on a small catchment might produce a few hundred cubic feet per second, a major river flood tens or hundreds of thousands, and culverts, bridges and levees in the United States are sized against a peak discharge expressed exactly this way.
Its metric counterpart is the cubic metre per second, which is 35.31 times larger. Hydrological literature moves constantly between the two, and the ratio is worth remembering: a hundred cusecs is a little under three cubic metres per second, and a thousand cubic metres per second is a large river in anyone's units.
One cubic foot per second equals about 28.32 litres per second, about 0.02832 cubic metres per second, or about 448.8 US gallons per minute.