| Cubic inches per second (in³/s) | Cubic millimeters per second (mm³/s) |
|---|---|
| 1 Cubic inch per second | 16387.064 mm³/s |
| 2 Cubic inches per second | 32774.128 mm³/s |
| 3 Cubic inches per second | 49161.192 mm³/s |
| 4 Cubic inches per second | 65548.256 mm³/s |
| 5 Cubic inches per second | 81935.32 mm³/s |
| 10 Cubic inches per second | 163870.64 mm³/s |
| 20 Cubic inches per second | 327741.28 mm³/s |
| 25 Cubic inches per second | 409676.6 mm³/s |
| 50 Cubic inches per second | 819353.2 mm³/s |
| 100 Cubic inches per second | 1638706.4 mm³/s |
| Reference | Cubic inches per second (in³/s) | Cubic millimeters per second (mm³/s) |
|---|---|---|
| A domestic shower | 9.15356 in³/s | 150000 mm³/s |
| A kitchen tap | 10.1706 in³/s | 166667 mm³/s |
| A garden hose | 15.2559 in³/s | 250000 mm³/s |
| The Amazon river | 1.2754 × 1010 in³/s | 2.09 × 1014 mm³/s |
The cubic inch per second is a unit of volumetric flow rate equal to one cubic inch passing a point every second. Its symbol is in³/s. A cubic inch is 16.387 cubic centimetres, a little over a tablespoon, so this unit describes the modest but visible flows of imperial engineering practice.
Hydraulics is where it survives most strongly. American hydraulic pumps and cylinders are still catalogued in inches, and a cylinder's speed follows directly from the flow divided by the piston area: a 2-inch bore cylinder has an area of 3.14 square inches, so 31.4 cubic inches per second extends it at 10 inches per second. Working in inches throughout avoids converting the bore, the stroke and the flow separately.
Machining uses the same idea for material removal. A milling cutter taking a 0.1-inch depth at 0.5 inch width and 20 inches per minute of feed removes one cubic inch per minute, and a modern machining centre roughing aluminium can exceed twenty. Tool manufacturers publish removal rates in these units because their customers' machines are dimensioned that way.
Small engines and pumps carry the unit too. An engine's displacement in cubic inches, multiplied by its speed, gives the air it swallows: a 350 cubic inch V8 at 3,000 revolutions per minute ingests 525,000 cubic inches a minute, or about 8,750 per second, ideal efficiency assumed. The old American habit of naming engines by cubic inches is the same measurement standing still rather than flowing.
Metering and dispensing in imperial industries follow. Adhesive dispensers, lubricators and grease systems on American plant are specified in cubic inches per second or per minute, and a shot of grease from an automatic lubricator is quoted in cubic inches per cycle, which the cycle time converts into a rate.
For a sense of scale, 61 cubic inches per second is about a litre per second, and one cubic inch per second fills a US gallon in a little under four minutes. That is roughly the rate of a garden tap opened a quarter turn, which makes the unit easy to picture despite its unfamiliarity outside the imperial trades.
One cubic inch per second equals about 16.39 cubic centimetres per second, 0.01639 litres per second, or about 0.2597 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.