Conversion from Liters per minute to Cubic millimeters per second

Information about the Liter per minute (L/min)

The litre per minute is a unit of volumetric flow rate equal to one litre passing a point every minute. Its symbol is L/min. It is the unit of taps, showers and small pumps — the flows a person meets directly, at a rate slow enough that a minute is the natural interval to count over.

Household plumbing is specified in it almost everywhere. A modern shower head delivers 6 to 9 litres per minute, an older one 15 or more, a kitchen tap 5 to 10, and a bath filler 15 to 20. Water-efficiency regulations in many countries set maximum figures in exactly these terms, because the flow rate multiplied by a typical shower length gives the volume of water and the energy needed to heat it.

That calculation is the reason the unit matters beyond plumbing. Reducing a shower from 12 to 8 litres per minute cuts both the water and the heating energy by a third, and heating water is one of the largest energy uses in a house. A restrictor costing very little changes a household's energy bill measurably.

Medicine uses the unit for gases. Oxygen therapy is prescribed in litres per minute — 2 through a nasal cannula for mild supplementation, 15 through a mask with a reservoir in an emergency — and the flowmeter on the wall of a hospital room is calibrated in exactly this unit. Anaesthetic machines are set the same way.

Engines and compressors also appear here. A small air compressor delivers 100 to 200 litres per minute of free air; a car's cooling system circulates tens of litres per minute; a garden pump moves 20 to 60. In each case the number is the useful one because the equipment runs for minutes at a time rather than seconds.

Sixty litres per minute is one litre per second, so the two units differ by the same factor as the two time units. That makes the conversion easy to do mentally, and it explains why the same equipment is often described in litres per minute by its manufacturer and litres per second by the engineer designing the system it goes into.

One litre per minute equals about 0.01667 litres per second, 1,000 millilitres per minute, or about 0.22 imperial gallons per minute.

Information about the Cubic millimeter per second (mm³/s)

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.