Conversion from Cubic meters per second to Cubic inches per hour

Information about the Cubic meter per second (m³/s)

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.

Information about the Cubic inch per hour (in³/h)

The cubic inch per hour is a unit of volumetric flow rate equal to one cubic inch passing a point every hour. Its symbol is in³/h. Since a cubic inch is a little over a tablespoon, an hour at this rate produces a small puddle — which is exactly why the unit belongs to slow losses, slow doses and slow wear rather than to transfers.

Seepage and weeping are its natural subject. A mechanical seal on a pump is allowed a small permanent leakage to lubricate its faces, and the specification is written in cubic inches per hour on American equipment. A packed gland on a valve stem is similar: a few drops an hour is correct operation, and a dry gland is a gland about to score its stem.

Oil consumption in engines is quoted this way in the imperial world. A large stationary engine's cylinder lubrication is metered at a few cubic inches per hour per cylinder, and the acceptable rate of oil loss past the rings on a diesel is expressed the same way. Because such engines run for thousands of hours between overhauls, an hourly figure is what turns into a drum of oil on the purchase order.

Slow-fill and top-up systems live here too. An automatic battery-watering system, a coolant make-up line, a header tank feeding a boiler and a chemical dosing pump on a cooling circuit all move volumes of this size, and their design lifetime is set by the reservoir divided by the hourly rate.

Corrosion, erosion and permeation figures convert into it when a rate must be given as a volume. A seal that permits so many cubic inches of refrigerant per hour, or a hose whose wall passes so much fuel vapour, is compared against a regulatory limit written as an annual figure, and the hourly rate is what the test bench actually measures.

The relation to larger units frames it clearly. There are 231 cubic inches in a US gallon, so one cubic inch per hour fills a gallon in about ten days, and 61 cubic inches per hour is roughly a litre per hour. A flow that takes a week and a half to fill a milk jug is the very definition of a rate you watch rather than use.

One cubic inch per hour equals about 16.39 cubic centimetres per hour, about 0.01667 cubic inches per minute, or about 0.004329 US gallons per hour.