Conversion from Cubic inches per second to Cubic feet per hour

Information about the Cubic inch per second (in³/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.

Information about the Cubic foot per hour (ft³/h)

The cubic foot per hour is a unit of volumetric flow rate equal to one cubic foot passing a point every hour. Its symbol is ft³/h, and in the gas trades it is abbreviated CFH. It is the unit of fuel gas supply throughout North America, where every appliance and every pipe is sized by it.

Natural gas is billed and metered in cubic feet, so the hourly rate is what a gas fitter works with. A domestic furnace consumes 80 to 150 cubic feet per hour, a water heater 40, a cooking range 65, and a whole house at design conditions perhaps 250. A residential meter is rated at 250 CFH and the service pipe at rather more.

Pipe sizing tables are built entirely around this unit. Given a length of pipe, a diameter and an allowable pressure drop, the table returns a capacity in cubic feet per hour, and the fitter compares it against the sum of the appliance ratings on that branch. Undersize the pipe and the burners starve when everything runs at once; oversize it and the material cost rises for no benefit.

The unit converts easily into heat. Natural gas carries roughly 1,000 British thermal units per cubic foot, so a rate in cubic feet per hour is very nearly the same number in thousands of British thermal units per hour. An appliance rated 100,000 British thermal units per hour therefore burns about 100 cubic feet per hour, which is why the two figures appear together on every rating plate.

Propane behaves differently and is worth stating separately. It carries about 2,500 British thermal units per cubic foot, so the same appliance needs less than half the volumetric flow, and a pipe sized for natural gas is generously large for propane. Confusing the two is a classic and dangerous error in the trade.

Beyond fuel gas, the unit describes slow air and gas flows in imperial practice: purge lines, instrument air, small blowers and laboratory gas supplies. Sixty cubic feet per hour is one cubic foot per minute, and 35.31 cubic feet per hour is one cubic metre per hour.

One cubic foot per hour equals about 0.02832 cubic metres per hour, about 28.32 litres per hour, or about 0.01667 cubic feet per minute.