Cubic metre

The cubic metre (in British English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the SI derived unit of volume.[1] Its SI symbol is m3.[1] It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with metric prefixes, was the stère, still sometimes used for dry measure (for instance, in reference to wood). Another alternative name, no longer widely used, was the kilolitre.

Metre-cube-beton-p1040192
One cubic metre of concrete (representing the world annual production per inhabitant)

Conversions

1 cubic metre = 1000 litres (exactly)[2][3]
≈ 35.3 cubic feet
≈ 1.31 cubic yards
≈ 6.29 oil barrels
≈ 220 imperial gallons
≈ 264 US fluid gallons

A cubic metre of pure water at the temperature of maximum density (3.98 °C) and standard atmospheric pressure (101.325 kPa) has a mass of 1000 kg, or one tonne. At 0 °C, the freezing point of water, a cubic metre of water has slightly less mass, 999.972 kilograms.

It is sometimes abbreviated to cu m, m3, M3, m^3, m**3, CBM, cbm when superscript characters or markup cannot be used (e.g. in some typewritten documents and postings in Usenet newsgroups).

Abbreviated CBM and cbm in the freight business and MTQ (or numeric code 49) in international trade.

Multiples and submultiples

Multiples

Cubic decametre
the volume of a cube of side length one decametre (10 m)
equal to a megalitre
1 dam3 = 1000 m3 = 1 ML
Cubic hectometre
the volume of a cube of side length one hectometre (100 m)
equal to a gigalitre
in civil engineering abbreviated MCM for million cubic metres
1 hm3 = 1000000 m3 = 1 GL
Cubic kilometre
the volume of a cube of side length one kilometre (1000 m)
equal to a teralitre
1 km3 = 1000000000 m3 = 1 TL (810713.19 acre-feet; 0.239913 cubic miles)

Submultiples

Cubic decimetre also known as DCM in Rubber compound processing (Deci Cubic Meter).
the volume of a cube of side length one decimetre (0.1 m)
equal to a litre
1 dm3 = 0.001 m3 = 1 L
Cubic centimetre[4]
the volume of a cube of side length one centimetre (0.01 m)
equal to a millilitre
1 cm3 = 0.000001 m3 = 10−6 m3 = 1 mL
Cubic millimetre
the volume of a cube of side length one millimetre (0.001 m)
equal to a microlitre
1 mm3 = 0.000000001 m3 = 10−9 m3 = 1 µL

Notes

  1. ^ a b Bureau International de Poids et Mesures. "Derived units expressed in terms of base units". 2014. Accessed 7 August 2014.
  2. ^ From 1901 to 1964 the litre was defined as the volume of one kilogram of pure water at 4°C and 760 millimetres of mercury pressure. During this time, a litre was about 1.000028 dm3. In 1964 the original definition was reverted to.
  3. ^ "Archived copy". Archived from the original on 2009-10-01. Retrieved 2010-03-05.CS1 maint: Archived copy as title (link)
  4. ^ The cubic centimetre is the base unit of volume of the CGS system of units. The colloquial abbreviations "cc" and "ccm" are not SI but are common in some contexts such as cooking, engine displacement and medicine.
Cubic centimetre

A cubic centimetre (or cubic centimeter in US English) (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that extends the derived SI-unit cubic metre, and corresponds to the volume of a cube that measures 1 cm × 1 cm × 1 cm. One cubic centimetre corresponds to a volume of 1/1,000,000 of a cubic metre, or 1/1,000 of a litre, or one millilitre; thus, 1 cm3 ≡ 1 mL. The mass of one cubic centimetre of water at 3.98 °C (the temperature at which it attains its maximum density) is closely equal to one gram. SI supports only the use of symbols and deprecates the use of any abbreviations for units. Hence cm3 is preferred to cc or ccm.

Many scientific disciplines have replaced cubic centimeter measurements with milliliters, but the medical and automotive fields in the United States still use the term cubic centimetre. Much of the automotive industry outside the U.S. has switched to litres. The United Kingdom uses millilitres in preference to cubic centimetres in the medical field, but not the automotive. Most other English-speaking countries follow the UK example.[citation needed]

There is currently a movement within the medical field to discontinue the use of cc in prescriptions and on medical documents, as it can be misread as "00". This could cause a hundredfold overdose of medication, which could be dangerous or even lethal. In the United States, such confusion accounts for 12.6% of all errors associated with medical abbreviations.

In automobile engines, "cc" refers to the total volume of its engine displacement in cubic centimetres. The displacement can be calculated using the formula

where d is engine displacement, b is the bore of the cylinders, s is length of the stroke and n is the number of cylinders.

Conversions

Cubic metre per second

A cubic metre per second (m3s−1, m3/s, cumecs or cubic meter per second in American English) is a derived SI unit of volumetric flow rate equal to that of a stere or cube with sides of one metre (~39.37 in) in length exchanged or moving each second. It is popularly used for water flow, especially in rivers and streams, and fractions for HVAC values measuring air flow.

The term cumec is also used, as shorthand for "Cubic metres per second", with the plural form cumecs also common in speech. It is commonly used between workers in the measurement of water flow through natural streams and civil works, but rarely used in writing. Data in units of cumec are used along the y-axis or vertical axis of a flow hydrograph, which describes the time variation of discharge of a river (the mean velocity multiplied by cross-sectional area). A moderately sized river discharges in the order of 100 cumecs.

Gravel

Gravel is a loose aggregation of rock fragments. Gravel is classified by particle size range and includes size classes from granule- to boulder-sized fragments. In the Udden-Wentworth scale gravel is categorized into granular gravel (2 to 4 mm or 0.079 to 0.157 in) and pebble gravel (4 to 64 mm or 0.2 to 2.5 in). ISO 14688 grades gravels as fine, medium, and coarse with ranges 2 mm to 6.3 mm to 20 mm to 63 mm. One cubic metre of gravel typically weighs about 1,800 kg (or a cubic yard weighs about 3,000 pounds).

Gravel is an important commercial product, with a number of applications. Many roadways are surfaced with gravel, especially in rural areas where there is little traffic. Globally, far more roads are surfaced with gravel than with concrete or tarmac; Russia alone has over 400,000 km (250,000 mi) of gravel roads. Both sand and small gravel are also important for the manufacture of concrete.

Humidity

Humidity is the amount of water vapour present in air. Water vapour, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present. The amount of water vapour needed to achieve saturation increases as the temperature increases. As the temperature of a parcel of air decreases it will eventually reach the saturation point without adding or losing water mass. The amount of water vapour contained within a parcel of air can vary significantly. For example, a parcel of air near saturation may contain 28 grams of water per cubic metre of air at 30 °C, but only 8 grams of water per cubic metre of air at 8 °C.

Three primary measurements of humidity are widely employed: absolute, relative and specific. Absolute humidity describes the water content of air and is expressed in either grams per cubic metre or grams per kilogram. Relative humidity, expressed as a percentage, indicates a present state of absolute humidity relative to a maximum humidity given the same temperature. Specific humidity is the ratio of water vapor mass to total moist air parcel mass.

Humidity plays an important role for surface life. For animal life dependent on perspiration (sweating) to regulate internal body temperature, high humidity impairs heat exchange efficiency by reducing the rate of moisture evaporation from skin surfaces. This effect can be calculated using a heat index table, also known as a humidex.

Kilogram per cubic metre

Kilogram per cubic metre (symbol: kg·m−3, or kg/m3) is an SI derived unit of density, defined by mass in kilograms divided by volume in cubic metres.

Koku

The koku (石) is a Japanese unit of volume, equal to ten cubic shaku. In this definition, 3.5937 koku equal one cubic metre, i.e. 1 koku is about 278.3 litres (61.2 imp gal; 73.5 US gal). The koku was originally defined as a quantity of rice, enough rice to feed one person for one year (one masu is enough rice to feed a person for one day). A koku of rice weighs about 150 kilograms (330 pounds).

In 1891, a smaller koku was defined such that one koku equalled exactly ​240100⁄1331 litres, which is about 180.39 litres (39.68 imp gal; 47.65 US gal), or ≈68.4% the size of the original "koku".

Under the Tokugawa shogunate of the Edo period (1603–1868) of Japanese history, each feudal domain had an assessment of its potential income known as kokudaka which in part determined its order of precedence at the Shogunal court. The smallest kokudaka to qualify the fief-holder for the title of daimyō was 10,000 koku (worth ¥705,528,600 in 2016) and Kaga han, the largest (other than that of the shōgun), was called the "million-koku domain". Its holdings totaled around 1,025,000 koku (worth ¥72.3 billion in 2016). Many samurai, including hatamoto, received stipends in koku, while a few received salaries instead. In the Tōhoku and Hokkaidō domains, where rice could not be grown, the economy was still measured in terms of koku, with other crops and produce converted to their equivalent value in terms of rice. The kokudaka was not adjusted from year to year, and thus some fiefs had larger economies than their nominal koku indicated due to land reclamation and new rice field development, which allowed them to fund development projects.

Koku was also used to measure how much a ship could carry when all its loads were rice. Smaller ships carried 50 koku (7.5 tonnes, 7.4 long tons, 8.3 short tons) while the biggest ships carried over 1,000 koku (150 tonnes, 150 long tons, 170 short tons). The biggest ships were larger than military vessels owned by the Shogunate.

The Hyakumangoku Matsuri (Million-Koku Festival) in Kanazawa, Japan celebrates the arrival of daimyō Maeda Toshiie into the city in 1583, although Maeda's income was not raised to over a million koku until after the Battle of Sekigahara in 1600.

The koku unit is still commonly used in the lumber industry in Japan.

Liquid-to-gas ratio

An important parameter in wet scrubbing systems is the rate of liquid flow. It is common in wet scrubber terminology to express the liquid flow as a function of the gas flow rate that is being treated. This is commonly called the liquid-to-gas ratio (L/G ratio) and uses the units of gallons per 1,000 actual cubic feet or litres per cubic metre (L/m3).

Expressing the amount of liquid used as a ratio enables systems of different sizes to be readily compared.

For particulate removal, the liquid-to-gas ratio is a function of the mechanical design of the system; while for gas absorption this ratio gives an indication of the difficulty of removing a pollutant. Most wet scrubbers used for particulate control operate with liquid-to-gas ratios in the range of 4 to 20 gallons per 1,000 actual cubic foot (0.5 to 3 litres per actual cubic metre).

Depending on scrubber design, a minimum volume of liquid is required to "wet" the scrubber internals and create sufficient collection targets. After a certain optimum point, adding excess liquid to a particulate wet scrubber does not increase efficiency and in fact, could be counter-productive by causing excessive pressure loss. Liquid-to-gas ratios for gas absorption are often higher, in the range of 20 to 40 gallons per 1,000 actual cubic foot (3 to 6 litres per actual cubic metre).

L/G ratio illustrates a number of points about the choice of wet scrubbers used for gas absorption. For example, because flue-gas desulfurization systems must deal with heavy particulate loadings, open, simple designs (such as venturi, spray chamber and moving bed) are used.

Also, the liquid-to-gas ratio for the absorption process is higher than for particle removal and gas velocities are kept low to enhance the absorption process.

Solubility is a very important factor affecting the amount of a pollutant that can be absorbed. Solubility governs the amount of liquid required (liquid-to-gas ratio) and the necessary contact time. More soluble gases require less liquid. Also, more soluble gases will be absorbed faster.

Litre

The litre (international spelling) or liter (American spelling) (symbols L, l or ℓ) is an SI accepted metric system unit of volume equal to 1 cubic decimetre (dm3), 1,000 cubic centimetres (cm3) or 1/1,000 cubic metre. A cubic decimetre (or litre) occupies a volume of 10 cm×10 cm×10 cm (see figure) and is thus equal to one-thousandth of a cubic metre.

The original French metric system used the litre as a base unit. The word litre is derived from an older French unit, the litron, whose name came from Greek — where it was a unit of weight, not volume — via Latin, and which equalled approximately 0.831 litres. The litre was also used in several subsequent versions of the metric system and is accepted for use with the SI, although not an SI unit — the SI unit of volume is the cubic metre (m3). The spelling used by the International Bureau of Weights and Measures is "litre", a spelling which is shared by almost all English-speaking countries. The spelling "liter" is predominantly used in American English.One litre of liquid water has a mass of almost exactly one kilogram, because the kilogram was originally defined in 1795 as the mass of one cubic decimetre of water at the temperature of melting ice. Subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact.

Meenachil River

The Meenachil (Malayalam: മീനച്ചിലാർ) River flows through the heart of Kottayam district of Kerala state, India. The river, 78 kilometres (48 mi) long, flows through Poonjar, Teekoy, Erattupetta, Palai, Ettumanoor and Kottayam before emptying itself into the Vembanad Lake at Kumarakom, the famous tourist place of Kerala.

The Meenachil River is formed by several streams originating from the Western Ghats. The general elevation ranges from 77 m to 1156 m in the high lands and less than 2 m in the lowlands and 8 to 68 m in the midlands. The Meenachil has a watershed area of 1208.11 km². The river has a total annual yield of 2,349 million cubic metre and an annual utilizable yield of 1110 million cubic metre. The river has 38 tributaries including major and minor ones. The river has 47 sub watersheds and 114 micro watersheds.

The river finds mention in Arundhati Roy's Booker Prize-winning novel, The God of Small Things.

Molar volume

The molar volume, symbol Vm, is the volume occupied by one mole of a substance (chemical element or chemical compound) at a given temperature and pressure. It is equal to the molar mass (M) divided by the mass density (ρ). It has the SI unit cubic metres per mole (m3/mol), although it is more practical to use the units cubic decimetres per mole (dm3/mol) for gases and cubic centimetres per mole (cm3/mol) for liquids and solids.

Recommended exposure limit

A recommended exposure limit (REL) is an occupational exposure limit that has been recommended by the United States National Institute for Occupational Safety and Health to the Occupational Safety and Health Administration (OSHA) for adoption as a permissible exposure limit. The REL is a level that NIOSH believes would be protective of worker safety and health over a working lifetime if used in combination with engineering and work practice controls, exposure and medical monitoring, posting and labeling of hazards, worker training and personal protective equipment. No REL has ever been adopted by OSHA, but they have been used as guides by some industry and advocacy organizations. RELs for chemical exposures are usually expressed in parts per million (ppm), or sometimes in milligrams per cubic metre (mg/m3). Although not legally enforceable limits, NIOSH RELs are considered by OSHA during the promulgation of legally enforceable PELs.

Reverse osmosis plant

A reverse osmosis plant is a manufacturing plant where the process of reverse osmosis takes place. An average modern reverse osmosis plant needs six kilowatt-hours of electricity to desalinate one cubic metre of water. The process also results in an amount of salty briny waste. The challenge for these plants is to find ways to reduce energy consumption, use sustainable energy sources, improve the process of desalination and to innovate in the area of waste management to deal with the waste. Self-contained water treatment plants using reverse osmosis, called reverse osmosis water purification units, are normally used in a military context.

SI derived unit

SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 or kg m−3), the SI derived unit of density.

The names of SI derived units, when written in full, are in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz"; but the symbol for metre is "m".

Sound energy density

Sound energy density or sound density is the sound energy per unit volume. The SI unit of sound energy density is the pascal (Pa), that is the joule per cubic metre (J/m3) in SI based units.

Standard cubic feet per minute

Standard cubic feet per minute (SCFM) is the molar flow rate of a gas corrected to "standardized" conditions of temperature and pressure thus representing a fixed number of moles of gas regardless of composition and actual flow conditions. It is related to the mass flow rate of the gas by a multiplicative constant which depends only on the molecular weight of the gas. There are different standard conditions for temperature and pressure, so care is taken when choosing a particular standard value. Worldwide, the "standard" condition for pressure is variously defined as an absolute pressure of 101,325 pascals (Atmospheric pressure), 1.0 bar (i.e., 100,000 pascals), 14.73 psia, or 14.696 psia and the "standard" temperature is variously defined as 68 °F, 60 °F, 0 °C, 15 °C, 20 °C, or 25 °C. The relative humidity (e.g., 36% or 0%) is also included in some definitions of standard conditions.

In Europe, the standard temperature is most commonly defined as 0 °C, but not always. In the United States, the standard temperature is most commonly defined as 60 °F or 70 °F, but again, not always. A variation in standard temperature can result in a significant volumetric variation for the same mass flow rate. For example, a mass flow rate of 1,000 kg/h of air at 1 atmosphere of absolute pressure is 455 SCFM when defined at 32 °F (0 °C) but 481 SCFM when defined at 60 °F (16 °C).

In countries using the SI metric system of units, the term "normal cubic metre" (Nm3) is very often used to denote gas volumes at some normalized or standard condition. Again, as noted above, there is no universally accepted set of normalized or standard conditions.

Stere

The stere or stère is a unit of volume in the original metric system equal to one cubic metre. The name was coined from the Greek στερεός stereos, "solid", in 1793 France as a metric analogue to the cord. The stère is typically used for measuring large quantities of firewood or other cut wood, while the cubic meter is used for uncut wood. It is not part of the modern metric system (SI).

In Dutch, there is also a kuub, short for kubieke meter which differs from a stere. Whereas a "kuub" is a solid cubic metre, as it was traditionally used for wood, a stère is a cubic metre pile of woodblocks. A stère is less than a kuub or full cubic metre of wood, because the spaces between the woodblocks are included in a stère, while they do not count towards a kuub. In Finnish, the same unit is known as motti (from Swedish mått, "measure").

Note that the stère as used in contexts outside the timber industry is not subject to the same ambiguity. In particular, stère and kilostère are sometimes used in hydrology, as the kilostere (1000 m3) is a slightly smaller metric analog of an acre-foot (≈ 1233 m3), similar to the relationship of the tonne and (short) ton.

Svartediket

Svartediket is a lake in the city of Bergen in Hordaland county, Norway. The 0.5-square-kilometre (0.19 sq mi) lake lies immediately north of the mountain Ulriken, northeast of the Store Lungegårdsvannet bay. Historically, this lake was called Ålrekstadsvannet, but in the late 19th century, a dam was built on the south end of the lake to create a reservoir for the city's drinking water. Since then it was called Svartediket, after the water plant built there.The lake is the main source of drinking water for the central parts of the city of Bergen. There is a pumping station and treatment facility build adjacent to the lake inside the mountain Ulriken. Drinking water is collected at a 28-metre (92 ft) depth in Svartediket. Inside the water treatment plant, the water is filtered and irradiated with UV light to kill harmful microorganisms. After treatment, the clean drinking water is stored in a 15,000-cubic-metre (530,000 cu ft) large water pool inside the mountain. This is the water that is pumped down to the city center for drinking water. In 2004, Bergen was hit by a Giardia lamblia epidemic which had its source in the lake Svartediket. The water treatment facility was upgraded in 2007.

Vembanad Rail Bridge

Vembanad Rail Bridge is a rail connecting Edappally and Vallarpadam in Kochi, Kerala. With a total length of 4,620 metres, it is the longest railway bridge in India. The line is dedicated solely for freight.

Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i. e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.

Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. Volumes of complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.

The volume of a solid (whether regularly or irregularly shaped) can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of just one of the substances. However, sometimes one substance dissolves in the other and in such cases the combined volume is not additive.In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian invariant.

In thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure.

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