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Standard cubic centimetres per minute

## Summary

Standard cubic centimeters per minute (SCCM) is a unit of flow measurement indicating cubic centimeters per minute (cm³/min) in standard conditions for temperature and pressure of a given fluid. These standard conditions vary according to different regulatory bodies. One example of standard conditions for the calculation of SCCM is ${\displaystyle T_{n}}$ = 0  °C (273.15 K) and ${\displaystyle p_{n}}$ = 1.01 bar (14.72 psia).

SCCM is a measure of molar flow rate (e.g., kmol/s) and in spite of its name it must not be confused with a measure of volumetric flow rate, ${\displaystyle {\dot {q}}}$, nor with a measure of mass flow rate, ${\displaystyle {\dot {m}}}$. However, it is useful to think of one SCCM as the mass flow rate of one cubic centimeter per minute of a fluid, typically a gas, at a density defined at some standard temperature, ${\displaystyle T_{n}}$, and pressure, ${\displaystyle p_{n}}$.

To convert one SCCM to the measure of mass flow rate in the SI system, kg/s, one relies in the fundamental relationship between mass flow rate and volumetric flow rate (see volumetric flow rate),[1]

${\displaystyle {\dot {m}}=\rho _{n}{\dot {q}},}$

where ${\displaystyle \rho _{n}}$ is density at some standard conditions, and an equation of state such as

${\displaystyle \rho _{n}={\frac {p_{n}M}{Z_{n}R_{u}T_{n}}},}$

with ${\displaystyle M}$ being the fluid molecular weight, ${\displaystyle Z_{n}}$ the fluid compressibility factor, and ${\displaystyle R_{u}}$ the universal gas constant. By including in the above relationship between ${\displaystyle {\dot {m}}}$ and ${\displaystyle {\dot {q}}}$ units of measurement and their conversion between square brackets one obtains

${\displaystyle {\dot {m}}\left[{\frac {kg}{s}}\right]=\rho _{n}\left[{\frac {kg}{m^{3}}}\right]{\dot {q}}\left[{\frac {cm^{3}}{min}}{\frac {1\,min}{60\,s}}{\frac {1m^{3}}{10^{6}\,cm^{3}}}\right],}$

where ${\displaystyle {\dot {m}}}$ is in ${\displaystyle kg/s}$, ${\displaystyle \rho _{n}}$ in ${\displaystyle kg/m^{3}}$, and ${\displaystyle {\dot {q}}}$ is in ${\displaystyle cm^{3}/min}$. Thereafter, by replacing ${\displaystyle \rho _{n}}$ with the above equation of state one obtains

${\displaystyle {\dot {m}}\left[{\frac {kg}{s}}\right]={\frac {p_{n}[Pa]M\left[{\frac {kg}{kmol}}\right]}{Z_{n}R_{u}\left[{\frac {J}{Kkmol}}\right]T_{n}[K]}}{\dot {q}}\left[{\frac {cm^{3}}{min}}{\frac {1\,min}{60\,s}}{\frac {1m^{3}}{10^{6}\,cm^{3}}}\right].}$

Using this last relationship, one can convert a mass flow rate in the more familiar unit of kg/s to SCCM and vice versa with

${\displaystyle 1\,{\frac {kg}{s}}=6E7{\frac {Z_{n}R_{u}\left[{\frac {J}{Kkmol}}\right]T_{n}[K]}{p_{n}[Pa]M\left[{\frac {kg}{kmol}}\right]}}SCCM,}$

and

${\displaystyle 1\,SCCM=1.6667E-8{\frac {p_{n}[Pa]M\left[{\frac {kg}{kmol}}\right]}{Z_{n}R_{u}\left[{\frac {J}{Kkmol}}\right]T_{n}[K]}}{\frac {kg}{s}}.}$

With this conversion from SCCM to kg/s, one can then use available unit calculators [2] to convert kg/s to other units, such as g/s of the CGS system, or slug/s.

Based on the above formulas, the relationship between SCCM and molar flow rate in kmol/s is given by

${\displaystyle 1\,{\frac {kmol}{s}}=6E7{\frac {Z_{n}R_{u}\left[{\frac {J}{Kkmol}}\right]T_{n}[K]}{p_{n}[Pa]}}SCCM,}$

and

${\displaystyle 1\,SCCM=1.6667E-8{\frac {p_{n}[Pa]}{Z_{n}R_{u}\left[{\frac {J}{Kkmol}}\right]T_{n}[K]}}{\frac {kmol}{s}}.}$

For some usage examples, consider the conversion of 1 SCCM to kg/s of a gas of molecular weight ${\displaystyle M}$, where ${\displaystyle M}$ is in kg/kmol. Furthermore, consider standard conditions of 101325 Pa and 273.15 K, and assume the gas is an ideal gas (i.e., ${\displaystyle Z_{n}=1}$). Using the unity bracket method (see conversion of units) one obtains:

${\displaystyle 1\,{\cancel {\text{SCCM}}}\cdot {\frac {1.6667E-8{\frac {101325[Pa]M\left[{\frac {kg}{kmol}}\right]}{8314\left[{\frac {J}{Kkmol}}\right]273.15[K]}}{\frac {kg}{s}}}{1\,{\cancel {\text{SCCM}}}}}=7.4364E-10\,\,M\left[{\frac {kg}{kmol}}\right]\,{\frac {kg}{s}}.}$

Considering nitrogen, which has a molecular weight of 28 kg/kmol, 1 SCCM of nitrogen in kg/s is given by:

${\displaystyle 7.4364E-10\,\cdot \,28=2.0822E-8{\frac {kg}{s}}.}$

To do the same for 1 SCCM of helium, which has a molecular weight of 4 kg/kmol, one obtains:

${\displaystyle 7.4364E-10\,\cdot \,4=2.9745E-9{\frac {kg}{s}}.}$

Notice that 1 SCCM of helium is less in kg/s than one SCCM of nitrogen.

To convert 50 SCCM of nitrogen with the above considerations one does

${\displaystyle 50\,{\cancel {\text{SCCM}}}\cdot {\frac {1.6667E-8{\frac {101325[Pa]28\left[{\frac {kg}{kmol}}\right]}{8314\left[{\frac {J}{Kkmol}}\right]273.15[K]}}{\frac {kg}{s}}}{1\,{\cancel {\text{SCCM}}}}}=1.04E-6{\frac {kg}{s}}.}$

A unit related to the SCCM is the SLM or SLPM which stands for Standard litre per minute. Their conversion is [3]

${\displaystyle 1\,SCCM=1E-3\,SLM,}$

and

${\displaystyle 1\,SLM=1E3\,SCCM.}$

Another unit is the SCFM which stands for standard cubic feet per minute.

Yet another unit related to SCCM (and SLM) is the PCCM (and PLM) which stands for Perfect Cubic Centimeter per Minute (Perfect Litre per Minute). One PCCM is one SCCM when the gas is ideal. In other words, one PCCM is exactly the same as one SCCM if and only if ${\displaystyle Z_{n}=1}$ in the above relationships.

## References

1. ^ Spitzer, D. W. (1991). Flow Measurement: Practical Guides for Measurement and Control. ISA. p. 341.
2. ^ "NIST Guide to the SI, Appendix B.9". Retrieved 2019-11-04.
3. ^ "NIST Gas Flow Unit Conversions". Retrieved 2019-11-04.