# List of dimensionless quantities

A dimensionless quantity is any number or defined expression which is either unitless or has composite dimensions which cancel out to unity. These are found in numerous fields such as mathematics, physics, engineering, and economics. In contrast, quantities containing dimensions include length, time, mass, temperature, luminosity, and electric charge, and products of these fundamental quantities such as volume, speed, and voltage.

In mathematics, numbers do not have a dimension; this includes 1, i, π, e, and others. Physics often uses dimensionless quantities to simplify the characterization of systems with multiple interacting physical phenomena. These may be found by applying the Buckingham π theorem or otherwise may emerge from making partial differential equations unitless by the process of nondimensionalization. Furthermore, dimensionless physical constants allow systems of units such as natural units to be constructed based on the known fundamental physical constants. Engineering, economics, and other fields often extend these ideas in design and analysis of the relevant systems.

## List

All pure numbers are dimensionless quantities by definition. The list below shows many of the well known dimensionless quantities to illustrate their variety of forms and applications. The table does not include dimensionless units such as percentage (%) and dozen or dimensionless physical constants such as the proton-to-electron mass ratio; these topics are discussed in the article on dimensionless quantities.

## References

- ↑
^{1.0}^{1.1}^{1.2}"Table of Dimensionless Numbers" (PDF). Retrieved 2009-11-05. - ↑ Bagnold number
- ↑ Bhattacharjee S., Grosshandler W.L. (1988). "The formation of wall jet near a high temperature wall under microgravity environment".
*ASME MTD*.**96**: 711–6. - ↑ Paoletti S., Rispoli F., Sciubba E. (1989). "Calculation of exergetic losses in compact heat exchanger passager".
*ASME AES*.**10**(2): 21–9. - ↑ Becker, A.; Hüttinger, K. J. (1998). "Chemistry and kinetics of chemical vapor deposition of pyrocarbon—II pyrocarbon deposition from ethylene, acetylene and 1,3-butadiene in the low temperature regime".
*Carbon*.**36**(3): 177. doi:10.1016/S0008-6223(97)00175-9. - ↑ Bond number
- ↑ "Home". OnePetro. 2015-05-04. Retrieved 2015-05-08.
- ↑ Courant–Friedrich–Levy number
- ↑ Schetz, Joseph A. (1993).
*Boundary Layer Analysis*. Englewood Cliffs, NJ: Prentice-Hall, Inc. pp. 132–134. ISBN 0-13-086885-X. - ↑ Fanning friction factor
- ↑ Feigenbaum constants
- ↑ Fresnel number
- ↑ Gain Ratio – Sheldon Brown
- ↑ Incropera, Frank P. (2007).
*Fundamentals of heat and mass transfer*. John Wiley & Sons, Inc. p. 376. - ↑ Tan, R. B. H.; Sundar, R. (2001). "On the froth–spray transition at multiple orifices".
*Chemical Engineering Science*.**56**(21–22): 6337. doi:10.1016/S0009-2509(01)00247-0. - ↑ Lockhart–Martinelli parameter
- ↑ Manning coefficient PDF (109 KB)
- ↑ Van Spengen, W. M.; Puers, R.; De Wolf, I. (2003). "The prediction of stiction failures in MEMS".
*IEEE Transactions on Device and Materials Reliability*.**3**(4): 167. doi:10.1109/TDMR.2003.820295. - ↑ Davis, Mark E.; Davis, Robert J. (2012).
*Fundamentals of Chemical Reaction Engineering*. Dover. p. 215. ISBN 978-0-486-48855-4. - ↑ Richardson number
- ↑ Schmidt number
- ↑ Sommerfeld number
- ↑ Strouhal number, Engineering Toolbox
- ↑ Straughan, B. (2001). "A sharp nonlinear stability threshold in rotating porous convection".
*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*.**457**(2005): 87–88. Bibcode:2001RSPSA.457...87S. doi:10.1098/rspa.2000.0657. - ↑ Petritsch, G.; Mewes, D. (1999). "Experimental investigations of the flow patterns in the hot leg of a pressurized water reactor".
*Nuclear Engineering and Design*.**188**: 75. doi:10.1016/S0029-5493(99)00005-9. - ↑ Kuneš, J. (2012). "Technology and Mechanical Engineering".
*Dimensionless Physical Quantities in Science and Engineering*. pp. 353–390. ISBN 978-0-12-416013-2. doi:10.1016/B978-0-12-416013-2.00008-7. - ↑ Weissenberg number
- ↑ Womersley number