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INTERNATIONAL ISO
STANDARD 80000-11
Second edition
2019-10
Quantities and units —
Part 11:
Characteristic numbers
Grandeurs et unités —
Partie 11: Nombres caractéristiques
Reference number
©
ISO 2019
© ISO 2019
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ii © ISO 2019 – All rights reserved
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Momentum transfer . 1
5 Transfer of heat .16
6 Transfer of matter in a binary mixture .24
7 Constants of matter.33
8 Magnetohydrodynamics.37
9 Miscellaneous .46
Bibliography .48
Alphabetical index .49
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
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any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
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.org/ iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 12, Quantities and units, in collaboration
with Technical Committee IEC/TC 25, Quantities and units.
This second edition cancels and replaces the first edition (ISO 80000-11:2008), which has been
technically revised.
The main changes compared to the previous edition are as follows:
— the table giving the quantities and units has been simplified;
— all items have been revised in terms of the layout of the definitions, and a worded definition has
been added to each item;
— the number of items has been increased from 25 to 108 (concerns all Clauses);
— item 11-9.2 (Landau-Ginzburg number) has been transferred in this document from
ISO 80000-12:2009 (revised as ISO 80000-12:2019).
A list of all parts in the ISO 80000 and IEC 80000 series can be found on the ISO and IEC websites.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
iv © ISO 2019 – All rights reserved
Introduction
Characteristic numbers are physical quantities of unit one, although commonly and erroneously
called “dimensionless” quantities. They are used in the studies of natural and technical processes, and
(can) present information about the behaviour of the process, or reveal similarities between different
processes.
Characteristic numbers often are described as ratios of forces in equilibrium; in some cases, however,
they are ratios of energy or work, although noted as forces in the literature; sometimes they are the
ratio of characteristic times.
Characteristic numbers can be defined by the same equation but carry different names if they are
concerned with different kinds of processes.
Characteristic numbers can be expressed as products or fractions of other characteristic numbers if
these are valid for the same kind of process. So, the clauses in this document are arranged according to
some groups of processes.
As the amount of characteristic numbers is tremendous, and their use in technology and science is not
uniform, only a small amount of them is given in this document, where their inclusion depends on their
common use. Besides, a restriction is made on the kind of processes, which are given by the Clause
headings. Nevertheless, several characteristic numbers are found in different representations of the
same physical information, e.g. multiplied by a numerical factor, as the square, the square root, or the
inverse of another representation. Only one of these have been included, the other ones are declared as
deprecated or are mentioned in the remarks column.
INTERNATIONAL STANDARD ISO 80000-11:2019(E)
Quantities and units —
Part 11:
Characteristic numbers
1 Scope
This document gives names, symbols and definitions for characteristic numbers used in the description
of transport and transfer phenomena.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
Names, symbols and definitions for characteristic numbers are given in Clauses 4 to 9.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
4 Momentum transfer
Table 1 gives the names, symbols and definitions of characteristic numbers used to characterize
processes in which momentum transfer plays a predominant role. The transfer of momentum
(ISO 80000-4) basically occurs during a collision of 2 bodies, and is governed by the law of momentum
conservation. Energy dissipation can occur. In a more generalized meaning momentum transfer occurs
during the interaction of 2 subsystems moving with velocity v relative to each other. Typically, one of
the subsystems is solid and possibly rigid, with a characteristic length, which can be a length, width,
radius, etc. of a solid object, often the effective length is given by the ratio of a body’s volume to the area
of its surface.
The other subsystem is a fluid, in general liquid or gaseous, with the following properties amongst others:
— mass density ρ (ISO 80000-4);
— dynamic viscosity η (ISO 80000-4);
— kinematic viscosity ν=ηρ/ (ISO 80000-4), or
— pressure drop Δp (ISO 80000-4).
The field of science is mainly fluid dynamics (mechanics). Characteristic numbers of this kind allow
the comparison of objects of different sizes. They also can give some estimation about the change of
laminar flow to turbulent flow.
2 © ISO 2019 – All rights reserved
Table 1 — Characteristic numbers for momentum transfer
No. Name Symbol Definition Remarks
11-4.1 Reynolds num- Re quotient of inertial forces and viscous forces in a fluid flow, ex- The value of the Reynolds number gives an estimate
ber pressed by on the flow state: laminar flow or turbulent flow.
In rotating movement, the speed v = ωl, where l is the
ρvvll
Re== ; where
distance from the rotation axis and ω is the angular
ην
velocity.
ρ is mass density (ISO 80000-4),
v is speed (ISO 80000-3),
l is characteristic length (ISO 80000-3),
η is dynamic viscosity (ISO 80000-4), and
ν is kinematic viscosity (ISO 80000-4)
11-4.2 Euler number Eu relationship between pressure drop in a flow and the kinetic energy The Euler number is used to characterize losses in
per volume for flow of fluids in a pipe, expressed by the flow.
Δp A modification of the Euler number is considering the
Eu= ; where
dimensions of the containment (pipe):
ρv
d
Δp is drop of pressure (ISO 80000-4),
Eu′= Eu ; where
l
ρ is mass density (ISO 80000-4), and
d is inner diameter (ISO 80000-3) of the pipe, and
v is speed (ISO 80000-3)
l is length (ISO 80000-3).
11-4.3 Froude number Fr quotient of a body’s inertial forces and its gravitational forces for The Froude number can be modified by buoyancy.
flow of fluids, expressed by
Sometimes the square and sometimes the inverse of
v the Froude number as defined here is wrongly used.
Fr= ; where
lg
v is speed (ISO 80000-3) of flow,
l is characteristic length (ISO 80000-3), and
g is acceleration of free fall (ISO 80000-3)
Table 1 (continued)
No. Name Symbol Definition Remarks
11-4.4 Grashof number Gr quotient of buoyancy forces due to thermal expansion which results Heating can occur near hot vertical walls, in pipes, or
in a change of mass density and viscous forces for free convection by a bluff body.
due to temperature differences, expressed by
The characteristic length can be the vertical height
of a hot plate, the diameter of a pipe, or the effective
Gr=ΔlgανT/ ; where
V
length of a body.
l is characteristic length (ISO 80000-3),
See also Rayleigh number (item 11-5.3).
g is acceleration of free fall (ISO 80000-3),
α is thermal cubic expansion coefficient (ISO 80000-5),
V
ΔT is difference of thermodynamic temperature T (ISO 80000-5)
between surface of the body and the fluid far away from the
body, and
ν is kinematic viscosity (ISO 80000-4)
11-4.5 Weber number We relation between inertial forces and capillary forces due to surface The fluids can be gases or liquids.
tension at the interface between two different fluids, expressed by
The different fluids often are drops moving in a gas or
bubbles in a liquid.
We=ργv l/ ; where
The characteristic length is commonly the diameter of
ρ is mass density (ISO 80000-4),
bubbles or drops.
v is speed (ISO 80000-3),
The square root of the Weber number is called Ray-
l is characteristic length (ISO 80000-3), and
leigh number.
γ is surface tension (ISO 80000-4)
Sometimes the square root of the Weber number as
defined here is called the Weber number. That defini-
tion is deprecated.
Interfaces only exist between two fluids which are not
miscible.
11-4.6 Mach number Ma quotient of the speed of flow and the speed of sound, expressed by The Mach number represents the relationship of iner-
tial forces compared to compression forces.
Ma=v/c ; where
For an ideal gas
v is speed (ISO 80000-3) of the body, and
p RT kT
c is speed of sound (ISO 80000-8) in the fluid
c==γ γγ= ; where γ is ratio of the
ρ M m
specific heat capacity (ISO 80000-5).
4 © ISO 2019 – All rights reserved
Table 1 (continued)
No. Name Symbol Definition Remarks
11-4.7 Knudsen number Kn quotient of free path length of a particle and a characteristic length, The Knudsen number is a
...