Quantities and units - Part 11: Characteristic numbers (ISO 80000-11:2019)

This document gives names, symbols and definitions for characteristic numbers used in the description
of transport and transfer phenomena.

Größen und Einheiten - Teil 11: Kenngrößen der Dimension Zahl (ISO 80000-11:2019)

Grandeurs et unités - Partie 11: Nombres caractéristiques (ISO 80000-11:2019)

Le présent document donne noms, les symboles et les définitions des nombres caractéristiques utilisés dans la description des phénomènes de transfert.

Veličine in enote - 11. del: Značilna števila (ISO 80000-11:2019)

General Information

Status
Published
Public Enquiry End Date
04-Apr-2017
Publication Date
10-Nov-2020
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
22-Nov-2019
Due Date
27-Jan-2020
Completion Date
11-Nov-2020

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SLOVENSKI STANDARD
SIST EN ISO 80000-11:2020
01-december-2020
Nadomešča:
SIST EN ISO 80000-11:2013
Veličine in enote - 11. del: Značilna števila (ISO 80000-11:2019)
Quantities and units - Part 11: Characteristic numbers (ISO 80000-11:2019)

Größen und Einheiten - Teil 11: Kenngrößen der Dimension Zahl (ISO 80000-11:2019)

Grandeurs et unités - Partie 11: Nombres caractéristiques (ISO 80000-11:2019)
Ta slovenski standard je istoveten z: EN ISO 80000-11:2020
ICS:
01.060 Veličine in enote Quantities and units
SIST EN ISO 80000-11:2020 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 80000-11:2020
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SIST EN ISO 80000-11:2020
EN ISO 80000-11
EUROPEAN STANDARD
NORME EUROPÉENNE
October 2020
EUROPÄISCHE NORM
ICS 01.060 Supersedes EN ISO 80000-11:2013
English Version
Quantities and units - Part 11: Characteristic numbers (ISO
80000-11:2019)

Grandeurs et unités - Partie 11: Nombres Größen und Einheiten - Teil 11: Kenngrößen der

caractéristiques (ISO 80000-11:2019) Dimension Zahl (ISO 80000-11:2019)
This European Standard was approved by CEN on 21 October 2020.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this

European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references

concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN

member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by

translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management

Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,

Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2020 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 80000-11:2020 E

worldwide for CEN national Members.
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SIST EN ISO 80000-11:2020
EN ISO 80000-11:2020 (E)
Contents Page

European foreword ....................................................................................................................................................... 3

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SIST EN ISO 80000-11:2020
EN ISO 80000-11:2020 (E)
European foreword

The text of ISO 80000-11:2019 has been prepared by Technical Committee ISO/TC 12 "Quantities and

units” of the International Organization for Standardization (ISO) and has been taken over as

EN ISO 80000-11:2020 by Technical Committee CEN/SS F02 “Units and symbols” the secretariat of

which is held by CCMC.

This European Standard shall be given the status of a national standard, either by publication of an

identical text or by endorsement, at the latest by April 2021, and conflicting national standards shall be

withdrawn at the latest by April 2021.

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. CEN shall not be held responsible for identifying any or all such patent rights.

This document supersedes EN ISO 80000-11:2013.

According to the CEN-CENELEC Internal Regulations, the national standards organizations of the

following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,

Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,

Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of

North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the

United Kingdom.
Endorsement notice

The text of ISO 80000-11:2019 has been approved by CEN as EN ISO 80000-11:2020 without any

modification.
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SIST EN ISO 80000-11:2020
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SIST EN ISO 80000-11:2020
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 80000-11:2019(E)
ISO 2019
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SIST EN ISO 80000-11:2020
ISO 80000-11:2019(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2019

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
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Phone: +41 22 749 01 11
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved
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SIST EN ISO 80000-11:2020
ISO 80000-11:2019(E)
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

© ISO 2019 – All rights reserved iii
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SIST EN ISO 80000-11:2020
ISO 80000-11:2019(E)
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

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

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).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see: www .iso

.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
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SIST EN ISO 80000-11:2020
ISO 80000-11:2019(E)
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.
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SIST EN ISO 80000-11:2020
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SIST EN ISO 80000-11:2020
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.
© ISO 2019 – All rights reserved 1
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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
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):
Δp is drop of pressure (ISO 80000-4),
Eu′= Eu ; where
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
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)
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© ISO 2019 – All rights reserved 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
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),
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).
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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 measure to estimate wheth-

expressed by er the gas in flow behaves like a continuum.
Kn=λ /l ; where The characteristic length, l, can be a characteristic
size of the gas flow region like a pipe diameter.
λ is mean free path (ISO 80000-9), and
l is characteristic length (ISO 80000-3)

11-4.8 Strouhal num- Sr, relation between a characteristic frequency and a characteristic The characteristic length, l, can be the diameter of an

ber; speed for unsteady flow with periodic behaviour, expressed by obstacle in the flow which can cause vortex shedding,

or the length of it.
Thomson num- Sr= fl/v ; where
ber
f is frequency (ISO 80000-3) of vortex shedding,
l is characteristic length (ISO 80000-3), and
v is speed (ISO 80000-3) of flow

11-4.9 drag coefficient c relation between the effective drag force and inertial forces for a The drag coefficient is strongly dependant on the

body moving in a fluid, expressed by shape of the body.
c = ; where
ρv A
F is drag force (ISO 80000-4) on the body,
ρ is mass density (ISO 80000-4) of the fluid,
v is speed (ISO 80000-3) of the body, and
A is cross-sectional area (ISO 80000-3)

11-4.10 Bagnold number Bg quotient of drag force and gravitational force for a body moving in a The characteristic length, l, is the body’s volume di-

fluid, expressed by vided by its cross-sectional area.
c ρv
Bg= ; where
lgρ
c is drag coefficient (item 11-4.9) of the body,
ρ is mass density (ISO 80000-4) of the fluid,
v is speed (ISO 80000-3) of the body,
l is characteristic length (ISO 80000-3),
g is acceleration of free fall (ISO 80000-3), and
ρ is mass density (ISO 80000-4) of the body
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© ISO 2019 – All rights reserved 5
Table 1 (continued)
No. Name Symbol Definition Remarks

11-4.11 Bagnold number Ba quotient of drag force and viscous force in a fluid transferring solid

particles, expressed by
ργd
s 12/
Ba =−11/ f ; where
2 s
ρ is mass density (ISO 80000-4) of particles,
d is diameter (ISO 80000-3) of particles,
γ=v/d is shear rate time-derivative of shear strain
(ISO 80000-4),
η is dynamic viscosity (ISO 80000-4) of fluid, and
f is volumic fraction of solid particles

11-4.12 lift coefficient c , quotient of the lift force available from a wing at a given angle The lift coefficient is dependant on the shape of the

and the inertial force for a wing shaped body moving in a fluid, wing.
expressed by
2F F
c == ; where
ρv S
F is lift force (ISO 80000-4) on the wing,
ρ is mass density (ISO 80000-4) of the fluid,
v is speed (ISO 80000-3) of the body,
S = A cos α is effective area (ISO 80000-3) when α is the angle
of attack and A is area of the wing, and
q=ρv /2 is dynamic pressure.

11-4.13 thrust coeffi- c quotient of the effective thrust force available from a propeller and The thrust coefficient is dependant on the shape of the

cient the inertial force in a fluid, expressed by propeller.
cF= / ρnd ; where
F is thrust force (ISO 80000-4) of the propeller,
ρ is mass density (ISO 80000-4) of the fluid,
n is rotational frequency (ISO 80000-3), and
d is tip diameter (ISO 80000-3) of the propeller
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6 © ISO 2019 – All rights reserved
Table 1 (continued)
No. Name Symbol Definition Remarks

11-4.14 Dean number Dn relation between centrifugal force and inertial force, for flows of

fluids in curved pipes, expressed by
2vrr
Dn= ; where
ν R
v is (axial) speed (ISO 80000-3),
r is radius (ISO 80000-3) of the pipe,
ν is kinematic viscosity (ISO 80000-4) of the fluid, and
R is radius of curvature (ISO 80000-3) of the path of the pipe

11-4.15 Bejan number Be quotient of mechanical work and frictional energy loss in fluid dy- A similar number exists for heat transfer (item 11-5.9).

namics in a pipe, expressed by
The kinematic viscosity is also called momentum
diffusivity.
Δpl ρΔpl
Be= = ; where
Δp is drop of pressure (ISO 80000-4) along the pipe,
l is characteristic length (ISO 80000-3),
η is dynamic viscosity (ISO 80000-4),
ν is kinematic viscosity (ISO 80000-4), and
ρ is mass density (ISO 80000-4).

11-4.16 Lagrange num- Lg quotient of mechanical work and frictional energy loss in fluid dy- The Lagrange number is also given by

ber namics in a pipe, expressed by
La=⋅Re Eu ; where
lpΔ
Re is the Reynolds number (item 11-4.1), and
Lg= ; where
Eu is the Euler number (item 11-4.2).
l is length (ISO 80000-3) of the pipe,
Δp is drop of pressure (ISO 80000-4) along the pipe,
η is dynamic viscosity (ISO 80000-4), and
v is speed (ISO 80000-3)
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© ISO 2019 – All rights reserved 7
Table 1 (continued)
No. Name Symbol Definition Remarks

11-4.17 Bingham num- Bm, quotient of yield stress and viscous stress in a viscous material for

ber; flow of viscoplastic material in channels, expressed by
plasticity num- τd
Bm= ; where
ber
τ is shear stress (ISO 80000-4),
d is characteristic diameter (ISO 80000-3), e.g. effective
channel width,
η is dynamic viscosity (ISO 80000-4), and
v is speed (ISO 80000-3)

11-4.18 Hedström num- He, quotient of yield stress and viscous stress of a viscous material at

ber flow limit for visco-plastic material in a channel, expressed by
τρd
He= ; where
τ is shear stress (ISO 80000-4) at flow limit,
d is characteristic diameter (ISO 80000-3), e.g. effective
channel width,
ρ is mass density (ISO 80000-4), and
η is dynamic viscosity (ISO 80000-4)

11-4.19 Bodenstein Bd mathematical expression of the transfer of matter by convection in The Bodenstein number is also given by

number reactors with respect to diffusion,
Bd==Pe Re⋅Sc ; where
Bd=vlD/ ; where
Pe is the Péclet number for mass transfer (item
v is speed (ISO 80000-3),
11-6.2),
l is length (ISO 80000-3) of the reactor, and
Re is the Reynolds number (item 11-4.1), and
D is diffusion coefficient (ISO 80000-9)
Sc=ηρ//()DD=ν is Schmidt number (item
11-7.2).
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8 © ISO 2019 – All rights reserved
Table 1 (continued)
No. Name Symbol Definition Remarks

11-4.20 Rossby number; Ro quotient of inertial forces and Coriolis forces in the context of trans- The Rossby number represents the effect of Earth's

fer of matter in geophysics, expressed by rotation on flow in pipes, rivers, ocean currents, tor-

Kiebel number
nadoes, etc.
Ro=v/2()lωϕsin ; where
The quantity ωϕsin is called Coriolis frequency.
v is speed (ISO 80000-3) of motion,
l is characteristic length (ISO 80000-3), the scale of the
phenomenon,
ω is angular velocity (ISO 80000-3) of the Earth's rotation, and
φ is angle (ISO 80000-3) of latitude

11-4.21 Ekman number Ek quotient of viscous forces and Coriolis forces in the context of trans- In plasma physics, the square root of this number is

fer of matter for the flow of a rotating fluid, expressed by used.
The Ekman number is also given by
Ek=νω/2l sinϕ ; where
Ek=Ro/Re ; where
ν is kinematic viscosity (ISO 80000-4),
Ro is the Rossby number (item 11-4.20), and
l is characteristic length (ISO 80000-3), the scale of the
phenomenon,
Re is the Reynolds number (item 11-4.1).
ω is angular frequency (ISO 80000-3) of the Earth’s rotation, and
φ is angle of latitude

11-4.22 elasticity num- El relation between relaxation time and diffusion time in viscoelastic See also Deborah number (item 11-7.8).

ber flows, expressed by
El=trν/ ; where
t is relaxation time (ISO 80000-12),
ν is kinematic viscosity (ISO 80000-4), and
r is radius (ISO 80000-3) of pipe
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© ISO 2019 – All rights reserved 9
Table 1 (continued)
No. Name Symbol Definition Remarks

11-4.23 Darcy friction f representation of pressure loss in a pipe due to friction within a

factor; laminar or turbulent flow of a fluid in a pipe, expressed by
Moody friction 2Δp d
f = ; where
factor
Δp is drop of pressure (ISO 80000-4) due to friction,
ρ is mass density (ISO 80000-4) of the fluid,
v is (average) speed (ISO 80000-3) of the fluid in the pipe,
d is diameter (ISO 80000-3) of the pipe, and
l is length (ISO 80000-3) of the pipe

11-4.24 Fanning number f , relation between shear stress and dynamic pressure in the flow of a The Fanning number describes the flow of fluids in

fluid in a containment, expressed by a pipe with friction at the walls represented by its

shear stress.
f = ; where
n Symbol f may be used where no conflicts are possible.
τ is shear stress (ISO 80000-4) at the wall,
ρ is mass density (ISO 80000-4) of the fluid, and
v is speed (ISO 80000-3) of the fluid in the pipe

11-4.25 Goertler num- Go characterization of the stability of laminar boundary layer flows in The Goertler number represents the ratio of centrifu-

ber; transfer of matter in a boundary layer on curved surfaces, ex- gal effects to viscous effects.

pressed by
Goertler param-
eter
vll
 
Go= ; where
 
ν r
 
v is speed (ISO 80000-3),
l is boundary layer thickne
...

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