FprEN ISO 80000-11

SLOVENSKI STANDARD
oSIST prEN ISO 80000-11:2017
01-marec-2017
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Quantities and units - Part 11: Characteristic numbers (ISO/DIS 80000-11:2017)
Größen und Einheiten - Teil 11: Kenngrößen der Dimension Zahl (ISO/DIS 80000-
11:2017)

Grandeurs et unités - Partie 11: Nombres caractéristiques (ISO/DIS 80000-11:2017)

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

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form

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written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of

Foreword ................................................................................................................................................................................... iv

1 Scope ............................................................................................................................................................................. 1

2 Normative references ............................................................................................................................................. 1

3 Names, symbols, and definitions ........................................................................................................................ 1

4 Momentum transfer................................................................................................................................................. 2

5 Transfer of heat...................................................................................................................................................... 15

6 Transport of matter in a binary mixture ...................................................................................................... 22

7 Constants of matter............................................................................................................................................... 29

8 Magnetohydrodynamics ..................................................................................................................................... 31

9 Miscellaneous ......................................................................................................................................................... 38

Bibliography........................................................................................................................................................................... 39

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ISO 80000 consists of the following parts, under the general title Quantities and units:

IEC 80000 consists of the following parts (in collaboration with IEC/TC 25), under the general title Quantities

ISO 80000-11 gives the names, symbols and definitions for characteristic numbers used in the description of

The following documents are referred to in the text in such a way that some or all of their content constitutes

requirements of this document. For dated references, only the edition cited applies. For undated references,

the latest edition of the referenced document (including any amendments) applies.

ISO 80000-9:2009, Quantities and units — Part 9: Physical chemistry and molecular physics

The names, symbols, and definitions for characteristic numbers are given on the following pages.

Characteristic numbers are physical quantities of dimension number 1, although commonly and falsely

called dimensionless quantities. They are used in the studies of natural and technical processes, and [may]

present information about the behaviour of the process, or reveal similarities between different processes.

Characteristic numbers often are described as ratios of forces; in some cases however they are ratios of

energy or work, although noted as forces in the literature; sometimes it is the ratio of characteristic times.

Characteristic numbers may be defined by the same equation, but carry different names if they are

Characteristic numbers may be expressed as products or fractions of other characteristic numbers if these

are valid for the same kind of process. So the following tables are arranged according to some groups of

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 here. The choice largely was depending of their common use.

Besides there was made a restriction on the kind of processes, which are displayed by the section 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 other

representation. Only one of these have been chosen, the other ones declared as deprecated or mentioned in

The transfer of momentum (ISO 80000-4:2006, item 4-8) basically occurs during a collision of 2 bodies, and is governed by the law of momentum conservation. Energy

dissipation may 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 may be a length, width, radi us, etc. of a solid object, often the effective length is

The other subsystem is a fluid, in general liquid or gaseous, with the following properties amongst others:

The field of science is mainly fluid dynamics (mechanics). Characteristic numbers of this kind allow the comparison of objects of different sizes. It also may give some

11-4.2 relationship between pressure drop in a flow to kinetic energy per The Euler number is used to characterize losses in the

11-4.3 Froude ratio of a body’s inertial forces to its gravitational forces for flow of

11-4.4 Grashof ratio of buoyancy forces due to thermal expansion which results in a Heating can occur near hot vertical walls, in pipes, or by a

11-4.5 Weber relationship of inertial forces compared to capillary forces for bubbles The characteristic length is commonly the diameter of

𝑙 is a characteristic length (ISO 80000-3:2006, item 3-1.1), and Sometimes the square root of the Weber number as

𝛾 is surface tension (ISO 80000-4:2006, item 4-25) defined here is called the Weber number. That definition

11-4.6 ratio of the speed of flow to the speed of sound The Mach number represents the relationship of inertial

11-4.7 Knudsen ratio of mean free path of a particle to characteristic length for gas flow The Knudsen number is a measure to estimate whether

11-4.8 Strouhal ratio of characteristic frequency to characteristic speed for unsteady The characteristic length 𝑙 can be the diameter of an

(11-4.8) number flow with periodic behaviour obstacle in the flow which can cause vortex shedding, or

11-4.9 drag ratio of the effective drag force to inertial forces for a body moving in a The drag coefficient is strongly dependant on the shape of

11-4.10 Bagnold ratio of drag force to gravitational force for a body moving in a fluid The characteristic length 𝑙 is the body’s volume divided by

11-4.11 Bagnold ratio of drag force to viscous force in a fluid transporting solid particles

11-4.12 ratio of the lift force available from a wing at a given angle of attack to

11-4.13 thrust ratio of the effective thrust force available from a propeller to the The thrust coefficient is dependent on the shape of the

11-4.14 Dean number ratio of centrifugal force to inertial force for flow of fluids in curved

11-4.15 ratio of mechanical work to frictional energy loss in fluid dynamics in a

11-4.16 Lagrange ratio of mechanical work to frictional energy loss in fluid dynamics in a

11-4.17 Bingham ratio of yield stress to viscous stress in a viscous material for flow of

11-4.18 Hedström ratio of yield stress to viscous stress of a viscous material at flow

11-4.19 Bodenstein representation of the transfer of matter by convection in reactors with The Bodenstein number is also given by

11-4.20 Rossby ratio of inertial forces to Coriolis forces in the context of transfer of The Rossby number represents the effect of earth's

- number; matter for the flow of a rotating fluid rotation on flow in pipes, rivers, ocean currents,

11-4.21 Ekman ratio of viscous forces to Coriolis forces in the context of transfer of In plasma physics the square root of this number is used.

11-4.22 Elasticity ratio of relaxation time to diffusion time in viscoelastic flows

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

11-4.25 Fanning ratio of shear stress to dynamic pressure in the flow of a fluid in a The Fanning number describes the flow of fluids in a pipe

- number , containment with friction at the walls represented by its shear stress.

11-4.26 Goertler characterization of the stability of laminar boundary layer flows in The Goertler parameter represents the ratio of centrifugal

11-4.27 Hagen generalization of Grashof number (11.-4.4) for forced or free convection

11-4.28 Laval number ratio of speed to the (critical) sound speed in the throat of the nozzle The Laval number is a specific kind of Mach number (item

11-4.29 Poiseuille ratio of propulsive force by pressure to viscous force for a flow of fluids

11-4.31 Richardson ratio of potential energy to kinetic energy for a falling body In geophysics differences of these quantities are of

11-4.32 Reech ratio of a speed of an object submerged in water to water wave The Reech number can be u