Fig.D-5
Viscosity as the property of fluids which determines their resistance against shifting (imaginary) layers relative to each other was introduced by I. Newton in 1687. From an experiment schematically shown in Fig.D-5, he deduced the connection between the friction force and other variables, which is nowadays expressed as the shear stress being proportional to transverse gradient of longitudinal velocity component . ( is the transverse co-ordinate, perpendicular to, which is aligned with local flow direction - cf. Fig. A-16). Newton originally defined the so called "dynamic viscosity" - for character of fluid flow, however, the decisive factor is the viscosity , more speficially called "kinematic", which is used exclusively in this text. (In case the "dynamic" viscosity is needed, it is obtained by dividing the viscosity used here by specific volume ).


Fig.D-7
A consequence of the Newton's definition of viscosity (introduced as the coefficient which converts a proportionality into an equation, leaving aside actual molecular mechanism behind the effect) is variation of with state of a liquid, especially with temperature and pressure. In the introductory calculations in the present text, it will be often taken as a material constant of a particular fluid. The table shown here as Fig.D-7 presents for some fluids at approximately atmospheric state - together with values of specific volume , specific thermal and for gases also the gas constant (which makes it possible to find for other states). Nevertheless, especially dependence of upon temperature is quite strong - Fig.D-6 presents it in diagrammatic form for two most important fluids, water and air. A formula very useful for calculations with air is as follows:

The fact that for liquids viscosity decreases with temperature while it increases for gases (Fig.D-6) is the result of different molecular mechanisms responsible for viscosity. In liquids

Fig.D-6
the mechanism is cohession interaction between molecules - mutual attraction which decreases in intensity if increased temperature leads to increased thermal agitation and longer paths of stochastic motions. In gases the mechanism is collison interaction (cf. Fig.D-10) which is more intensive at a higher temperature
Sir Isaac NEWTON
Born:4 Jan 1643 in Woolsthorpe, Lincolnshire, England
Died: 31 March 1727 in London, England
(that is, at higher kinetic energy of molecular motions).



Going to another page: click
This is page Nr. D03 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
Any comments and suggestions concerning this text may be mailed to the author to his address tesar@fsid.cvut.cz

WWW server administrators: Jiri Kvarda, Zdenek Maruna ...... Contact: webmaster@vc.cvut.cz
Last change : 26.03.1997