PHYSICAL CHEMISTRY IN BRIEF

CHAP. 10: TRANSPORT PROCESSES [CONTENTS] 338

without any internal friction. It would flow out through the smallest possible hole in the bottom
of a vessel instantaneously.

Note:The ratio of viscosity and densityη/%is called thekinematic viscosity. In order

to distinguish the two, the viscosityηis sometimes called thedynamic viscosity.

10.3.3 Poiseuille’s equation

Let us consider a fluid flowing laminarly through a tube of diameterr, lengthLand volumeV
=πr^2 L. At its beginning there is pressurep 1 and at its end pressurep 2. For the volume flow

rate

.

V≡

dV

dτ

we have from (10.9)

.

V=

π r^4

8 η

dp

d`

, (10.11)

where

dp

d`

is the change of pressure with the distance from the beginning of the tube. By

integrating this equation with respect to`andτ, on condition that neither

.
V norηdepends
on pressure, we obtainPoiseuille’s equation:

V=

π r^4 (p 1 −p 2 )

8 η L

τ , [T,incompressible liquid] (10.12)

If Boyle’s law applies for the pressure dependence of the gas volume (fluid is an ideal gas),
we obtain by integrating (10.11)

V =

π r^4 (p^21 −p^22 )

16 η L p 0

τ , [T,ideal gas] (10.13)

wherep 0 is the pressure at which the volumeV is measured.

Note:Relations (10.12) and (10.13) are used to measure viscosity.r,L, p 1 ,p 2 are known,

V andτare measured,ηis calculated. Relation (10.12) is suitable for liquids at common

temperatures and pressures, relation (10.13) can be used for gases in the temperature and

pressure range in which the state equation of an ideal gas applies.