c11 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come
VISCOSITY OF LIQUIDS 169in this respect to the law of Dulong and Petit, which predicts a heat capacity of
25 J K−^1 mol−^1 forsolidmetals. As usual, theoretical treatment of liquids is difficult
because their behavior is between that of a perfectly ordered crystal and that of a
perfectly random (statistical) gas.11.3 VISCOSITY OF LIQUIDS
The viscosity of a liquid often reflects the degree of entanglement of molecules as
they are moved past each other. The viscosity of heavy lubricating oil is greater than
that of gasoline because the average molecular length is greater in oil than in gasoline.
It takes some amount of work to push one molecule past its neighbors.
Consider a liquid flowing through a tube of radiusR. At different radial distances
from the center of the tube, the liquid is flowing at different rates. The greatest
rate is precisely at the center of the tube, whereas the lowest rate occurs where the
liquid experiences maximum frictional drag against its inner surface. It is convenient
to consider the liquid flow as consisting of a large number of concentric laminar
“sleeves” of thicknessdr, whereris the radial distance from the center of the tube
(Fig. 11.6). The viscous drag retarding the flow on one laminar sleeve relative to its
neighbor sleeve is proportional to the difference in speed of adjacent laminadv/dr
times the surface area over which the lamina bear against each other. This is the
circumference of the laminar sleeve times its lengthl:drag∝Adv
dr=ηAdv
dr=η 2 πrldv
dr=fviscousThe proportionality constantηin this equation is theviscosity coefficient. Because
pressure is force per unit areap=f/A, the force driving the liquid through the tube
under gravity flow is fgrav=pA, whereAis the area of the end of the sleeve indrdvflowFIGURE 11.6 Approximation of laminar flow inside a tube. The difference in speed of flow
between the inner and outer surfaces of a lamina isdv/dr.