Physics for Geologists, Second edition

112 Fluids and fluid flow
Figure 12.1 Speed of non-turbulent flowing water at the surface in a channel
(in plan). The vertical profile is similar to the bottom half of this
diagram.
the viscosity of the water, provide the retarding forces; and when these forces
have reached equilibrium, the water will have constant velocity - constant
on all scales above the molecular if the flow is laminar, only in a gross sense
if it is turbulent. The resistance at the sides means that there will be a velocity
pattern in the surface water, with the greatest velocity at the centre, least at
the sides, decreasing to zero in contact with the sides at what is called the
wetted surface (Figure 12.1). Similarly, there is a vertical velocity profile,
from zero in contact with the base, to a maximum near the surface (why
near, not at? Because there is air resistance to flow at the surface - less,
certainly, than at the sides and bottom, but nevertheless a resistance).
What then do we mean by velocity of a water stream when it is different in
different positions in the water? In laminar flow we can say that the velocity is
constant in any one position in the channel, but the variation of velocity with
position means that we must define velocity of the channel water as a whole
as the volumetric rate of flow divided by the normal cross-sectional area.
Dimensionally that is L3~-l/L2
= LT-l. In units, it is m3 s-I m-2 -
- ms-I.
Wind velocity also has a profile. That is why the stipulated height of
anemometers is 10 m above the ground.
Capillarity
The water of a fountain breaks up into drops that are nearly spherical; a tap
drips drops that are nearly spherical; gas bubbles in soda water are nearly
spherical, and you can remove a fly from water by dipping your finger on
the fly and it is retained in the drop of water you extract. Some insects can
walk on water, and if you look at them carefully you will see that their feet
depress the surface slightly. You can fill a glass with water above the level
of the rim. Capillarity is involved in all these things, and in the underground
fluids, water, crude oil and gas. Soils retain moisture because of capillarity;
crude oil and natural gas reservoirs retain water because of capillarity.
Copyright 2002 by Richard E. Chapman