Physics for Geologists, Second edition

12 Fluids and fluid flow
Introduction
Fluid flow is an important process in geology: it is also one of the least
well understood, and the literature is full of errors. These errors arise mainly
from ignorance and carelessness, as you would expect; but it is also a difficult
subject. Its difficulty lies not so much in the mathematics involved as in the
physical concepts. The fundamental cause of the error and its propagation
is confusion between pressure and energy, and the erroneous statement that
'water flows from high pressure to low'. We saw in Chapter 3 examples of
gravity-driven processes in which water flows from low pressure to high.
General geology requires a good understanding of the principles of fluid
flow for the various processes of sediment distribution (wind, water) and vol-
canic activity. Groundwater geology and petroleum geology require a good
understanding of the physics involved in fluid flow, but it is one of the
tragedies of science that some of the definitions are erroneously stated. Ignore
the fluid flow part of Jaeger and Cook's Fundamentals of rock mechanics
in all three editions (I have a letter from Jaeger dated 26 April 1976 to this
effect). The greatest tragedy is perhaps the erroneous or incomplete defin-
ition of the darcy, the unit of permeability in petroleum studies. This also
shows some of the complexity of the concepts because the four authors of
the papers defining the darcy were physicists and mathematicians.
Do not despair, even if your mathematics is weak, because it is not as
difficult as all that. By the end of this chapter, the principles at least will be
clear to you.
If you watch the smoke rising from a cigarette in a still room, it rises
first in a vertical straight line and then suddenly breaks up into eddies and
whorls. Similarly, a stream may flow with a smooth upper surface until it
narrows, where it breaks in rough water. The smooth flow is called laminar;
the rough, turbulent. Laminar flow is amenable to general mathematical
treatment: turbulent flow is more difficult.
Consider water flowing in a channel of rectangular cross-section and gentle
slope. The component of weight down the slope provides the force that
accelerates the water. Frictional resistance on the bottom and the sides, and
Copyright 2002 by Richard E. Chapman