Forces and dynamics - Physical Processes in Earth and Environmental Sciences - page 50

Fluid

- F AB

A

F AC

Pressure intensity in
stationary fluid acts normal
to any surface, equal in all
possible directions

Solid

C B

- F AB = F BC = F AC

F BC

Pascal

Fig. 3.20 Forces acting on a neutrally buoyant solid prism totally immersed in constant-density fluid.

High

Low

990

980 990

980 1000 980

1010

980

Iceland
low

1020 980

Note high
pressure
gradients in
North Atlantic

1000

980

High

980 1030

1010

High

1020

980

1020

980

Azores
high

1020

980

Fig. 3.21 Atmospheric pressure over North Atlantic, Europe, and North Africa, winter 2003: pressures varying over the area by an extreme 6%.

motion of molecules that we realize the solution to the
paradox: gravity increases the frequency of molecular colli-
sions in direct proportion to the quantity of fluid matter
lying above. The concept of random molecular motions is
the stuff of kinetic theory (see Section 4.18).
A final ponder on pressure in solid Earth. Although a
mean lithostatic pressure gradient can be defined as the
gradient of

much individual principal stresses diverge from the mean
stress by subtracting the latter from the former.
This defines the differential normal stress (see Section
3.13.6), for example, x ( x p ).

3.5.2 Vertical gradient in hydrostatic pressure

is rock density and z is depth, any
analogy with hydrostatic pressure is misleading because of
elastic behaviour in the upper crest and the existence of
tectonic stresses . These exist generally in the solid Earth and
cause the principal normal stresses defined above to be
unequal. The mean pressure is then given by p

g z , where

Hydrostatic pressure is independent of direction, that is, it is
a scalar property, just like temperature and density. However,
gradients of pressure can certainly exist, giving rise to net
forces. This is best appreciated by considering a definition
diagram for another interesting thought experiment
(Fig. 3.22). An imaginary small cylinder, open at both

1/3

( x y z ) and it is convenient to then define by how