Page 60 - Sedimentology and Stratigraphy

Final Proof page 47
26.2.2009 8:16pm Compositor Name: ARaju
Nichols/Sedimentology and Stratigraphy 9781405193795_4_004
The Behaviour of Fluids and Particles in Fluids 47
from and where it is ending up are the same. Kinetic
2
energy (ry =2) is changed as the velocity of the flow is
increased or decreased. If the total energy in the
system is to be conserved, there must be some change
in the final term, the pressure energy (p). Pressure
energy can be thought of as the energy that is stored
when a fluid is compressed: a compressed fluid (such
as a canister of a compressed gas) has a higher energy
than an uncompressed one. Returning to the flow in
the tapered tube, in order to balance the Bernoulli
equation, the pressure energy (p) must be reduced to

compensate for an increase in kinetic energy (ry =2)
2

caused by the constriction of the flow at the end of the

tube. This means that there is a reduction in pressure

at the narrower end of the tube.

If these principles are now transferred to a flow
along a channel (Fig. 4.4) a clast in the bottom of

! " # # $ the channel will reduce the cross-section of the flow
% $
over it. The velocity over the clast will be greater than
$
upstream and downstream of it and in order to bal-
ance the Bernoulli equation there must be a reduction
in pressure over the clast. This reduction in pressure
Fig. 4.3 Flow of a fluid through a tapered tube results in an
provides a temporary lift force that moves the clast
increase in velocity at the narrow end where a pressure
off the bottom of the flow. The clast is then temporar-
drop results.
ily entrained in the moving fluid before falling under
gravity back down onto the channel base in a single
saltation event.
amount of fluid through a smaller gap it must move at
a greater velocity through the narrow end. This effect
is familiar to anyone who has squeezed and constricted
4.2.4 Grain size and flow velocity
the end of a garden hose: the water comes out as a
faster jet when the end of the hose is partly closed off.
The fluid velocity at which a particle becomes
The next thing to consider is the conservation of
entrained in the flow can be referred to as the critical
mass and energy along the length of the tube. The
variables involved can be presented in the form of the velocity. If the forces acting on a particle in a flow are
Bernoulli equation: considered then a simple relationship between the
critical velocity and the mass of the particle would
2 be expected. The drag force required to move a parti-
total energy ¼ rgh þ ry =2 þ p
cle along in a flow will increase with mass, as will the
lift force required to bring it up into the flow. A simple
where r is the density of the fluid, y the velocity, g the
linear relationship between the flow velocity and the
acceleration due to gravity, h is the height difference
drag and lift forces can be applied to sand and gravel,
and p the pressure. The three terms in this equation
2
are potential energy (rgh), kinetic energy (ry =2) and but when fine grain sizes are involved things are more
pressure energy (p). This equation assumes no loss of complicated.
¨
energy due to frictional effects, so in reality the rela- The Hjulstrom diagram (Fig. 4.5) shows the rela-
tionship is tionship between water flow velocity and grain size
and although this diagram has largely been super-
2
rgh þ ry =2 þ p þ E loss ¼ constant seded by the Shields diagram (Miller et al. 1977) it
nevertheless demonstrates some important features
The potential energy (rgh) is constant because the of sediment movement in currents. The lower line
difference in level between where the fluid is starting on the graph displays the relationship between flow