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which was devised by the American hydraulic engineer
Robert Manning at the end of the nineteenth century,
is a more commonly used formula for estimating flow
velocity:
( ) Hydraulic jump
a
Supercritical flow
Subcritical flow
R 2/3 s 1/2
n
=
v
( ) Hydraulic drop
b
where R is the hydraulic radius, s the channel gradient,
and n the Manning roughness coefficient , which is an
index of bed roughness and is usually estimated from
standard tables or by comparison with photographs of
channels of known roughness. Manning's formula can
be useful in estimating the discharge in flood conditions.
The height of the water can be determined from debris
stranded in trees and high on the bank. Only the channel
cross-section and the slope need measuring.
Subcritical flow
Supercritical flow
Figure 3.10 (a) Hydraulic jump. (b) Hydraulic drop.
Fluvial erosion and transport
depth (Figure 3.10a). A hydraulic drop marks a change
from subcritical to supercritical flow and is accompa-
nied by a reduction in water depth (Figure 3.10b). These
abrupt changes in flow regimes may happen where there
is a sudden change in channel bed form, a situation
rife in mountain streams where there are usually large
obstructions such as boulders.
Flow velocity in streams is affected by the slope
gradient, bed roughness, and cross-sectional form of the
channel. It is very time-consuming to measure stream-
flow velocity directly, and empirical equations have been
devised to estimate mean flow velocities from read-
ily measured channel properties. The Chézy equation ,
named after the eighteenth-century French hydraulic
engineer Antoine de Chézy, estimates velocity in terms
of the hydraulic radius and channel gradient, and a
coefficient expressing the gravitational and frictional
forces acting upon the water. It defines mean flow
velocity, v , as:
Streams are powerful geomorphic agents capable of
eroding, carrying, and depositing sediment. Stream
power is the capacity of a stream to do work. It may
be expressed as:
= ρ
gQs
where
(omega) is stream power per unit length of
stream channel,
(rho) is water density, Q is stream
discharge, and s is the channel slope. It defines the rate
at which potential energy, which is the product of the
weight of water, mg (mass, m , times gravitational accel-
eration, g ), and its height above a given datum, h ,is
expended per unit length of channel. In other words,
stream power is the rate at which a stream works to
transport sediment, overcome frictional resistance, and
generate heat. It increases with increasing discharge and
increasing channel slope.
ρ
C Rs
Stream load
=
v
All the material carried by a stream is its load . The
total load consists of the dissolved load (solutes),
the suspended load (grains small enough to be sus-
pended in the water), and the bed load (grains too large
where R is the hydraulic radius, s is the channel gradient,
and C is the Chézy coefficient representing gravita-
tional and frictional forces. The Manning equation ,
 
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