Morris & Fan. Reservoir Sedimentation Handbook

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HYDRAULICS OF SEDIMENT TRANSPORT 9.4











Bed shear or tractive force (N/m

, lb/ft

). It is the frictional force at

the boundary of a moving fluid which resists forward motion. The

unit of N/m

= kg/m/s

is also known as the pascal (Pa), the unit of

pressure in the SI system. To convert into N/m

: multiply g/cm

98; multiply dynes/cm

by 0.1; multiply lb/ft

by 47.88. The term 

is used to designate the bed shear stress and 

the critical value of

bed shear at the initiation of particle motion.

 Terminal fall velocity of a sediment particle in a quiescent fluid

(m/s).

Subscripts:

cr Critical condition of incipient motion

s Sediment

 Side slope

An unsubscripted variable (, , etc.) refers to the fluid.

Most channels are constructed with a trapezoidal cross section, and for ease of

computation many river and reservoir problems can be roughly approximated by using a

trapezoidal section. The definition sketch for a trapezoidal section is given in Fig. 9.1.

9.2 FLOW RESISTANCE EQUATIONS

9.2.1 Chézy Equation

In 1775, the French engineer Chézy presented the relationship bearing his name, the first

equation to successfully relate uniform open-channel flow to bed resistance. Chézy

related the average velocity V of steady uniform open channel flow to three parameters:

channel slope S, the hydraulic radius R, and a coefficient which expresses the boundary

roughness. The equation is usually written in the form:

V = C(RS)

1/2

(9.1)

in which C is the Chézy coefficient of friction.

9.2.2 Manning Equation

The equation developed in 1889 by the Irish engineer Robert Manning may be derived

from the Chézy equation if the Chézy friction coefficient is set equal to C = R

1/6

/n. The

Manning equation has the following form:

V = (1/n) R

2/3

1/2

(9.2)

The n value in the Manning equation represents the roughness or flow-resistance

characteristics of the boundary. When written in fps units, this formula includes the unit

conversion factor 1.486 in the numerator, giving the following form:

V = (1.486/n) R

2/3

1/2

(9.3)

By multiplying both sides of the equation by the wetted cross-sectional area, Manning's

equation can be solved for discharge in SI or fps units:

HYDRAULICS OF SEDIMENT TRANSPORT 9.5

Q = (1/n)AR

2/3

1/2

or Q = (1.486/n)AR

2/3

1/2

(9.4)

In the English-speaking world, the Manning equation is the most widely used hydraulic

resistance equation for open channel flow.

9.2.3 Darcy-Weisbach Equation

Originally developed for flow in pipes, the Darcy-Weisbach equation has the following

form:

V = (8gRS/ƒ)

1/2

or V/U

= (8/f)

1/2

(9.5)

Unlike the friction coefficient in the Chézy and Manning equations, the Darcy Weisbach

friction factor ƒ is dimensionless, and can be read from a Moody diagram.

9.3 HYDRAULIC FLOW-RESISTANCE FACTORS

Hydraulic flow resistance has two components: grain roughness and form loss. Grain

roughness refers to the shear forces created by sediment particles, vegetation, or other

roughness elements at the flow boundary. Form loss is the large-scale turbulent loss

caused by the irregularity of the channel geometry along its length because of

constrictions, expansions, bends, bed forms, and similar geometric features. Both types of

flow resistance are important in natural channels. More extensive information on n value

determination may be found in Chow (1959), Barnes (1967), and Arcement and

Schneider (1989). Chow includes tables and photographs to aid in the evaluation of the

roughness in excavated and natural channels, and also describes the U.S. Soil

Conservation Service procedure for estimating the n value on the basis of vegetal

retardance. Barnes presents the Manning roughness values for a range of natural

channels, illustrating each channel with color photographs, while Arcement and

Schneider provide similar information and photographs for floodplain forests.

9.3.1 Grain Roughness

The Strickler formula, developed in 1923, defined Manning's n value for grain roughness

as a function of particle size:

n 

1/6

21.1

(9.6)

where d = particle diameter in meters. The Federal Highway Administration (1975)

equation to estimate the roughness for gravel beds or riprap has the same form but with a

coefficient value of 20.8 in the denominator. Equations of this type are relatively

insensitive to changes in grain diameter and do not include the effect of form losses due

to irregular channel geometry.

HYDRAULICS OF SEDIMENT TRANSPORT 9.6

9.3.2 Estimating Total Roughness

A tabulation of representative roughness values for common engineering materials and

natural channels are summarized in Table 9.1.

TABLE 9.1 Representative Values of Manning's n Value for Open Channels

Type of channel Minimum Normal Maximum

Lined channels

Concrete channels

Trowel finish 0.011 0.013 0.015

Float finish 0.013 0.015 0.016

Finished, gravel on bottom 0.015 0.017 0.020

Unfinished 0.014 0.017 0.020

Gunite, good section 0.016 0.019 0.023

Gunite, wavy section 0.018 0.022 0.024

On good excavated rock 0.017 0.020

On irregular excavated rock 0.022 0.027

Gravel bottom with sides of

Formed concrete 0.017 0.020 0.025

Random stone in mortar 0.020 0.023 0.026

Dry rubble or riprap 0.023 0.033 0.036

Gabion-lined channels

Unvegetated 0.025 0.028 0.030

Vegetated channels

Vegetation erect 0.030

0.500

Vegetation flattened

0.030

0.070

Excavated or dredged channels

Earth, straight and uniform

Clean, recently completed 0.016 0.018 0.020

Clean, after weathering 0.018 0.022 0.025

Gravel, uniform section, clean 0.022 0.025 0.030

With short grass, few weeds 0.022 0.027 0.033

Earth, winding and sluggish

No vegetation 0.023 0.025 0.030

Grass, some weeds 0.025 0.030 0.033

Dense weeds or aquatic plants in deep

channels

0.030 0.035 0.040

Earth bottom and rubble sides 0.028 0.030 0.035

Stony bottom and weedy banks 0.025 0.035 0.040

Cobble bottom and clean sides 0.030 0.040 0.050

Dragline-excavated or dredged

No vegetation 0.025 0.028 0.033

Light brush on banks 0.035 0.050 0.060

Rock cuts

Smooth and uniform 0.025 0.035 0.040

Jagged and irregular 0.035 0.040 0.050

HYDRAULICS OF SEDIMENT TRANSPORT 9.7

TABLE 9.1 Representative Values of Manning’s n Value for Open Channels (Continued)

Type of channel Minimum Normal Maximum

Excavated or dredged channels

Channels not maintained, weeds and brush uncut

Dense weeds, high as flow depth 0.050 0.080 0.120

Clean bottom, brush on sides 0.040 0.050 0.080

Same, highest stage of flow 0.045 0.070 0.110

Dense brush, high stage 0.080 0.100 0.140

Natural Streams

Minor streams (top width at flood stage <100 ft)

Streams on plain

1. Clean, straight, full stage, no rifts 0.025 0.030 0.033

or deep pools

2. Same as above, but more stones and weeds 0.030 0.035 0.040

3. Clean, winding, some pools and shoals 0.033 0.040 0.045

4. Same as above, but some weeds and stones 0.035 0.045 0.050

5. Same as above, lower stages, more 0.040 0.048 0.055

ineffective slopes and sections

6. Same as 4, but more stones 0.045 0.050 0.060

7. Sluggish reaches, weedy, deep pools 0.050 0.070 0.080

8. Very weedy reaches, deep pools, 0.075 0.100 0.150

or floodways with heavy stand of

timber and underbrush

Mountain streams, no vegetation in channel,

banks usually steep, trees and brush

along banks submerged at high stages

Bottom: gravels, cobbles, and few 0.030 0.040 0.050

Boulders

Bottom: cobbles with large 0.040 0.050 0.070

Boulders

Flood plains

Pasture, no brush

Short grass 0.025 0.030 0.035

High grass 0.030 0.035 0.050

Cultivated areas

No crop 0.020 0.030 0.040

Mature row crops 0.025 0.035 0.045

Mature field crops 0.030 0.040 0.050

TABLE 9.1 Representative Values of Manning's

Value for Open Channels

tinued)

(Con

HYDRAULICS OF SEDIMENT TRANSPORT 9.8

TABLE 9.1 Representative Values of Manning's n Value for Open Channels (Continued)

Type of channel Minimum Normal Maximum

Natural streams

Brush

Scattered brush, heavy weeds 0.035 0.050 0.070

Light brush and trees, in winter 0.035 0.050 0.060

Light brush and trees, in summer 0.040 0.060 0.080

Medium to dense brush, in winter 0.045 0.070 0.110

Medium to dense brush,

in summer

0.070 0.100 0.160

Trees

Dense willows, summer, straight 0.110 0.150 0.200

Cleared land with tree stumps, no

sprouts

0.030 0.040 0.050

Same as above, but with heavy

growth of sprouts

0.050 0.060 0.080

Heavy stand of timber, a few

down trees, little undergrowth,

flood stage below branches

0.080 0.100 0.120

Same as above, but with flood

stage reaching branches

0.100 0.120 0.160

Major streams (top width at flood stage

>100 ft). The n value is less than for minor

streams of similar description because banks

offer proportionally less effective resistance.

Regular section with no boulders or brush

0.025

0.060

Irregular and rough section 0.035 0.100

Source: Chow (1959) and others.

9.3.3 Cowan's Method

Specific procedures that can be used to determine Manning's n values for channels and

floodplains, described by Arcement and Schneider (1989), are based on Cowan's (1956)

method, work on channel roughness by Aldridge and Garrett (1973), and floodplain

studies. Cowan's procedure determines roughness values using a base n value which is

then modified incorporate additional factors which influence flow resistance. The basic

form of the relationship is

n = (n

+ n

) m (9.7)

where n

= base n value for a straight, uniform, smooth channel in natural materials

= factor for the effect of surface irregularities

= factor for variations in shape and size of the channel cross section

= factor for obstructions

= factor for vegetation and flow conditions

and m = factor for channel meandering

The base n value may be selected from Table 9.2, and then modified according to the

HYDRAULICS OF SEDIMENT TRANSPORT 9.9

parameters given in Table 9.3 for channels or Table 9.4 for floodplains. The adjustment

for meanders in Table 9.3 refers only to the case when flow is contained within the

channel; it does not apply to downvalley overbank flow which crosses meanders. For

floodplains the base n value is selected for the natural bare soil surface without

considering the vegetative cover. Arcement and Schneider noted that the n values given

in Table 9.2 cover a wide range because the effects of bed roughness are difficult to

separate from the effects of other roughness factors. The selection of the base n value

from within the ranges given in the table will be influenced by personal judgment and

experience.

For channels, the selection of the base n value depends on whether the channel bed is

unstable or stable. Sand-bed rivers with an unlimited supply of sediment are classified as

unstable because bed geometry is affected by bed forms; this classification does not

include channels in rock or clay transporting only a thin layer of sand which may be

entirely mobilized during large events. Channels which do not develop bed forms are

classified as stable and include streams with beds consisting of rock, cohesive alluvial

materials, and gravel or larger material. In sand-bed channels the flow regime should be

determined by the method in Sec. 9.4. The base roughness values for sand-bed channels

in Table 9.2 are given for upper regime. The n values for transitional- and lower-regime

conditions are primarily determined by bed form, are generally much larger than the val-

ues shown in Table 9.2, and cannot be assigned reliably using this method. Characteristic

TABLE 9.2 Guidelines for Selecting Base n Value in Channels and Floodplain

Base n value

Bed material

Median size of

bed material,

Straight

uniform

channel

Smoothest

possible

channel

Unstable channels (san bed, upper

regime):

0.2 0.012 —

0.3 0.017 —

0.4 0.020 —

0.5 0.022 —

0.6 0.023 —

0.8 0.025 —

1.0 0.026 —

Stable channels and floodplains:

Concrete — 0.012-0.018 0.011

Rock cut — — 0.025

Firm soil — 0.025-0.032 0.020

Coarse sand 1-2 0.026-0.035 0.020

Fine gravel — — 0.024

Gravel 2-64 0.028-0.035 —

Coarse gravel — — 0.026

Cobble 64-256 0.030-0.050 —

Boulder >256 0.040-0.070 —

Notes: Values for straight uniform channel are from Benson and Dalrymple (1967) and represent conditions

close to average. Values for smoothest possible channel are from Chow (1959).

Source: Arcement and Schneider (1989).

HYDRAULICS OF SEDIMENT TRANSPORT 9.10

TABLE

9.3

Adjustment Values for Factors Affecting Channel Roughness

Channel conditions

n value

adjustment

Example

Degree of

irregularity (n

)

Smooth 0.000 Compares to the smoothest channel

attainable in a given bed material.

Minor 0.001-0.005 Compares to carefully dredged channels in good

condition but having slightly eroded or

scoured side slopes.

Moderate 0.006-0.010 Compares to dredged channels having moderate

to considerable be roughness and moderately

sloughed or eroded side slopes.

Severe 0.011-0.020 Badly sloughed or scalloped banks of natural

streams; badly eroded on sloughed sides of

canals or drainage channels; unshaped, jagged

and irregular surfaces of channels in rock.

Variation in channel

cross section (n

)

Gradual 0.000 Size and shape of channel cross sections change

gradually.

Alternating

occasionally

0.001-0.005 Large and small cross sections alternate

occasionally, or the main flow occasionally

shifts from side to side owing to changes in

cross-sectional shape.

Alternating

frequently

0.010-0.015 Large and small cross sections alternate

frequently, or the main flow frequently shifts

from side to side owing to changes in cross-

sectional shape.

Effect of obstruction

)

Negligible 0.000-0.004 A few scattered obstructions, which include

debris deposits, stumps, exposed roots, logs,

piers, or isolated boulders, that occupy less

than 5% of the cross sectional area.

Minor 0.005-0.015

Obstructions occupy less than 15% of the cross

sectional area, and the spacing between

obstructions is such that the sphere of

influence around one obstruction does not

extend to the sphere of influence around

another obstruction. Smaller adjustments are

used for curved smooth-surfaced objects than

are used for sharp-edged angular objects.

Appreciable 0.020-0.030 Obstructions occupy from 15 to 50% of the cross

sectional area, or the space between

obstructions is small enough to cause the

effects of several obstructions to be a additive,

thereby blocking an equivalent part of a cross

section.

Severe 0.040-0.050 Obstructions occupy more than 50% of the cross

sectional area, or the space between

obstructions is small enough to cause

turbulence across most of the cross section.

HYDRAULICS OF SEDIMENT TRANSPORT 9.11

TABLE

9.3

Adjustment Values for Factors Affecting Channel Roughness (Continued)

Channel conditions

n value

adjustment

Example

Amount of

vegetation

)

Small 0.002-0.010 Dense growths of flexible turf grass, such as Bermuda,

or weeds growing where the average depth of flow

is at least two times the height of the vegetation;

supple tree seedlings such as willow, cottonwood,

arrowweed, or saltcedar growing where the average

depth of flow is at least 3 times the height of the

vegetation.

Medium 0.010-0.025 Turf grass growing where the average depth of flow is

from 1 to 2 times the height of the vegetation;

moderately dense stemmy grass, weeds, or tree

seedlings growing where the average depth of flow

is from two to three times the height of the

vegetation; brushy, moderately dense vegetation,

similar to 1- to 2-year-old willow trees in the

dormant season, growing along the banks, and no

significant vegetation is evident along the channel

bottoms where the hydraulic radius exceeds 2 ft.

Large 0.025-0.050 Turf grass growing where the average depth of flow is

about equal to the height of the vegetation: 8- to 10-

year-old willow or cottonwood trees intergrown with

some weeds and brush (none of the vegetation in

foliage) where the hydraulic radius exceeds 2 ft;

bushy willows about 1 year old intergrown with

some weeds along side slopes (all vegetation in full

foliage), and no significant vegetation exists along

channel bottoms where the hydraulic radius is

greater than 2 ft.

Very large 0.050-0.100 Turf grass growing where the average depth of flow is

less than half the height of the vegetation; bushy

willow trees about 1 year old inter-grown with

weeds along side slopes (all vegetation in full

foliage), or dense cattails growing along channel

bottom; trees inter-grown with weeds and brush (all

vegetation in full foliage).

Minor

1.00

Ratio of the channel length to valley length is 1.0 to

1.2.

Appreciable 1.15

Ratio of the channel length to valley length is 1.2 to

1.5.

Degree of

meandering

(m)

Severe

1.30

Ratio of the channel length to valley length is greater

than 1.5.

Source: Arcement and Schneider (1989)

HYDRAULICS OF SEDIMENT TRANSPORT 9.12

TABLE 9.4 Adjustment Values for Factors Affecting Floodplain Roughness

Floodplain conditions

n value

adjustment

Example

Smooth 0.000

Compares to the smoothest, flattest flood plain

attainable in a given bed material.

Minor 0.001-0.005 Is a flood plain slightly irregular in shape. A few rises

and dips or sloughs may be visible on the flood

plain.

Moderate 0.006-0.010 Has more rises and dips. Sloughs and hummocks ma

occur.

Degree of

irregularity

)

Severe 0.011-0.020 Flood plain very irregular in shape. Many rises and

dips or sloughs are visible. Irregular ground

surfaces in pastureland and furrows per pendicular

to the flow are also included.

Variation of

floodplain

cross section

)

0.0 Not applicable.

Negligible 0.000-0.004 Few scattered obstructions, which include debris

deposits, stumps, exposed roots, logs, or isolated

boulders, occupy less than 5% of the cross-

sectional area.

Minor 0.005-0.019 Obstructions occupy less than 15% of the cross

sectional area.

Effect of

obstructions

)

Appreciable 0.020-0.030 Obstructions occupy from 15 to 50% of the cross

sectional area.

Small 0.001-0.010 Dense growth of flexible turf grass, such aa

Bermuda, or weeds growing where the average

depth of flow is at least two times the height of the

vegetation, or supple tree seedlings such as willow,

cottonwood, arrowweed, or saltcedar growing

where the average depth of flow is at least three

times the height of the vegetation.

Medium 0.011-0.025 Turf grass growing where the average depth of flow

is from 1 to 2 times the height of the vegetation, or

moderately dense stemmy grass, weeds, or tree

seedlings growing where the average depth of flow

is from 2 to 3 times the height of the vegetation;

brushy, moderately dense vegetation, similar to 1-

to 2-year-old willow trees in the dormant season.

Amount of

vegetation

)

Large 0.026-0.050 Turf grass growing where the average depth of flow

is about equal to the height of the vegetation, or 8-

to 10-year-old willow or cotton wood trees

intergrown with some weeds and brush (none of

the vegetation in foliage) where the hydraulic

radius exceeds 2 ft, or mature row crops such as

small vegetables, or mature field crops where depth

of flow is at least twice the height of the

vegetation.

HYDRAULICS OF SEDIMENT TRANSPORT 9.13

TABLE 9.4 Adjustment Values for Factors Affecting Floodplain Roughness

Floodplain conditions

n value

adjustment

Example

Very large 0.051-0.100

Amount of

vegetation

(n4)

Turf grass growing where the average depth of flow

is less than half the height of the vegeta tion, or

moderate to dense brush, or heavy stand of timber

with few down trees and little undergrowth where

depth of flow is below branches, or mature field

crops where depth of flow is less than the height

of the vegetation.

Extreme 0.101-0.200

Dense bushy willow, mesquite and saltcedar (all

vegetation in full foliage), or heavy stand of

timber, few down trees, depth of flow reaching

branches.

Degree of

meander (m)

1.0 Not applicable.

Source: Arcement and Schneider (1989)

n value ranges as a function of bed form given by Simons, Li & Associates (1982) are

presented in Table 9.5. They suggest that values in the higher portion of the range be used

in applications such as flood control where maximum water depth is the critical

parameter of concern, and values near the lower limit of the range be used for velocity-

critical applications such as sediment transport, scour, bank erosion, and riprap design.

Brownlie (1983) described a method for determining the roughness in sand beds

attributable to both grain size and bed forms. His procedure is also explained in Chang

(1988).

9.3.4 Effect of Vegetation on Flow Resistance

Vegetation presents a special problem in hydraulic computations because the boundary

roughness changes greatly as a function of factors such as flow depth, velocity, and the

TABLE 9.5 Manning's n Values for Channels with Beds of Fine to Medium Sand

Suggested values

Bed form Range Max. depth Max. velocity

Ripples 0.018-0.030 0.030 0.022

Dunes 0.020-0.035 0.035 0.030

Transition 0.014-0.025 0.030 0.025

Plane bed 0.012-0.022 0.022 0.020

Standing waves 0.014-0.025 0.025 0.020

An idunes t 0.015-0.031 0.030 0.025

Source: Simons, Li & Associates (1982)

biomechanical characteristics of the vegetation. Vegetation is also of special interest in

problems involving reservoir sedimentation. Delta deposits in reservoirs will raise the

backwater profile upstream of the normal pool by changing both the cross-section

geometry and hydraulic roughness. Hydraulic roughness effects can be particularly

important if the delta becomes vegetated with brush or trees. Vegetation can also enhance

sediment trapping on deltas by creating lower flow velocities, plus the physical trapping

Morris &amp; Fan. Reservoir Sedimentation Handbook

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Morris & Fan. Reservoir Sedimentation Handbook