CHAPTER 2: PROPERTIES OF OPEN CHANNELS 
2.1 KINDS OF OPEN CHANNELS
The
 There are two kinds of channels:
 Artificial (prismatic)
 Natural (nonprismatic)
Tinajones feeder canal, Chiclayo, Peru


Rio La Silla Natural Park, Monterrey, Mexico.


 Other waterresourcesrelated fields:
 Hydrology: the study of water in the hydrologic cycle.
 Hydroclimatology: the study of climate and the hydrologic cycle.
 Fluvial geomorphology: the study of the shape of streams and rivers.
 River mechanics: the study of the mechanical properties and behavior or rivers.
 Sedimentology: the study of sediment.
 Potamology: the study of rivers.
Lower Mississippi river near Baton Rouge, Louisiana.


 Uses of artificial channels:
 Navigation channels
 Water conveyance channels (Example: the Dulzura conduit,
which links Barrett reservoir with drainage to Lower Otay reservoir, in San Diego County)
The Dulzura conduit, San Diego County, California.


 Power canals
 Irrigation canals (Example: the AllAmerican canal, in the Imperial valley)
The AllAmerican canal, Imperial County, California.


Location of the AllAmerican canal, Imperial County, California.


Location of the AllAmerican canal, Imperial County, California.


Indus Basin Link Canals, Pakistan.


 Flood control channels, floodways.
Rio Santa Catarina, Monterrey, Mexico.


 Drainage ditches (drainage ditches in Imperial valley, draining to the Salton Sea).
Imperial Valley irrigation drain.


 Names for channels:
 Canal: long, mildsloped, lined/unlined, groundsupported, masonry/concrete/wood/asphalt.
 Flume: supported above ground (lab flume), wood/metal/concrete/masonry.
 Chute: channel with steep slope, usually supercritical.
 Drop: Chute with very short distance.
 Culvert: covered channel of comparatively short length, flowing partially full.
Drainage drop structure in Tijuana, Baja California.


Tinajones drop structure, Chiclayo, Peru.


Chute at Taymi Canal, Chiclayo, Peru.


Canal with falls, La Joya, Arequipa, Peru.


Junction of main irrigation canal with main drain, La Joya, Arequipa, Peru.


Crossing of Tinajones Feeder Canal with Chiriquipe Wash, Chiclayo, Peru.


Crossing of Arroyo Rosa de Castilla with Mexico Highway 2, Tecate, Baja, California.


2.2 CHANNEL GEOMETRY
The
 A prismatic channel has a constant cross section and constant bottom slope.
 The channel section is the cross section normal to the direction of flow.
 A trapezoid is the most common crosssectional shape. It provides bank stability.
 A rectangular section is used in laboratory flumes.
 Channels built of stable materials (rock, concrete) can be rectangular.
 Triangular channels are used in ditches, roadside gutters.
 Depth of flow y: vertical distance from the free surface to the lowest point in channel cross section.
 Depth of flow section d: height of channel cross section; depth normal to direction of flow.
 For a channel with a longitudinal slope angle θ:
Fig. 29 (Chow)


 Stage y: elevation of the free surface.
 Top width T: width of channel cross section at free surface.
 Flow area A: area of flow in channel cross section.
 Wetted perimeter P: important in determining friction.
 Hydraulic radius R: ratio A/P.
 Hydraulic depth D: ratio A/T.
 For hydraulically wide channels: T ≈ P
 For hydraulically wide channels: D ≈ R
 In a channel section, the velocities near the surface and near the bottom differ.
 Velocities near the boundary are close to zero (noslip condition).
 Large velocity gradients near the boundary produce large shear stresses
(which entrain and transport sediment).
 The maximum velocity occurs near the surface, at a distance of 0.05 to 0.25 of the flow depth.
 Velocities also vary transversally along horizontal bends; they are larger on the outside of the bend.
 Channel roughness will cause the curvature of the vertical velocity profile to increase.
 In a wide open channel, the sides have no influence on the velocity profile.
 The flow has a tendency to be 2D instead of 3D.
 Ratio T/D > 10 will assure widechannel condition.
 Often a hydraulic analysis is carried out per unit of channel width.
 In a rectangular channel:
2.3 VELOCITY DISTRIBUTION
The
2.4 MEASUREMENTS OF VELOCITY
The
 Measurements are taken with a current meter positioned at 0.6 d, measured from the surface.
 Also, at 0.2 d and 0.8 d, and then find the average of these two values.
Price AA current meter (Courtesy of the U.S. Geological Survey).


USGS gaging stating at Campo Creek, San Diego County, California.


2.5 VELOCITY DISTRIBUTION COEFFICIENTS
The
 Due to nonuniform distribution of velocities over a cross section, the true velocity head is usually greater than the value
computed based on the mean (average) velocity.
 The true velocity head is:
h_{v} = α [V_{m}^{2}/(2g)]

 α is the energy coefficient or Coriolis coefficient.
 The value of α is typically in the range 1.031.36 for fairly straight prismatic channels.
 The value is greater for small channels, and smaller for large channels.
 The true momentum flux is:
 β is the momentum coefficient or Boussinesq coefficient.
 The value of β is typically in the range 1.011.12 for fairly straight prismatic channels.
 The values of α and β are slightly greater than 1.
 α is always greater than β.
 In channels of complex cross section, the values of α and β can easily get to be 1.6 and 1.2, respectively.
 Values of α greater than 2 have been observed in very irregular cross sections.
 The true velocity head is usually greater than the value
computed based on the average velocity.
 Assume:
 A = total area of the cross section [L^{2}]
 ΔA = incremental area [L^{2}]
 V_{m} = mean velocity of the cross section [L T^{1}]
 V = velocity through ΔA [L T^{1}]
 The weight flux through ΔA is:
 The weight flux through A is:
 Kinetic energy = force × distance = (mass × acceleration) × distance = (1/2) mV^{2} [M L^{2} T^{2}]
 Momentum = force × time = (mass × acceleration) × time = mV [M L T^{1}]
 Velocity head = kinetic energy per unit of weight
 Velocity head = [(1/2) m V^{2}] / (mg) = V^{2}/(2g) [L]
 Kinetic energy flux [through incremental area ΔA] =
kinetic energy per unit of weight × weight flux =
[V^{2}/(2g)] [γ V ΔA]= γ V^{3} ΔA /(2g)
 For all the increments of area ΔA:
∑ γ V^{3} ΔA /(2g)
 Kinetic energy flux [through total area A] =
kinetic energy per unit of weight × weight flux =
[αV_{m}^{2}/(2g)] [γ V_{m} A] = α γ V_{m}^{3} A /(2g)
 Therefore:
∑ V^{3} ΔA = α V_{m}^{3} A
α = ∑ V^{3} ΔA / (V_{m}^{3} A)

 Momentum β coefficient:
 The mass flux through ΔA is:
 The mass flux through A is:
 Momentum = force × time = mass × velocity = m V [M L T^{1}]
 Momentum flux = mass flux × velocity [F]
 The momentum flux through ΔA is:
ρ V^{2} ΔA
 [F = M L T^{2}] 
 For all the increments of area ΔA:
∑ ρ V^{2} ΔA
 The momentum flux through A is:
β ρ V_{m}^{2} A
 [F = M L T^{2}] 
 Therefore:
∑ V^{2} ΔA = β V_{m}^{2} A
β = ∑ V^{2} ΔA / (V_{m}^{2} A)

 Energy flux = (weight flux) × (velocity head) [(F/T) L = FL/T]
 Momentum flux (force) = (mass flux) × (velocity) [(M/T) (L/T) = M (L/T^{2})]
 Note that the mean velocity is defined as:
 For approximate values, α and β can be computed as follows:
with
2.6 PRESSURE DISTRIBUTION
The
 The pressure is measured by the height of the water column at any point in the vertical.
 The pressure at any point is directly proportional to the depth of the point and equal to the hydrostatic pressure
corresponding to this depth.
 The distribution is linear, and is known as the hydrostatic law of pressure distribution.
 This assumes no vertical accelerations.
 This type of flow is known as parallel flow.
 The streamlines have no substantial curvature.
 Uniform flow is practically parallel flow.
 Gradually varied flow may be regarded as parallel flow.
 If the curvature is substantial, the flow is curvilinear flow.
 In curvilinear flow, the pressure distribution is not hydrostatic.
Fig. 27 (Chow)


 The centrifugal pressure p is [mass (per unit of area) × centrifugal acceleration]:
p = (γ/g) d (V_{m}^{2}/r)

 The pressure rise c is:
c = p/γ = (d/g) (V_{m}^{2}/r)

 The rise is positive for concave flow, and negative for convex flow.
QUESTIONS
PROBLEMS
REFERENCES
Chow, V. T. 1959. Openchannel Hydraulics. McGraw Hill, New York.
http://openchannelhydraulics.sdsu.edu 

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