Open channels & Their Properties

1. ADVANCED OPEN CHANNEL
HYDRAULICS (CHAPTER NO 2)
REFERENCE BOOK:OPEN CHANNEL HYDRAULICS BY “VENTE CHOW”
Presented By: Hadiqa Qadir
2k22-MS-HIE-02
Civil Engineering Department (CED), UCE&T, BZU, Multan 1

2. CHAPTER 2. OPEN CHANNEL & THEIR PROPERTIES
Content:
1. Kinds of Open Channel
2. Channel Geometry
3. Geometric Elements of Channel Section
4. Velocity Distribution in a Channel Section
5. Wide Open Channel
6. Measurement ofVelocity
7. Velocity-distribution Coefficient
8. Determination ofVelocity-distribution Coefficients
9. Pressure Distribution in a Channel Section
10. Effect of Slope on Pressure Distribution 2

3. INTRODUCTION
 Open Channel
 Aconduit in whicha liquid flows with a free surface
 any flow path with a freesurface,whichmeansthat the flow path is open to the atmosphere
 Open channel hydraulics
 Thestudyof the physicsof fluids flow in conveyancesin whichthe following fluids formsa free
surface and isdriven by gravity
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4. 1. KIND OF OPEN CHANNEL
 There are 2 types of open channel; natural and artificial
 Natural open channel are rivers, creeksand .... (have irregular
cross section)
 All channels which have been developed by natural processesand
have not been significant improved by humans
 Artificial open channel (humanconstruction) are flumes and canals.
 All channels which have been developed by human efforts
 Within the broad category of artificial, open channel are following
subdivisions
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5. CATEGORY OFARTIFICIALOPEN CHANNEL
Category of artificial open channel
Under various circumstances in engineering practices the artificial open channel is given
different names such as:
 Canal: the term canal refer to a rather long channels may be either unlined or lined with concrete,
cement, grass, wood, bituminous materials or artificial membrane.
 Flume: In practice, the term refers to a channels built above the ground surface to convey a flow
across a depression. Flumes are usually constructed of wood, metal, masonry or concrete. The term
flumes is also applied to laboratory channels constructed for basic and applied research.
 Chute & Drop: A chute is a channel having a steep slope. A drop channel also has a steep slope but
is much shorter than a chute.
 Culvert: A culvert flowing only partially full is a covered channel of comparatively short length installed
to convey a flow under highways, railroad embankments or runways.
 Open flow Tunnel: A comparatively long covered channel used to carry water through a hill or any
obstruction on the ground. 5

6. Category of artificial open channel
Open-channel
flume in
laboratory
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7. 2. CHANNEL GEOMETRY
 Depending upon the shape, a channel is either
prismatic or non-prismatic.
 Prismatic: The channel which cross-sectional
shape, size and bottom slope are constant. Most
of the man-made (artificial) channels are prismatic
channels over long stretches.
Ex. Rectangular, trapezoidal, circular, parabolic.
 Non-Prismatic: All natural channels generally
have varying cross-sections and therefore are
non-prismatic
Ex: River, Streams & Estuary.
Free
surface
Datum

y
A
B
T
Figure. Sketch of open channel
geometry
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8. 2. CHANNEL GEOMETRY (CONT.)
 The trapezoid is the commonest shape for channels with unlined earth banks, for it provides side slopes for
stability.
 The rectangle has vertical sides, it is commonly used for channels built od stable materials. Such as lined
masonry, rocks, metals, or timber.
 The triangular section is used only for small ditches, roadside gutters, and laboratory works.
 The circle is the popular section for sewers and culverts of small and medium sizes.
 The parabola is used as an approximation of section small and medium size natural channels.
 Hydrostatic catenary or linlearia is the shape of the cross section of trough, formed of flexible sheets assumed
to be weightless, filled with water up to the top of the section, and firmly supported at the upper edges of the
sides but with no effects of fixation. Mostly has been used for the design of the sections of some elevated
irrigation flumes.
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9. 9

10. 3.GEOMETRIC ELEMENTS OF CHANNEL SECTION
 Geometric elements are properties of a channel section that can be defined entirely by the
geometry of the section and depth of flow.
 For simple regular channel sections, the geometric elements can be expressed
mathematically in terms of depth of flow and other dimensions of the section.
 For complicated sections and sections of natural streams, no simple formula can be written to
express these elements, but curves representing the relation between these elements and
depth of flow can be prepared for use in hydraulic computations.
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11. GEOMETRIC ELEMENTS
1. Depth of flow y is the vertical measure of water depth.
2. Normal depth d is measured normal to the channel
bottom.
d = y cos
For most applications, d  y when   10%. cos 0.1 = 0.995
3. Flow or discharge Q is the volume of fluid passing a cross-
section perpendicular to the direction of flow per unit
time.
4. Mean velocity V is the discharge divided by the cross-
sectional area
Free
surface
Datum


So = bottom slope
Sw = water surface
slope
A
Q
V 
11

12. GEOMETRIC ELEMENTS
5. Wetted perimeter P is the length of channel perimeter that is wetted or covered by flowing water.
6. Hydraulic radius R is the ratio of the flow area A to wetted perimeter P.
7. Hydraulic depth D is the average depth of irregular cross section.
8. Section Factor Z for critical flow computation is the product of the water
area and the square root of the hydraulic depth
9. For uniform flow computation
P
A
R 
T
A
D 

width
top
area
flow
B
T
A
P
y
Z= 𝐴√D = A√
𝐴
𝑇
Z= 𝐴𝑅 Τ
2
3
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13. 13

14. 4.VELOCITY DISTRIBUTION IN A CHANNEL SECTION
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15. VELOCITY DISTRIBUTION IN A CHANNEL SECTION
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16. VELOCITY DISTRIBUTION IN A CHANNEL SECTION
 Looking to the flow in a channel at first instant, one can say that flow
is occurring in longitudinal direction or there is a velocity component in
longitudinal direction only.
 But due to presence of corners and boundaries in an open channel, the
velocity vectors are having three components viz; Vx, Vy, Vz
(corresponding to longitudinal, lateral and normal or perpendicular to
flow).
 Mostly Vx is only considered and small vectors Vy and Vz ignored.
 This property of the velocity distribution commonly used in the
calculation of discharge of rivers and canals using area-velocity
method.
y
0.2y
Channel Bed
0.8y
V0.4
V0.8
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17. TYPICAL CURVES OF EQUALVELOCITY INVARIOUS CHANNEL
SECTION
Typical curves of equal velocity in various channel section
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18. 5.WIDE OPEN CHANNEL
 The velocity distribution in the central region of the section of wide
open channel is same as the rectangular channel of infinite width.
 In other words, under this condition the sides of the channel have
practically no influence on the velocity distribution in the central
region and flow in the central region can be regarded as two-
dimensional in hydraulic analysis
 Central region exists in rectangular channel only when the width is
greater than 5 to 10 times the depth of flow, depending on the
condition of surface roughness. 18

19. 6- MEASUREMENT OFVELOCITY
 To measure velocity of open channel at required depth, Pitot tube
or current meter are used.
 In general, to find average velocity of a particular open channel,
velocity at a depth of 0.6 m from free water surface is measured.
 In the other case, velocity at 0.2 m depth, 0.8 m depth from free
water surface is taken and average velocity of these two values is
considered as channel average velocity.
y
0.2y
Channel Bed
0.8y
V0.4
V0.8
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20. 7.VELOCITY DISTRIBUTION COEFFICIENTS
Energy Coefficient α
 Due to non-uniform distribution of velocities over a
channel section, the velocity head of an open-channel
flow is generally greater than the value computed
according to the expression 𝑉2
/2g, where V is mean
velocity.
 When the energy principal is used in computation, the
true velocity head may be expressed as α𝑽𝟐/2g. Here α
is known as energy coefficient or Coriolis coefficient.
 Experimental data indicates for straight prismatic channel
α varies from 1.03 to 1.036.
 The value is generally higher for small channels and
lower for large streams of considerable depth.
Momentum Coefficient β
 The non-uniform distribution of velocities also affects the
computation of momentum in open-Channel flow.
 From the principle of mechanics, the momentum of fluid-
passing through a channel section per unit time is
expressed by β(wQV/g). Here β is known as
momentum coefficient or Boussinesq coefficient,
where w is unit weight of water.
 Experimental data indicates for straight prismatic channel
β varies from 1.01 to 1.112.
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21. VELOCITY DISTRIBUTION COEFFICIENTS (CONT.)
 For channels of regular cross section and fairly straight alignment, the coefficients are often
assumed to be unity(1), as the effect of non uniformity velocity distribution is small on the
computed velocity head and momentum.
 In channels of complex cross section, the coefficients for energy and momentum can easily
be as great as 1.6 and 1.2, respectively, and can vary quite rapidly from section to section in
case of irregular alignment.
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22. 8. DETERMINATION OFVELOCITY-DISTRIBUTION COEFFICIENTS
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23. DETERMINATION OF ENERGY COEFFICIENT
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24. DETERMINATION OF MOMENTUM COEFFICIENT
(1-DIMENSIONALAPPROACH)
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25. 9. PRESSURE DISTRIBUTION IN A CHANNEL SECTION
• The hydrostatic law states that the rate of increment of pressure is
equal to the specific weight of the fluid at any point in a static fluid
system.
• The distribution of pressure over the cross section of channel is same
as the hydrostatic pressure(hs), that is; the distribution is linear and can
be represented by a straight line AB. This is known as the hydrostatic
law of pressure distribution.
• This is valid only if flow filaments have no acceleration components in
the plan of cross section. This type of flow is known as parallel flow,
such as uniform flow.
• GVF may also be regarded as parallel flow, that is curvature and
divergences are so small that can be neglected.
• If the curvature of streamline is substantial, the flow is theoretically
known as curvilinear flow. 25

26. PRESSURE DISTRIBUTION (CONT.)
 If curvilinear flow occurs in vertical plan, then pressure distribution over
the section deviates from the hydrostatic.
 These curvilinear flow may be either convex or concave (fig b, c).
 Concave curvilinear: centrifugal forces are acting d/w to reinforce the
gravity action, so resulting pressure is greater than (hs).
h=hs+ c.
 Convex curvilinear: h=hs-c. (c is the deviation from hs)
 For channel has curved longitudinal profile the centrifugal pressure may
be computed by Newton’s law of acceleration. P =
𝑤𝑑
𝑔
𝑣2
𝑟
 The pressure head correction is, therefore, c=
𝑑
𝑔
𝑣2
𝑟
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27. PRESSURE DISTRIBUTION (CONT.)
 In parallel flow the pressure is hydrostatic, and the pressure head may be represented by the depth of
flow y. For simplicity the pressure head of curvilinear flow may be represented by α՛y,
where α՛ is a correction factor for curvature effect known as pressure distribution coefficient
 The pressure coefficient is expressed by a’ = 1+
1
𝑄𝑦
‫׬‬0
𝐴
𝑐𝑣 𝑑𝐴
 a' is greater than 1.0 for concave flow, less than 1.0 for convex. flow, and equal to 1 for parallel flow.
 In RVF the change n depth and flow is so rapid & abrupt that streamline possess substantial curvature and
divergence. Hence hydrostatic law of pressure distribution doesn't hold for RVF
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28. 10. EFFECT OF SLOPE ON PRESSURE DISTRIBUTION
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29. EFFECT OF SLOPE ON PRESSURE DISTRIBUTION (CONT.)
 Apparently, if the angle Θ is small, this factor will not differ
appreciably from unity.
 In fact, the correction tends to decrease the pressure head by an
amount less than 1% until theta is nearly 6 degree or a slope of about
1 in 10. Since the slope of ordinary channels is far less than 1 in 10;
the correction for slope effect can usually be safely ignored. A
channel with a slope greater than 1 in 10 is hereafter called a channel
of large slope.
 If a channel of large slope ,has a longitudinal vertical profile of
appreciable curvature the pressure head should be corrected for the
effect of the curvature of streamlines (Fig. 2-9). In simple notation, the
pressure head may be expressed as α՛ycos²ϴ.
 In channels of large slope the velocity of slop is usually high then the
critical velocity. When this velocity reaches a certain magnitude, the
flowing water will entrain air producing a swell in its volume and an
increase in depth.
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