1.
1

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2
Why water measurement is required????
 To determine the amount of water to be applied to the crops.
 Accurate measurement of irrigation water is necessary in field
experiments on soil-water-plant relationship.
 Required in testing wells for their yield.
 Measurement of runoff from particular area and measurement
steam flow are required in planning suitable soil and water
conservation measure.

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3
 Units of measurement
 Water at rest (as a tank, reservoir or standing water
in field) are cubic metre, litre and hectare centimetre,
cubic feet, gallons, acre-inch, acre-feet .
 Flowing water (as in a channel or pipeline) are m3/s,
lps, ft3/s, gpm.

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4
Fundamental equation
 Based on the principle of conservation of mass and energy.
 Considering water as an incompressible liquid,the principle of
conservation of mass leads to the continuity eqn
Where; Q=discharge
A=c/s area
V=velocity(assumed constant across the section)
Q = AV

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5
 Conservation of energy is stated by the bernoulli’s as that along
a stream line
Where; P= pressure.
V=velocity.
z=elevation above a datum level.
g=acceleration due to gravity.
=sp.weight of the liquid

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 Water measurement are the flow through open channels and
flow through pipes.
Measurement of flow in open channels
1. indirect discharge methods.
a. velocity-area methods.
I. Float method
II. Current meter
b. Dilution technique
c. Electromagnetic method
d. Ultrasonic method

7.
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2. Direct discharge methods.
a. Hydraulic structure
A. Orifices
B. Mouthpieces
C. Weirs
D. Notchs
E. Flumes
b. slope-area method

8.
8
a. velocity-area methods
1. Indirect discharge methods.
 The velocity of flow in the channel is measured by some mean
and the discharge is calculated from the velocity and area of c/s
I. Float method
 A float is a small object made of wood or other suitable material
which is lighter than water.
criteria
A small stream in flood
Small steam with rapidly changing water surface
Preliminary or exploratory surveys.

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 A simple float moving on stream surface is called surface float.
affected by surface wind and easy to use.
 Rod float consist of a vertical wooden rod which is weighted at
the bottom to keep it vertical with its top end emerging out of free
water surface when floating.
It will travel with a velocity equal to mean velocity of flow.

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Velocity is estimated by timing how long a floating object
takes to travel a pre-determined distance.
Observed velocity is adjusted by some factor to estimate
average velocity.
Determine cross-sectional flow area.
Use continuity equation to estimate Q.

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 Advantages
 economical and simple
 Disadvantages
not very accurate
gives only approximate measure of the rate of flow

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II. Current meter
 It consist of a wheel having several cups or wheel, attached to a
Streamlined weight and the assembly suspended by means of
cables or mounted on straight rods.
 The wheel in current meter is rotated by the action of flowing water.
 The number of revolutions of the wheel per unit time are
proportional to the velocity of the flowing water.
 It can be used for measuring velocities in irrigation channels, stream
or large river.

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Types of current meter
1. Anemometer and propeller velocity meter
2. Electromagnetic velocity meters
3. Doppler velocity meters
4. Optical strobe velocity meters
1. Anemometer and Propeller Current Meters
 used for irrigation and watershed measurements.
 It use anemometer cup wheels or propellers to sense velocity.
 It does not sense direction of velocity, which may cause problems
in complicated flow where backflow might not be readily apparent.
 For irrigation needs, this problem can be avoided by proper gage
station or single measurement site selection.

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Anemometer type current meter

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2. Electromagnetic Current Meters
 It produce voltage proportional to the velocity.
 The working principle of these meters is the same as the
pipeline electromagnetic flow meter.
 measure crossflow and are directional.
Advantage :- direct analog reading of velocity; counting of
revolutions is not necessary.
Limitation:- use near metallic objects

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3. Doppler Type Current Meters
 It determine velocity by measuring the change of source light
or sound frequency from the frequency of reflections from
moving particles such as small sediment and air bubbles.
 Laser light is used with laser Doppler velocimeters (LDV),
and sound is used with acoustic doppler velocimeters (ADV).
 Acoustic Doppler current profilers ADCP measurements are
becoming more frequent for deep flow in reservoirs, oceans,
and large rivers.
 Most of the meters in this class are multidimensional or can
simultaneously measure more than a single directional
component of velocity at a time.

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4. Optical Strobe Velocity Meters
 It is developed by the U.S. Geological Survey (USGS) and the
California Department of Water Resources use optical methods to
determine surface velocities of streams (USGS, 1965).
 This meter uses the strobe effect.
 Mirrors are mounted around a polygon drum that can be rotated
at precisely controlled speeds. Light coming from the water
surface is reflected by the mirrors into a lens system and an
eyepiece. The rate of rotation of the mirror drum is varied while
viewing the reflected images in the eyepiece.
 At the proper rotational speed, images become steady and appear
as if the surface of the water is still. By reading the rate of rotation
of the drum and knowing the distance from the mirrors to the
water surface, the velocity of the surface can be determined.

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 Advantages:-
 No parts are immersed in the flowing stream.
it can be used for high-velocity flows and for flows carrying
debris and heavy sediment.
It can measure large flood flows from bridges.
 Limitation:-
However, the meter measures only the water surface
velocity.
It dependent upon the selection of the proper coefficient.

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b. Dilution technique/chemical method

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The material balance eqn
QC0+q1C1 = (Q+q1)C2
Then rate of flow Q is
Q = q1
(C2-C1)
(C0-C2)

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c. Electromagnetic method
 It is based on faraday’s principle that an emf is induced in the
conductor when it cuts a normal magnetic field.

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Where; d= depth of flow
I=current in the coil
n, K1,K2 = system constant
 It gives the total discharge when it is has been calibrated, makes it
Specially suited for field situations where the c/s properties can
change with time due to weed growth in , sedimentation, etc.
 Specific application is in tidal channels where the flow undergoes
rapid changes both in magnitude as well as in direction.
Accuracy ±3%
Maximum channel width is 100m,and detectable velocity 0.005m/s.

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d. Ultrasonic method
It was first reported by swengel (1955).
Velocity measured by ultrasonic signals.

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If C= velocity of sound in water
Where ; L = length of path from A to B
vp =component of the flow velocity in the sound path=vcosθ
similarly
Thus,

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Advantages
 It is rapid and gives high accuracy.
 It is suitable for automatic recording of data.
 It can handle rapid changes in the magnitude and direction of
flow as in tidal river .
 The cost of installation is independent of the size of river.

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 The accuracy is limited by the factors that affect the signal velocity
and averaging of flow velocity such as
i. Unstable cross-section
ii. Fluctuating weed growth
iii. High loads of suspended solids
iv. Air entrainment
v. Salinity and temperature change

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2. Direct discharge methods.
a. Hydraulic structure
A. Orifices
 It is a small opening of any cross section on the side or at the
bottom of a tank ,through which a fluid is flowing
Classification of orifice
 According to size
a)Small orifice
(head of liquid >5d; d=depth of orifice)
b) Large orifice
(head of liquid <5d; d=depth of orifice)

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 According to c/s area
a) Circular orifice
b) Triangular orifice
c) Rectangular orifice
d)Square orifice
 According to shape of u/s edge
a) Sharp-edged orifice(minimum contact with fluid)
b) Bell-mouthed orifice(saturated orifice)
 According to nature of discharge
a) Free discharging orifice
b) Drowned or sub-merged orifice
1) Fully sub-merged orifice
2) Partially sub-merged orifice

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 Flow through on orifice
 The section cc is approximately at a distance of half of dia. of the
orifice. At this section, the stream line are straight and parallel to
each other and perpendicular to the plane of the orifice
 This section is called venacontract.

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 Let the flow is steady and at a constant head H. applying
Bernoulli's equation
But z1=z2
now
and
(v1 <<< v2 and tank area is very large
compared to the area jet)

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 Hydraulic co-efficient
velocitylTheoretica
contracta-at venajetofvelocityActual
=)(cvelocityofefficient-Co v
gH
v
2

 The value cv of varies from 0.95 to 0.99 for different orifices,
 depending on the shape, size of the orifice and on the head under
which flow take place
Co-efficient of velocity (cv)

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orificeofArea
contracta-at venajetofArea
=)n(ccontractioofefficient-Co c
Co-efficient of contraction(cc)
a
ac

 The value cc of varies from 0.61 to 0.69 for different orifices,
 depending on the shape, size of the orifice and on the head under
which flow take place

35.
35
th
d
Q
Q
c 
Co-efficient of discharge(cd)
velocitylTheoreticaarealTheoretica
velocityActualareaActual



cvd ccc 
 The value cd of varies from 0.61 to 0.65 for different orifices,

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 Flow through large orifice
Note:-in case of small orifice, the velocity in the entire c/s of the jet is
consider constant then discharge can be calculated by
ghacQ d 2
But in large orifice the velocity is not constant
 Discharge through large rectangular orifice
 Consider a orifice in one side of the tank discharging freely into
atmosphere under a constant head H.
Let, H1 = height of liquid above top edge of orifice
H2 = height of liquid above bottom edge of orifice
b = breadth of orifice
d = depth of orifice = H2 - H1
cd = co- efficient of discharge

37.
37

38.
38
dhbstripofArea 
2ghstripoughwater throfvelocitylTheoretica 
Discharge through elementary strip
velocitystripofAreacdQ d 
ghdhbcd 2
dhghbcd  2
Integrating above equation betn H1 and H2
Now ,Total discharge = Q
 
2
1
2
H
H
d dhghbcQ
dhhgbc
H
H
d 
2
1
2
2
1
2/3
2
2/3 H
H
d
h
gbc 






 2/3
2
2/3
22
3
2
HHgbcd 

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 Discharge through fully sub-merged orifice
 It is one which has its whole of the outlet side sub-merged under
liquid.
Let, H1 = height of water above the top of the orifice on the u/s side.
H2 = height of water above bottom of the orifice
H = difference in water level
b = width of orifice
cd = co- efficient of discharge

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 Height of water above the center of orifice on u/s side
2
12
1
HH
H


2
21 HH 

 Height of water above the center of orifice on d/s side
H
HH



2
21
Now applying Bernoulli's eqn
(z1=z2 )
2
211 HH
g
p 


H
HH
g
p



2
212

and
And V1is negligible

41.
41
g
v
H
HHHH
22
0
2
2
22121





H
g
v

2
2
2
ghv 2
2
2 
 12HborificeofArea H
VelocityAreacd  orificethroughDischarge
  ghHHbcQ d 212 

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 Discharge through partially sub-merged orifice
 It is one which has its outlet side partially sub-merged under
liquid.
 The upper portion behaves as orifice discharging free & lower
portion behaves as a partially sub-merged orifice.
 Only large orifice behaves as a partially sub-merged orifice.

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Total discharge = discharge through free + sub-merged portion
 Discharge through sub-merged portion,
 2/3
1
2/3
2 2
3
2
HHgbcQ d 
  gHHHbcQ d 221 
 Discharge through free portion,
    gHHHbcHHgbc dd 22
3
2
2
2/3
1
2/3


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B. Mouthpieces
 A mouthpiece is a short length of a pipe which is two to three
times its diameter in length fitted in a tank or vessel containing the
fluid
Classification of Mouthpieces
 According to their position with respect to tank
a) External Mouthpieces
b) Internal Mouthpieces
 According to shape
a) Cylindrical Mouthpieces
b) Convergent Mouthpieces
c) divergent Mouthpieces
d) Convergent-divergent Mouthpieces

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 According to nature of discharge at outlet/re-entrant/borda’s
(only for internal)
a) Mouthpieces running full
If jet of liquid after expand and fills the whole mouthpiece
b) Mouthpieces running free
If jet of liquid after contraction does not touch the side of mouthpiece

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 Discharge through external cylindrical mouthpiece
Let, H = height of liquid above the centre of mouthpiece
vc = velocity of liquid at c-c section
ac = area of flow at vena- contracta
v1 = velocity of liquid at outlet
a1 = area of mouthpiece at outlet
cc = co- efficient of contraction

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47
Applying continuity eqn at c-c and (1)-(1)
11 vava cc 
c
c
a
va
v 11 

But ncontractioofefficient-co
1
 c
c
c
a
a
Taking cc = 0.62
1
1
a
a
v
c

62.0,,
1

a
a
getwe c
62.0
1v
vc 

48.
48
 The jet of liquid from section c-c suddenly enlarges at section (1)-(1).
Due to sudden enlargement , there will be a loss of head, hL
 
g
vv
h c
L
2
2
1

But
62.0
1v
vc 
g
v
v
hL
2
62.0
2
1
1








22
1
1
62.0
1
2 






g
v
g
v
2
375.0
2
1


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49
Now applying Bernoulli's eqn to point A and (1)-(1)
LA
AA
hz
g
v
g
p
z
g
v
g
p
 1
2
11
2
22 
01
 pressurecatmospheri
g
p

Where, zA = z1 , vA is negligible
g
v
g
v
H
2
375.0
2
000
2
1
2
1

g
v
H
2
375.1
2
1

375.1
2
1
gH
v 
gHv 2855.01 

50.
50
Theoretical velocity of liquid at outlet is = gH2
Co-efficient of velocity for mouthpiece
VelocitylTheoretica
VelocityActual
cv 
855.0
2
2855.0

gH
gH
 Cc for mouthpiece = 1 .
 area of jet of liquid at outlet = area of mouthpiece at outlet
855.01855.0  cvd ccc
 Value of Cd for mouthpiece > Value of Cd for orifice
 Discharge through mouthpiece will be more.

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51
 Discharge through internal or re-entrant or borda’s mouthpiece
i) Borda’s mouthpiece running free
 If the length of the tube is equal to its dia., the jet of liquid comes out
from mouthpiece without touching the sides of the tube is known as
running free
Let, H = height of liquid above the mouthpiece
vc = velocity through mouthpiece
ac = area of contracted jet in the mouthpiece
a1 = area of mouthpiece

52.
52
hagentranceonforcepressureTotal 
Where, a = area of mouthpiece
h = distance of c.g. of area a from free surface = H
Hag
 According to Newton's 2nd law, net force = rate of change of momentum
cv cacflowing/seliquidofmass,Now 
Initial velocity of fluid=0 & final velocity of fluid = vc
 VelocityInitial-VelocityFinalcflowing/seliquidofmassmomentumofchangeofrate 
 0 ccc vva
2
ccva
………(i)
………(ii)

53.
53
Equating eqn (i) & (ii)
2
Hag ccva 
Now applying Bernoulli's eqn to free surface of liquid and section (1)-(1)
1
2
11
2
22
z
g
v
g
p
z
g
v
g
p


Taking the centre line of mouthpiece as datum, we have
0
0
0
1
1
1





v
vv
p
g
p
g
p
z
Hz
c
atm

………(iii)

54.
54
g
v
H
g
v
H cc
2
0
2
000
22

gHvc 2
Substituting the value vc in eqn (iii)
Hgac 2Hag  
v
c
c c
a
a
aa  5.0
2
1
2
There is no head loss, cv = 1
5.015.0,  vcd cccNow
gHacQeDisch d 2)(arg 
gHa 25.0 

55.
55
ii) Borda’s mouthpiece running full
 If the length of the tube is about 3 times its dia., the jet of liquid
comes out with dia. equal to the dia. of mouthpiece at outlet is
known as running full
Let, H = height of liquid above the mouthpiece
vc = velocity through mouthpiece
ac = area of the flow at c-c
a = area of mouthpiece
v1 = velocity at outlet

56.
56
 The jet of liquid after passing through c-c, suddenly enlarges at
section (1)-(1).Due to sudden enlargement ,there will be a loss of head
 
g
vv
h c
L
2
2
1

Applying continuity eqn at c-c and (1)-(1)
11 vava cc 
c
c
a
va
v 11 

1
1
a
a
v
c

5.0
11 v
c
v
c

12vvc 
…………..(i)
Substituting the value vc in eqn (i)
 
g
v
g
vv
hL
22
2
2
1
2
11




57.
57
Now applying Bernoulli's eqn to free surface of liquid and section (1)-(1)
Lhz
g
v
g
p
z
g
v
g
p
 1
2
11
2
22 
Taking the centre line of mouthpiece as datum,
g
v
g
v
H
2
0
2
000
2
1
2
1

g
v
g
v
H
22
2
1
2
1

g
v
H
2
1

gHv  1 (Actual velocity)
gHvVelocitylTheoreticaBut th 2, 

58.
58
VelocitylTheoretica
VelocityActual
cv 
Co-efficient of velocity cv
707.0
2
1
2

gH
gH
 Cc for mouthpiece = 1 .
 area of jet of liquid at outlet = area of mouthpiece at outlet
707.01707.0  cvd ccc
gHacQeDisch d 2)(arg 
gHa 2707.0 

59.
59
 Discharge through convergent – divergent mouthpiece
 If a mouthpiece converges up to vena- contracta and then diverge
is called convergent – divergent mouthpiece.
 There is no sudden enlargement of the jet, the loss of energy due to
sudden enlargement is eliminated. And cd =1
Let , H = head of liquid over the mouthpiece

60.
60
Now applying Bernoulli's eqn to free surface of liquid and section c -c
c
cc
z
g
v
g
p
z
g
v
g
p

22
22

Taking the centre line of mouthpiece as datum,
0,,0,  cca zH
g
p
H
g
p
vHz

0
2
0
2

g
v
HHH c
ca
ca
c
HHH
g
v

2
2
)(2 cac HHHgv 
………(i)

61.
61
Now applying Bernoulli's eqn at section c –c & (1) – (1)
1
2
11
2
22
z
g
v
g
p
z
g
v
g
p
c
cc


ac H
g
p
andzzBut 

1
1,
g
v
H
g
v
H a
c
c
22
2
1
2

From eqn (i)
g
v
HHHHH acac
2
2
1

H
g
v

2
2
1
gHv 21 

62.
62
Applying continuity eqn at c-c and (1)-(1)
11 vava cc 
gH
HHHg
v
v
a
a cac
c 2
(2
1
1


H
H
H
H ca
 1
H
HH ca 
 1
gHaQeDisch c 2arg 
Where , ac = area at vena- contracta

63.
63
C. Weirs
Classification of Weirs
 According to shape of opening
a) Rectangular Weir
b) Triangular Weir
c) Trapezoidal Weir( Cippoletti Weir)
 According to shape of crest
a) Sharp–crested Weir
b) Broad-crested Weir
c) Narrrow-crested Weir
d) Ogee –shaped Weir
 It is generally in the form of vertical wall ,with a sharp edge at
the top , running all the way across the open channel.

64.
64
 The edge over which water flows is called the crest.
 The height of the weir between the crest and the channel
bottom is called the crest height.
 The height of the discharge over the crest is called the nappe.
 The air space under the nappe, downstream from the weir, is
called the ventilation.

65.
65
 Factors Affecting Flow over Weirs
• The head
• Fluid properties and Temperature Effects
• Approach and tail water conditions
• Weir Geometry
• Measurement inaccuracies

66.
66
 Advantages
 Capable of accurately measuring a wide range of flows
 Tends to provide more accurate discharge ratings than flumes and
orifices
 Easy to construct
 Can be used in combination with turnout and division structures
 Can be both portable and adjustable
 Most floating debris tends to pass over the structure

67.
67
 Disadvantages
 Relatively large head required, particularly for free flow conditions.
This precludes the practical use of weirs for flow measurement in
flat areas.
 The upstream pool must be maintained clean of sediment and kept
free of weeds and trash, otherwise the calibration will shift and the
measurement accuracy will be compromised

68.
68
 Short crested weirs
 In general, short-crested weirs are those overflow structures, in
which the streamline curvature above the weir crest has a
significant influence on the head-discharge relationship of the
structure.
Weir sill with rectangular control section

69.
69
 Limits of application
 The practical lower limit of h, is related to the magnitude of the
influence of fluid properties, to the boundary roughness in the
approach section, and to the accuracy with which h, can be
determined. The recommended lower limit is 0.09 m;
The crest surface and sides of the control section should have
plane surfaces which make sharp 90-degree intersections with the
upstream weir face;
The bottom width of the trapezoidal approach channel should be
1.25 b,;
The upstream head h1, should be measured 1.80 m upstream of
the down streamweir face. Consequently, h, should not exceed
half of this distance, i.e. 0.90 m;
 To obtain modular flow the submergence ratio h,/h, should not
exceed 0.20.

70.
70
 V-Notch Weir
 it is also called Thomson Weir or Gourley Weir.
 This weir features a weir plate standing vertical to the flow
direction with a sharp-edged triangular cutout.
The backwater level in front of the weir is directly proportional
to the flow volume.
 Due to its special cutout the V-Notch weir is especially suitable
for small volume measurement (0.05 l/s - 30 l/s; 0.79 - 475.59
gpm).
 it is primarily suitable for the evaluation of clean media like
spring water, small sewage plant’s drains or partially even for
volume measuring of percolating waters in dumps

71.
71
 Prerequisites
 no backwater
 low oncoming flow velocity
 no sedimentation
 clean media without slubs, fibers or similar

72.
72
 Limits of application
The head over the weir crest should be at least 0.03 m and should
be measured a distance of 3.00 m upstream from the weir.
The notch should be at least O. 15 m from the bottom or the sides
of the approach channel.
The approach channel should be reasonably straight and level for
15.0 m upstream from the weir.
To obtain modular flow the submergence ratio h2/h1 should not
exceed 0.30.

73.
73
 Advantages
 low costs for the needed measurement technique
 accurate measurement results (even at low volumes)
 easy to verify
 Disadvantages
 partially high mechanical expenses needed to realize the
necessary hydraulic conditions
 no measurement in polluted or sediment carrying media
 no measurement of very high volumes

74.
74

75.
75
D. Notchs
 It may be defined as an opening in the side of a tank or a small
channel in such a way that the liquid surface in the tank or
channel is below the top edge of the opening.
Classification of Notch
 According to shape of opening
a) Rectangular Notch
b) Triangular Notch
c) Trapezoidal Notch
d) Stepped Notch
 According to the effect of the sides on the nappe
a) Notch with end contraction
b) Notch without end contraction or suppressed

76.
76
Big in size. Small in size.
Made of concrete or
masonary structure.
Made of metallic plate.
Weirs Notchs

77.
77
 Discharge over a rectangular notch or weir
Let , H = head of water over the crest
L = length of the notch or weir
 Consider an elementary horizontal strip of water of thickness dh
and length L at a depth h from the free surface of water.
Are of strip =L * dh
gHstripthroughflowingwaterofVelocitylTheoretica 2

78.
78
The discharge dQ through strip is
velocitylTheoreticastripofAreacdQ d 
gHdhLcd 2
Now total discharge Q
dhhgLcdhghLcQ
H
d
H
d  
00
22
H
d
h
gLc
0
2/3
2/3
2 






  2/3
2
3
2
HgLcQ d 

79.
79
 Discharge over a triangular notch or weir
Let , H = head of water above v-notch
θ = angle of notch
 Consider a horizontal strip of water of thickness dh at a depth of
h from the free surface of water.
From fig. we have,
2
tan)(
)(2
tan

hHAC
hH
AC
OC
AB




80.
80
2
tan)(22

hHACABstripofWidth 
dhhHstripofArea 
2
tan)(2

ghstripthroughwaterofVelocitylTheoretica 2
Discharge ,dQ through the strip is
)( ltheoreticavelocitystripofAreacdQ d 
ghdhhHcd 2
2
tan)(2 

dhghhHcd 2
2
tan)(2 


81.
81
Total discharge Q is
 
H
d dhghhHcQ
0
2
2
tan)(2

 
H
d dhhhHgc
0
)(2
2
tan2

 
H
d dhhHhgc
0
2/32/1
)(2
2
tan2

H
d
hHh
gc
0
2/52/3
2/52/3
2
2
tan2 














2/52/3
2
2
tan2
2/52/3
HHH
gcd





 2/52/5
5
2
3
2
2
2
tan2 HHgcd


82.
82




 2/5
15
4
2
2
tan2 Hgcd

2/5
2
2
tan
15
8
Hgcd 

For a right angled V- notch , if cd =0.6
1
2
tan900



2/5
81.9216.0
15
8
arg HeDisch 
2/5
417.1 H

83.
83
Advantages of triangular notch or weir over rectangular notch or weir
 The expression for discharge for V- notch or weir is very simple .
 For measuring low discharge, a triangular notch gives more accurate
results than a rectangular notch.
 In triangular notch , only 1 reading i.e.H is required for computation
of discharge.
 Ventilation of triangular notch is not necessary.

84.
84
 Discharge over a trapezoidal notch or weir
Total discharge = discharge through rectangular notch or weir +
discharge through triangular notch or weir
Let , H = height of water over the notch
L = length of crest of notch
1dc = co –efficient of discharge for rectangular portion
2dc = co –efficient of discharge for triangular portion

85.
85
Discharge through rectangular portion ABCD
  2/3
1 2
3
2
HgLcQ d 
Discharge through 2 triangular notches FDA & BCF =
discharge through single triangular notch
2/5
2 2
2
tan
15
8
HgcQ d 

Discharge through trapezoidal notch or weir = Q1+ Q2
  2/52/3
2
2
tan
15
8
2
3
2
HgcHgLc dd 


86.
86
 Discharge over a stepped notch
Discharge through stepped notch =
sum of discharge through different rectangular notch
Let , H1 = height of water above the crest of notch (1)
L1 = length of notch (1)
H2 , L2 & H3 , L3 are corresponding value for notch (2) &(3)
respectively.
cd = co –efficient of discharge for all notch

87.
87
321)(arg QQQQedischTotal 
 
 
2/3
33
2/3
3
2/3
22
2/3
2
2/3
11
2
3
2
2
3
2
2
3
2
HgLc
HHgLc
HHgLcQ
d
d
d




88.
88
 Cipolletti weir or notch
 Cipolletti weir is trapezoidal weir, which has side slopes of 1:4(H:V)
'214
4
1
tan
2
4
14
2
tan
0




H
H
BC
AB

89.
89
The discharge through a rectangular weir with two end contractions is
2/3
2)2.0(
3
2
HgHLcQ 
2/52/3
2
15
2
2)2.0(
3
2
HgcHgHLc d 
Let the slope is given by θ/2, now discharge through V- notch is
2/5
2
2
tan
15
8
Hgcd 

2/52/5
2
15
2
2
2
tan
15
8
, HgcHgcThus dd 

'214
4
1
tan
24
1
8
15
15
2
2
tan 01






 

90.
90
The discharge through cipolletti weir is
  2/3
2
3
2
HgLcQ d 
If velocity of approach , va is to be taken in to consideration
  2/32/3
2
3
2
aad hhHgLcQ 

91.
91
 Discharge over a broad –crested weir
 A weir have wide crest is known as broad –crested weir
Let , H = height of water over the crest
L = length of the crest
h = head of water at the middle of weir which is constant
v = velocity of flow over the weir
If 2l > H , the weir is called broad –crested weir

92.
92
 Now applying Bernoulli's eqn to the still water surface on the
u/s side and running at the end of weir
h
g
v
H 
2
000
2
hH
g
v

2
2
 hHgv  2
The discharge over weir is
velocityflowofAreacQ d 
 hHghLcd  2
 32
2 hHhgLcd  ………….(i)

93.
93
The discharge will be maxm , if (Hh2 –h3 ) maxm
  0Hh 32
h
dh
d
hHhHh 32032 2

Hh
3
2

Substituting value of h in eqn (i)





















32
max
3
2
3
2
2 HHHgLcQ d
32
27
8
9
4
2 HHHgLcd 

94.
94
33
27
8
9
4
2 HHgLcd 
 
27
812
2
3
H
gLcd


27
4
2
3
H
gLcd 
2/3
3849.02 HgLcd 
2/3
81.923849.0 HLcd 
2/3
705.1 HLcd 

95.
95
 Discharge over a narrow –crested weir
 If 2l < H , the weir is called narrow –crested weir. It is similar to
Rectangular weir or notch
2/3
2
3
2
HgLcQ d 

96.
96
 Discharge over a ogee weir
 In which the crest of the weir rises up to maxm height of 0.115 * H
where H = height of water above inlet of weir
 The discharge through ogee weir is same as that of rectangular weir
2/3
2
3
2
HgLcQ d 

97.
97
 Discharge over submerged weir or drowned weir
 When the water level on the d/s side of weir is above the crest of the
weir ,then the weir is called to be submerged weir drowned weir
 Divided in to two portion. the portion betn u/s and d/s water surface
may be treated as free weir and portion betn d/s water surface and
crest of weir as a drowned weir
Let , H = height of water on the u/s of the weir
h = height of water on the d/s of the weir

98.
98
Then , portionupperovereDischQ arg1 
  2/3
2
3
2
1
hHgLcd 
portiondroenedthrougheDischQ arg2 
flowofvelocityflowofAreacd  2
 hHghLcd  22
Total discharge, 21 QQQ 
 
 hHghLc
hHgLc
d
d


2
2
3
2
2
1
2/3

99.
99
E. Flumes
 Flumes are shaped open channel flow sections in which flow is
measured
DESCRIPTION
1. Flumes force flow to accelerate
 Converging sidewalls
 Raised bottom
 Combination
2. Flumes force flow to pass through critical depth
 Unique relationship between water surface profile and
discharge

100.
100
 Advantages
 Minimal drop in pressure.
 Enables measurement in a large range of flow.
 The flow rate in flumes is usually high enough to prevent
sedimentation; they are therefore self-cleaning.
 Provides a reliable measurement in free flow and submerged flow
conditions.

101.
101
Disadvantages
 Installation is usually expensive.
 Installation requires extremely careful work.
 Requires a secure watertight base.
 Flow at the entrance must be evenly distributed, with little
turbulence, to produce accurate measurements.

102.
102
Two basic classes of flumes
1. Long throated flumes
 Parallel flow lines in control section
 Accurately rate with fluid flow analysis
2. Short throated flumes
 Curvilinear flow in control section
 Calibrated with more precise measurement devices
 Types of flume

103.
103
 Long throated flumes (Replogle flume )
 Long-throated flumes have one-dimensional flow in the
control section -- Long-throated means long enough to
eliminate lateral and vertical contraction of the flow at
the control section…streamlines are essentially parallel
 Can be calibrated using well-established hydraulic
theory
No laboratory testing needed
 Calculations are iterative, so computer models that
do the calculations have made long-throated flumes
reasonable to implement in recent years

104.
104
Classified under the term ‘long-throated flumes’ are those
structures which have a throat section in which the streamlines
run parallel to each other at least over a short distance.
Because of this, hydrostatic pressure distribution can be
assumed at the control section.
This assumption allowed the various head-discharge equations
to be derived, but the reader should note that discharge
coefficients are also presented for high H1/L ratios when the
streamlines at the control are curved.
Long-throated flumes are the measurement device of choice for
most open channel applications, having significant advantages
over Parshall flumes and other traditional devices.

105.
105
These older devices were laboratory-calibrated, because the flow
through their control sections is curvilinear. In contrast,
streamlines are essentially parallel in the control sections of long-
throated flumes, making them ratable using straightforward
hydraulic theory.
The crest level of the throat should not be lower than the dead
water level in the channel, i.e. the water level downstream at zero
flow.
The throat section is prismatic but the shape of the flume cross-
section is rather arbitrary, provided that no horizontal planes, or
planes that are nearly so, occur in the throat above crest (invert)
level, since this will cause a discontinuity in the head-discharge
relationship.

106.
106
 The flume comprises a throat of which the bottom (invert) is
truly horizontal in the direction of flow.
 Advantages
 Minimal head loss required ,
 Economical construction techniques
 Adaptable to existing control sections
 Variety of construction materials
 Rating table accuracy of ±2%
 Choice of various shapes and configurations
 Calibration based on the as-built dimensions
 User-friendly software WinFlume
 Proven track record
 Accurate over the entire flow range
 Minimal problems with trash and debris
 Ability to pass sediment

107.
107

108.
108
Long-Throated Flumes (Ramp Flumes)

109.
109
 Limits of application
 The practical lower limit of h, is related to the magnitude of
the influence of fluid properties, boundary roughness, and the
accuracy with which h, can be determined. The recommended
lower limit is 0.07 L.
 To prevent water surface instability in the approach channel
the Froude number Fr = v1/(gA1/B1)² should not exceed 0.5.
 The upper limitation on the ratio H1/L arises from the
necessity to prevent streamline curvature in the flume throat.
Values of the ratio H1/L should be less than 1.0
 The width B, of the water surface in the throat at maximum
stage should not be less than L/5.
 The width at the water surface in a triangular throat at
minimum stage should not be less than 0.20 m.

110.
110
Trapezoidal Replogle flume
Rectangular Replogle flume

111.
111
 Other flumes
a) H-Flumes
 H flumes are a hybrid between flumes and weirs.
 H flumes can measure a wide variety of flows, from very low
to extremely high volumes.
 H flumes were designed in the mid-1930s by the USDA Agricultural
Research Service
 The measuring point of the H flume, selected during development,
is in the draw down effect, this means that H flumes are very
sensitive to slight errors in measuring point position.
 A straight uniform approach must be provided that matches the
inlet width of the H flume. H flumes require a non-impeded
discharge so that there can be no submergence.

112.
112
 H flumes are capable of monitoring flows that vary over wide
ranges with a high degree of accuracy.
 H flume is capable of providing accurate measurement for
applications with flow ranges of 100:1 or more.
 On natural streams where it is necessary to measure a wide
range of discharges, a structure with a V-type control has the
advantage of providing a wide opening at high flows so that it
causes no excessive backwater effects, whereas at low flows its
opening is reduced so that the sensitivity of the structure
remains acceptable.

113.
113
 To serve this purpose the U.S. Soil Conservation Service
developed the H-type flume, of which three geometrically
different types are available
1. HS flumes
2. H flumes
3. HL flumes

114.
114
 Operating principle
 An H flume operates according to the Venturi principle.
 Due to lateral restrictions, the flume restricts the flow area,
causing the water level upstream from the throat to rise.
 The flow can be obtained by simply measuring the water
depth, because this depth varies proportionally with flow.
 Applications
 An H flume was developed to measure the flow of irrigation water
from small catchment areas and surface water.
 it is generally used to measure the flow of irrigation water, slow-
flowing watercourses and water in sewer systems.

115.
115
 The geometry and operating principle of an H flume make it a
very useful tool for measuring the flow of water that contains
solids.
 This type of flume can measure a variety of different flows and
provides good precision.
 Ranges of measurement
 H flumes can be used to measure flowrates between 0.3981 m3
per day, for an Hs flume 122 mm (0.4 ft) high, and 286,251 m3
per day, for an HL flume 1219 mm (4 ft) high.

116.
116
1. HS flumes
 Of this ‘small’ flume, the largest size has a depth D equal to
0.305 m (1 ft) and a maximum capacity of 0.022 m³/s.
 HS flumes are typically recommended for lower flows not
exceeding 0.8 cfs.

117.
117
2. H flumes
 Of this ‘normal’ flume, the largest size has a depth D equal to
1.37 m (4.5 ft) and a maximum capacity of 2.36 m³/s.
 Fiberglass H flumes are available in a variety of sizes and can
be used to measure flows ranging from zero to 80 cfs.

118.
118

119.
119
1. HL flumes
 The use of this ‘large’ flume is only recommended if the
anticipated discharge exceeds the capacity of the normal H-
flume. The largest HL-flume has a depth D equal to 1.37 m (4.5
ft) and a maximum capacity of 3.32 m³/s.
 The 4.0’ HL flume may be recommended for larger flows up to
111 cfs.

120.
120

121.
121
 ADVANTAGES OF H FLUMES
Three types of flumes—HS, H, and HL—are available for
small-, medium-, and high-discharge rates, respectively.
They have different specifications to suit various ranges of
water flow. The shape of flume provides the following
distinct advantages that favor its use under a variety of
flow conditions (USDA 1979):
1. The increase of throat opening with the rise of stage
facilitates accurate.
2. Measurement of both low and high flow of water.
3. The converging section of flume makes it self-cleaning
because of increased velocity.

122.
122
Consequently, the flume is suitable for measuring flows having
sediment in suspension and low bed-loads.
4. It is simple to construct, rigid and stable in operation, and
requires minimal maintenance for retaining its rating.
5. Its installation is simple and is generally not affected by the
steepness of the channel gradient.

123.
123
 Submergence of H flume
 Flumes should be installed with free outfall or no submergence
wherever possible. If submergence occurs, the free discharge
head (H) can be computed by using the following equation,
presented in non-metric units to be consistent with those given
in USDA (1979):
H = d1/{1 + 0.00175[exp (d2/d1)5.44]}
Where,
H is the free flow head (in ft)
d1 is the actual head with submergence (in ft)
d2 is the tail water depth (in ft) above flume zero head
and 0.15 < d2/d1 < 0.90.

124.
124
 H flumes Discharge equations
FLUME SIZE EQUATION
HS-Type 0.4' Q=294.50*H^2.23815
0.6' Q=322.569*H^2.2405
0.8' Q=345.10*H^2.23173
1.0' Q=366.13*H^2.22258
H-Type 0.5' Q=767.5*H^2.31
0.75' Q=830.3*H^2.31
1.0' Q=875.2&H^2.31
1.5' Q=947.0*H^2.31
2.0' Q=1000.8*H^2.31
3.0' Q=1081.6*H^2.31
4.5' Q=1166.9*H^2.31
HL-Type 4.5' Q=1156.46&H^2.31716

125.
125

126.
126
 Evaluation of discharge
All three types of H-flumes have a rather arbitrary control
while an upstream piezometric head ha is measured at a
station in the area of water surface drawdown.
Under these circumstances, the only accurate method of
finding a head-discharge relationship is by calibration in a
hydraulic laboratory. Based on this calibration, an empirical
formula, expressing the discharge in m³/s as a function of
the head ha in metres, could be established of the general
form
log Q = A + B log ha + C[log ha]² ……………(1)
Values of the numbers A, B, and C appear in Table

127.
127

128.
128
 Modular limit
 The modular limit is defined as the submergence ratio h2/ha
which produces a 1% reduction from the equivalent modular
discharge as calculated by Equation …..(1)
 Results of various tests showed that the modular limit for HS-
and H-flumes is h2/ha = 0.25, for HL-flumes this limit is 0.30.
 Rising tail water levels cause an increase of the equivalent
upstream head ha at modular flow. Because of the complex
method of calculating submerged flow, all HS- and H-flumes
should be installed with a submergence ratio of less than 0.25
(for HL-flumes 0.30).

129.
129
 Limits of application
a. The inside surface of the flume should be plane and smooth
while the flume dimensions should be in strict accordance
with Figure.
b. The practical lower limit of ha, is mainly related to the
accuracy with which ha, can be determined. For heads less than
0.06 m, point gauge readings are required to obtain a
reasonably accurate measurement. The lower limit of ha for
each type of flume can be read from Tables 7.13 to 7.15.
c. To obtain modular flow the submergence ratio h2/ha should not
exceed 0.25.
d. To prevent water surface instability in the approach channel,
the Froude number Fr, = v1/(gA1/B)^1/2 should not exceed 0.5.

130.
130
b) Parshall flume
 The Parshall flume was designed in the later 1920s to measure
the flow of irrigation water.
 It is often used to measure the flow of wastewater, for permanent
or temporary installations
 DESCRIPTION
 A Parshall flume consists of a converging section, a throat
section and diverging section.
 The crest of the throat section is tilted downstream. In other
words, there is a sill between the horizontal crest and converging
section and the crest of the throat section.

131.
131
 For channels smaller than 2.44 m (8 ft), the inlet of the
converging section may be rounded, and larger channels may
have vertical walls at a 45° angle.
 To prevent erosion due to water fall, the diverging section is
usually extended by means of vertical walls, and the angle of
these walls will be steeper than the angle of the walls of the
diverging section
1. Dimensions are standardized for each flume
 Not hydraulic scale models of each other
 A 12 ft flume is not simply 3 multiply by
a 4 ft flume
2. Designated by throat width
 Measure 0.01 cfs with 1 inch flume
 Measure 3000 cfs with 50 foot flume

132.
132
3. Relate Ha (or Ha and Hb ) to discharge with rating
equation, or consult appropriate chart
4. Flow rate through the critical section is a function of the
upstream head, acceleration of gravity, and the control
section size
 Operating principle
 A Parshall flume operates according to the Venturi principle.
 Due to lateral restrictions, the flume restricts the flow area,
causing the water level upstream from the throat section to rise.
 A sudden or steep drop in water level at the throat section
creates an increase in flow velocity.

133.
133
 The flowrate can be obtained simply by measuring the water depth,
because it has been established that depth varies proportionally with
flow.
 Applications
 initially developed to measure flow in natural open channels
such as rivers, streams, drainage ditches, etc.,
 widely used to measure flow in man-made open channels, such
as storm and domestic drainage systems, sewage treatment
plant inlets and outlets, etc.
 Because of its geometry and operating principle, a Parshall
flume is extremely effective for measuring the flow of water that
contains solids. Because it creates little loss of depth, it can be
easily adapted to existing sewer systems.

134.
134

135.
135
 Dimensions
 The dimensions of a Parshall flume are defined by the width of
constriction

136.
136
 CLASSES OF PARSHAL FLUMES
 On the basis of the throat width, Parshall flumes have been
classified into three main groups.
(i) Very small - 25.4 mm to 76.2 mm.
(ii) Small 152.40 mm to 2438.4 mm.
(iii) Large 3048 mm to 15240 mm.

137.
137
1. VERY SMALL FLUMES
Discharge capacity ranges from 0.09 l/s to 32 l/s.
Turbulence makes difficult to read Hb – gauge
Hc – gauge included downstream end of diverging section
to provide readings during submergence
 Hc – gauge readings are converted to Hb – gauge by using
a graph & used to determine discharge .

138.
138
2. SMALL FLUMES
 Discharge capacity ranges from 0.0015m3/s to 3.95 m3/s
 Length of side wall of converging section, A, of (1ft -8ft)
throat width (m) is given as;
Where; bc= throat width (m)
 Ha – gauge located at distance of a = upstream from the
end of the horizontal crest
 Hb – gauge location is the same in all small flumes (X = 2inch
upstream from the low point in the sloping throat floor ) &
(Y= 3 inch above it)
219.1
2
 cb
A
A
3
2

139.
139
3. LARGE FLUMES (10 ft up to 50 ft)
Discharge capacity ranges from 0.16m3/s to 93.04 m3/s
Length of side wall of converging section is longer than in
small flumes
Ha – gauge located at distance of m
upstream from the end of the horizontal crest
Hb – gauge location is the same in all large flumes (X =
12inch upstream from the floor at downstream edge of the
throat ) & (Y= 9 inch above it)
813.0
3
 cb
a

140.
140

141.
141
 ADVANTAGES
 Relatively low head loss (1/4 of sharp crested weir)
 Handle some trash and sediment
 Well accepted
• May be mandated
 Many sizes are commercially available
 DISADVANTAGES
 Complicated geometry for construction
 Tight construction tolerances
 Aren’t amenable to fluid flow analysis
 BoR does not recommend for new construction

142.
142
 Range of measurements
 Parshall flumes can measure flows varying from 70.7 m3 per day,
for a 76 mm (3 in) channel, to 8,038,656 m3 per day, for a 15.24 m
(50 ft) channel.
 For the purposes of this document, only data that apply to
channels with dimensions between 76 mm (3 in) and 36.57 m (12 ft),
have been included.

143.
143
c) Palmer-Bowlus Flume
 A Palmer-Bowlus flume was designed in the 1930s for use as a
flume that can be inserted in an existing channel with a slope
of less than 2 %.
 Description
 This flume is rounded to create a restriction and produce a
greater flow velocity in the throat of the flume.
 It is a Venturi type flume with a uniform throat.
 The length of the throat is equal to the diameter of the
corresponding flume. Different types of restrictions have been
developed, but the restriction most frequently used is
trapezoidal in shape.

144.
144
 It is usually made of prefabricated fibreglass that is reinforced
with plastic. Although rare, also made of stainless steel.
 A Palmer-Bowlus flume is manufactured in sizes ranging from
102 mm (4 in) to 1067 mm (42 in).
 Operating principle
 Vertical and lateral restrictions on the flume reduce the flow
area, causing the water level upstream from the throat section
to rise, which is followed by a drop in water level in the throat
section, resulting also in an increased flow velocity.
 Flowrate can be determined simply by measuring water
depth upstream from the flume, since it has been established
that variations in depth are proportional to flow.

145.
145
 Applications
 it is designed to measure flow in sewer systems and existing
channels, a Palmer-Bowlus flume is not a temporary device.
 In fact, the difference in measurement between a minimum and
maximum flow is relatively small
 if a system is expanded, the size of the flume must also be
changed.
 Like all flumes, a Palmer-Bowlus flume is an effective tool for
flow measurement of water that contains solids.
 It is also relatively easy to install because it does not require a
crest differential upstream or downstream.

146.
146
 Dimensions
 Dimensions of a Palmer-Bowlus flume depend on the diameter of
the channel in which it is installed.
SHAPE OF A PALMER-BOWLUS FLUME ACCORDING TO
LUDWIG

147.
147
 Ranges of Measurement
 Palmer-Bowlus flumes can measure flows varying between 2.4
m3 per day, in the case of a 102 mm (4 in) flume, and 49,200 m3
per day, in the case of a 762 mm (30 in) flume.
d) Leopold-Lagco flume
 The Leopold-Lagco flume was developed in the early 1960s and
introduced on the market in 1965 by F.B. Leopold Company Inc.
of Pennsylvania.

148.
148
 Description
 It has a round shape.
 The purpose of its rounded shape is to create a restriction in the
conduit, which causes a greater flow velocity in the throat of the
flume.
 This flume operates according to the Venturi principle. The
throat is uniform and its length is equal to the diameter of the
channel for which it was designed.
 its throat section has a rectangular shape.
 It consists of three sections: a converging section, throat section
and diverging section

149.
149
 There are three models:
permanent installation model: there is a slight extension of the
converging and diverging sections;
insertion model: outer radius of the flume corresponds to the
inner radius of the channel in which it is to be installed;
cutthroat model: the diverging section is not as high. This flume
is used on a temporary basis only.
 The inner surface of the flume must be made of material that is
smooth and free of irregular edges.
 The outer surface is made of a material that facilitates adhesion
to a concrete surface.

150.
150
 The flume is made of fiberglass in standard sizes varying between
152 mm (6 in) and 1219 mm (48 in).
 Operating principle
 Due to vertical and lateral restrictions, a Leopold-Lagco reduces
the flow area, causing the water level upstream from the throat
section to rise, followed by a drop in water level and an increased
flow velocity.
 Flow can be determined by simply measuring the water level
upstream from the flume, since it has been established that depth
varies according to flow.
 Literature provides no information about use of this flume in
submerged flow conditions and no correction formula. Use in only
free flow conditions is therefore recommended.

151.
151
 Applications
 It is used as a main measuring device on a temporary or permanent
basis. Like all flumes, it is an effective tool for measuring the flow of
water that contains solids.
 Due to their relatively small volume, flumes with a diameter of 381
mm (15 in) or less can be inserted in a standard sewer manhole,
without the need to modify access.
 It is relatively easy to install because there is no need for a required
distance from the bottom of the channel in which it is inserted.

152.
152
 Dimensions
 The dimensions of a Leopold-Lagco flume are a function of the
diameter of the conduit in which it is installed.

153.
153
 Range of measurements
 Leopold-Lagco flumes can measure flows varying between 84.2
m3 per day, for a 152 mm (6 in) flume, and 108,445 m3 per day, for
a 1219 mm (48 in) flume.
e) Cutthroat flume
 It was developed in the mid-1960s by Utah State University Water
Resources Laboratory. It is used to measure flow in locations where
there is no slope or very little slope.

154.
154

155.
155
 Description
 A cutthroat flume consists of a converging section and diverging
section.
 The control section (W) does not have parallel sides because the
flume consists only of a converging and diverging section.
 The bottom of the entire length of the flume is flat.
 For flumes that are less than 1.37 m (4.5 ft) long (L) and 15.2
cm (0.5 ft) wide in the control section (W), the inlet of the
converging section may be rounded. For larger flumes, the inlet
of the converging section may have vertical walls at a 30° angle.
 To prevent erosion due to water fall, the diverging section is
usually extended by means of vertical walls, and the angle of
these walls is steeper than the angle of the walls in the diverging
section.

156.
156
 Operating principle
 Cutthroat flumes operate according to the Venturi principle.
Due to the lateral shape of its walls, the flume restricts the flow
area, which causes the water level upstream from the control
section to rise, followed by a sudden and significant drop of the
water level in the control section, accompanied by an increase in
flow velocity.
 The flow can be determined by simply measuring the water
depth, because depth varies proportionally with flow.
 Although this flume can be used in submerged flows, use in free
flow conditions is strongly recommended

157.
157
 Applications
 It was developed to measure flow in open natural channels, such
as rivers, streams, drainage ditches, etc. with a small slope.
 It has been the subject of several studies that demonstrate its
effectiveness as a measuring device in sewer systems and water
treatment plants.
 The geometry and operating principle of a cutthroat flume make
it an effective device for measuring flow in water that contains
solids.
 Because this flume causes only a small loss of head and requires
no difference in height between the bottom of the channel and
base of the flume, it is relatively easy to adapt to existing sewer
systems.

158.
158
 A cutthroat flume is simple and inexpensive to manufacture.
 It is also perfectly suited to a temporary measurement system.
 Dimensions
 The dimension of a cutthroat flume is defined by the total
length of the flume (L) and the width of the control section
(constriction) (W).

159.
159

160.
160

161.
161
Range of measurements
 Cutthroat flumes can measure flows varying between 32 m3 per
day, for a flume 457 mm (1.5 ft) long with a constriction of 25 mm
(0.083 ft), and 210,555 m3 per day, for a flume 2,743 mm (9 ft) long
with a constriction of 1,829 mm (6 ft).
Disadvantages when it compared with long-throated flumes:
The discharge coefficient Cd is rather strongly influenced by H1
and H2;
The modular limit varies with H1 and has a lower value;
The control section can only be rectangular;
Cd value has high error of about 8 percent.

162.
162
f) Trapezoidal Flumes
These are some what similar to Parshall flumes but different in
shape. These were originally developed in Washington State
College and as such are referred to WSC flume.
 Advantages
1) A large range of flows can be measured with a comparatively
small change in head;
2) Sediment deposits in the approach does not change the head
discharge relationship noticeably;
3) Extreme approach conditions seem to have a minor effect upon
head discharge relationship;

163.
163
4) The flumes will operate under greater submergence than
rectangular shaped ones without corrections for submergence;
5) The trapezoidal shape fits the common channel sections more
closely than a rectangular one.

164.
164
Schematic view of truncated flume for earthen channel.
 Shortening of the full length structure is possible by deleting the
diverging section and the tailwater section if the head loss over the
section exceeds 0.4 times the head causing the flow, as measured
from the crest of the throat section. Such a structure is called a
truncated flume.
g) Truncated Flume

165.
165
Triangular throated flumes are adapted to measure a wide range
of discharges, including low flows like return flows to drainage
system operational spillage from irrigation systems.
It also permits wide variations in the flow rate.
The ratio between the maximum and minimum flow is high in case
of triangular throated flume.
h) Triangular Throated Flume

166.
166
Schematic view of triangular throat flume.`

167.
167
b. Slope-Area Method
 This consists of using the slope of the water surface in a uniform
reach of channel and the average cross-sectional area of that
reach to give a rate of discharge.
 The discharge may be computed from the Manning formula:
2/13/21
sRA
n
Q h
where:
Q = discharge (m3/s)
A = mean area of the channel cross section (m2)
Rh = mean hydraulic radius of the channel (m)
S = energy slope of the flow
n = a roughness factor depending on the character
of the channel lining

168.
168
 Measurement of flow in pipe
 measuring the time required for the flow to fill a container of
known volume.
 Volumetric measurement
time
volume
flowofRate 
 Advantages
 It is very simple and requires little equipment.
Disadvantages
 where the flow rate is not uniform over a period of time, frequent
measurements are to be taken to get accurate data

169.
169
 FLOW RATE MEASUREMENTS
 The different methods used for measuring the rate of flow in pipes
are:
1. Venturimeters
2. Orifice plate
3. Pitot tube
4. Elbow meter
5. Co –ordinate method

170.
170
1. Venturi Meters.
 It consists of converging and expanding section of short length.
 It is useful for measuring the flow of water in pipes under pressure.
 It utilises the principle that the flow passing through a constricted
section of pipe is accelerated and the pressure head lowered.
 The drop in the pressure head is measured by providing openings in
the Venturi meter at the points shown in the figure and connecting
these openings to a U-tube manometer.
 Considering points (1) and (2) with cross-sectional areas A1 and A2
respectively and assuming horizontal pipe, from Bernoulli theorem,
neglecting friction

171.
171

172.
172
g
v
g
P
g
v
g
P
22
2
22
2
11









g
P
g
P
gvv

212
1
2
2 2
 The pressure head difference is indicated by the manometer
reading, h, hence,





 


M
ghvv 2
2
1
2
2
where, ρM is the density of the gauge fluid.
Q = V1A1 = V2A2
 By continuity,

173.
173
 Substituting for V2 in terms of V1 yields





 


















M
gh
A
A
v 21
2
2
12
1
 Solving for V1





 


















M
gh
A
A
v 2
1
1
2
2
1
1





 


















M
ideal gh
A
A
A
vAQ 2
1
2
2
1
1
11
idealdactual QCQ Hence,
dC = coefficient of discharge

174.
174
2.Orifice plate
 Its function is similar to the venturi meter.
 major difference between the devices lies in the fact that,
downstream of the orifice piate, the flow area expands
instantaneously while the fluid is unable to expand at the same rate.
 This creates a 'separation zone' of turbulent eddies in which large
energy losses occur. Cd is considerably lower than that for the
Venturi meter.
Advantages
 its lower cost and its compactness.

175.
175
 The orifice can be put at the end of the pipe (Fig.) and is known
as pipe orifice.
 The ratio of the orifice diameter to the pipe diameter should be
between 0.5 and 0.8 and is selected in such a way that the pipe
flows full.

176.
176
 The discharge is computed using the equation.
ghaCQ d 2
Where a = area of orifice
h = head of flow measured from center of pipe

177.
177
3.Pitot tube
 The pitot tube is an open L shaped tube useful for measuring
velocity of flows in an open channels as well as in pipes.
000
2
21
2


PP
g
v
h
PP
g
v




12
2
2
ghv 2
 The velocity at point 2 immediately at the nose of the tube is zero
as water is at rest here. The Pitot tube gives the velocity at the
point at which the open end is placed

178.
178
 The use of the Pitot tube for measuring flow when the pipe is
flowing under pressure the static pressure of the water is to be
taken into consideration.
 Fig. 4.18 illustrates how this is done using an inverted U-
tube.

179.
179
 The velocity of flow is given by the equation.
ghcv 2
Where, C is known as the Pitot tube coefficient (usually 0.95 to 1.0).
4. Elbow meter
 Pressure differences between the outside and inside walls of
an elbow are related to volumetric flow rate.
Q = CeKA(Po-Pi)l/2
where, Q = discharge (l/min);
Ce = elbow meter flow coefficient
A = c/s area of elbow (cm2);
Po = pressure on outside of elbow (kPa);
Pi = pressure on inside of elbow (kPa);
k = unit constant(k=8.49)

180.
180

181.
181
5. Co –ordinate method
 measurements are taken of the jet of water issuing from the end of
the pipe and these are used for calculating the rate of discharge.

182.
182
 The formula to be used is obtained by combining the following
equations :
Q = AV………………(i)
t
XVVtX 
g
Y
tgtY
2
2
1 2

Substituting in Eq.(i) and introducing C, the coefficient of discharge
y
g
CAXQ
2

Where, Q = discharge (l/s)
X = horizontal distance
Y = vertical distance
A = area (square centimeter)
g = 980 cm/sec2

183.
183
Y
CAX
Q 02.0

184.
184
 METERS FOR MEASURING CUMULATIVE FLOW
1. Propeller Meters
2. Deathridge Meter
3. Water Meter
1. Propeller Meters
 record the cumulative flow of water.
 widely used in USA in the farm irrigation systems at the canal
outlets.
 The flow from the canal outlet is allowed to pass through a pipe
into a basin.
 A propeller which rotates due to the flow of water is installed at
the pipe outlet.

185.
185
 The number of rotations indicated by a counter will give the
cumulative water flow.
 Calibration and maintenance are important to get accurate
readings.

186.
186
Advantages
Commercially available
Totalizing meter
Can achieve good accuracy
Disadvantages
 Operating conditions different from manufacturer’s calibration
conditions will affect accuracy
 Only tolerate small amount of weeds and debris
 Moving parts operating underwater
 Can require a good deal of maintenance and inspection

187.
187
 used in Australia operates on the same principle as the
propeller meter but the construction is different
 The size of the rotating wheel depends upon the
discharges to be measured.
 The number of rotations are recorded on a counter.
 The device is to be calibrated in situ to obtain accurate
readings.
2. Deathridge Meter

188.
188

189.
189
3. Water Meter
 designed for measuring pipe flow.
 generally used for measuring municipal water supplies and
are rarely used for measuring water on the farm.
 These consist of a| multiblade propeller made of metal, plastic
or rubber, connected to a counter by means of a gear system.
 The counter readings are calibrated to give the volumetric
flow in the desired units.
 Water meters are made in different sizes to suit the different
pipe diameters and ranges of flow.

190.
190
 The basic requirements for using the water meters are :
(1) the rate of flow should be within the designed range.
(2) The pipe must always flow full.
(3) the water should not contain any debris.

191.
191
 References
R. K. Bansal, A Text Book Of Fluid Mechanics And Hydraulic Machines
P. N. Modi & S. M. Seth, Hydraulics And Fluid Mechanics.
K. Subramanya, Engineering Hydrology.
V. V. N. Murthy & M. K. Jha, Land And Water Management Engg..
M.G. Boss, Discharge measurement structure.