contents

CONTENTS
Flow measurement
1 Introduction
...........................................................................................................................................................................................................................................
8.1
2 Weirs .............................................................................................................................................................................................................................................................
2.1 Terminology pertaining to weirs ..................................................................................................................................................................
2.1.1 Approach velocity at weirs ..................................................................................................................................................................
2.1.2 End contractions ..............................................................................................................................................................................................
2.1.3 Submerged weirs .............................................................................................................................................................................................
2.1.4 Nappe types .........................................................................................................................................................................................................
2.2 Choice of weir ....................................................................................................................................................................................................................
2.3 Setting up of weirs ........................................................................................................................................................................................................
2.4 Equations to determine flow through weirs .....................................................................................................................................
8.1
8.2
8.2
8.3
8.4
8.5
8.6
8.6
8.7
3 Flow over weirs
8.9
................................................................................................................................................................................................................................
4 Parshall flumes ................................................................................................................................................................................................................................ 8.13
4.1 Flow characteristics of the Parshall flume ...................................................................................................................................... 8.14
4.2 Equations for free flow in Parshall flumes ..................................................................................................................................... 8.16
4.3 Dimensions of Parshall flumes ...................................................................................................................................................................... 8.17
4.4 Installation of a Parshall flume .................................................................................................................................................................... 8.19
4.5 Examples ............................................................................................................................................................................................................................... 8.19
5 Crump weir
.........................................................................................................................................................................................................................................
6 Maintenance of weirs and flumes
.............................................................................................................................................................................
7 Orifices for determining flow in channels
......................................................................................................................................................
8.21
8.24
8.25
8 Flow speed ― Area methods for flow measurement in channels .......................................................................................... 8.27
8.1 Flowmetering by means of floats................................................................................................................................................................. 8.27
8.2 Current meters .................................................................................................................................................................................................................... 8.28
9 Other methods .................................................................................................................................................................................................................................. 8.29
9.1 Volumetric flow measurement ..................................................................................................................................................................... 8.29
9.2 Gravimetric flow measurement ................................................................................................................................................................... 8.30
9.3 Co-ordinate methods ................................................................................................................................................................................................ 8.31
9.3.1 Vertically upwards ..................................................................................................................................................................................... 8.31
9.3.2 Horizontal ............................................................................................................................................................................................................. 8.32
10 References
........................................................................................................................................................................................................................................
All rights reserved
Copyright  2003 ARC-Institute for Agricultural Engineering (ARC-ILI)
ISBN 1-919849-24-6
8.33
Flow measurement
8.1
1 Introduction
The increasing demand on existing water sources, continually increasing costs of irrigation schemes and
accompanying development costs necessitate that existing water be used economically and effectively.
Regular measurements provide valuable information to the irrigation farmer or irrigation board, that can be
used very effectively to:
•
•
•
•
•
•
•
•
•
evaluate the performance of a scheme or system;
facilitate the fair division of water between irrigators and thereby reduce the risk of faulty divisions
and shortages;
ease the administration of division and distribution;
show up possible shortcomings or problem areas in a scheme or system;
build up a data base which can be used for future planning;
serve as a source of reference for irrigation research and technology development;
determine the time and extent of system maintenance;
enable control of and over stream sizes and volumes; and
simplify scheduling management.
The following apparatus are suitable for measurement of irrigation water:
•
•
•
•
•
•
•
Rectangular weir (with or without end contractions)
Cipolletti weir
V-notch
Parshall flume
Crump weir
Water-meter (see Chapter 9: Irrigation accessories)
Long throated flume and variations thereof
Flow measurement with structures in open channels depends on the flow rate to flow depth relation, which
is determined for each structure by means of calibration. Besides the physical structure to be installed in
open channels, it is necessary to measure the flow depth at the structure so that the relation can be used to
determine the flow rate.
The flow depth can be measured with various instruments, which varies from measuring plates, which do
not collect continuity data, to mechanical or electronic sensors with automatic registers. The sensors can
be in contact with the water, such as submersible pressure sensors or float-and-counterweight mechanisms,
or it can make a distance observation, as in the case of ultrasonic sensors.
A further component sometimes found with measuring apparatus, is telemetric communication systems
that make it possible to collect data from the automatic register per radio or modem over a relatively far
distance. This makes it possible to monitor the measurement at distant points without physically visiting
the measuring point.
2 Weirs
The weir is one of the oldest, cheapest, most straightforward and reliable structures for the determination
of flow in channels where sufficient water depth is available.
A simple weir consists of a structure in wood, metal or concrete placed perpendicular to the flow in a
channel. The structure has a sharp-edged opening or notch of specific shape and dimension through which
the water can flow. Weirs are identified by shape as indicated below.
8.2
Irrigation Design Manual
Figure 8.1: Typical weir shapes
2.1 Terminology pertaining to weirs
Figure 8.2: Weir terminology
2.1.1 Approach velocity at weirs
The approach velocity of the water in the pool formed upstream of a weir should preferably be
lower than 0,1 m/s. Therefore the cross-sectional area of the pool should be relatively large
compared to the cross-sectional area of the stream flowing through the weir.
Where it is not practically possible to keep the approach velocity within acceptable limits, relevant
improvements to the specific flow equations should be made.
Figure 8.3: Approach velocity at weirs
Flow measurement
8.3
The approach velocity can be determined by the following equation:
va =
where
va
Q
y
b
=
=
=
=
Q
yb
(8.1)
approach velocity [m/s]
flow through weir [m3/s]
water depth in channel before weir [m]
channel width [m]
If the approach velocity (va) is known, the velocity head (ha) can be determined by the equation:
ha =
where
ha
g
va 2
2g
(8.2)
= velocity head [m]
= gravitational acceleration (10 m/s2)
The total energy head of water (H) is determined by the equation:
H = h+
where
H
h
va 2
2g
(8.3)
= total energy head of water [m]
= overflow depth [m]
By repeated calculations of ha and va for improved values of the flow rate (Q), the approach
velocity can be determined to the required accuracy thereby giving an acceptable flow rate. In
most cases one repetition would be sufficient.
2.1.2 End contractions
When the channel feeding the water to the weir is wider than the weir crest, the sides of the stream
will narrow where it crosses the weir. The width of the stream flowing over the weir will be
slightly narrower than crest width. The phenomenon is known as end contraction.
To make allowance for end contractions, the overflow width in the basic equation must be
modified as follows:
L' = L - 0,1nh
where
L'
L
n
h
=
=
=
=
effective length of weir [m]
measured length of weir [m]
number of end contractions
overflow depth [m]
(8.4)
8.4
Irrigation Design Manual
Figure 8.4: End contraction at weirs
2.1.3 Submerged weirs
Free overflow occurs when the flow after the weir is not backed up. With flood run-off, the water
level on the downstream side of the weir may rise above the weir crest height. This reduces the
overflow capacity and is known as a submerged condition.
Figure 8.5: Submerged weirs
α =
where
α
h
hB
hB
h
(8.5)
= degree of submergence [fraction]
= upstream height of water level above crest height [m]
= downstream height of water level above crest height [m]
Flow measurement
8.5
Table 8.1: Reduction factors for different degrees of submergence for sharp-crested weirs
α
Reduction in discharge
0,2
0,4
0,6
0,8
0,9
0,07
0,15
0,26
0,42 (unstable)
0,55 (unstable)
2.1.4 Nappe types
With water measurement it must be attempted to always achieve a ventilated nappe, thereby
ensuring reasonable accuracy of the observed readings. When water flowing over the weir does
not make direct contact, an air bubble will be formed below the nappe. A certain amount of the air
will be drawn along with the overflowing water. If an air bubble is not sufficiently aerated, a
vacuum will be formed which increases the curvature of the nappe and leads to an increase in
discharge over the weir. The problem can be solved by installing an aeration tube downstream of
the weir (see Figure 8.7).
Figure 8.6: Different nappe types
The following discharge correction should be made for the different nappe types:
•
•
•
Depressed nappe:
Drowned nappe:
Clinging nappe:
Increase measured discharge by 8 - 10%
Decrease measured discharge according to Table 8.1
Decrease measured discharge by 20 - 30%
8.6
Irrigation Design Manual
2.2 Choice of weir
Each type of weir has certain advantages under specific conditions. Generally, for accurate readings, a
standard V-notch or a rectangular suppressed (parallel sides with no side contractions) weir should be
used. The Cipolletti and rectangular weirs with full end contractions are especially suited for water
division.
Normally the observer has a reasonable idea of the quantities to be measured and taking the following
into account, a choice can be made of the suitable weir for particular circumstances:
•
The maximum expected water height above the weir must be at least 60 mm to prevent the nappe
from adhering to the weir crest. Furthermore it is difficult to take accurate readings on the
measuring scale if (h) is too low.
•
The length of the rectangular and Cipolletti weirs must be at least equal to three times the water
height above the weir crest.
•
The V-notch is the most suitable for measurements smaller than 100 m³/h.
•
The V-notch is as accurate as the other weir types for flows between 100 and 1 000 m³/h provided
that submergence does not occur.
•
The weir crest must be as high above the channel floor as possible so that free overflow (of the
nappe) will take place.
•
The flow depth over the weir should not exceed 600 mm.
2.3 Setting up of weirs
Figure 8.7: Setting up of weirs
•
The structure must be sturdy and placed as close to perpendicular to the flow direction as possible,
in a straight section of the channel.
•
The inner face of the structure must be smooth and set up vertically to the water surface.
Flow measurement
8.7
•
The crest must be level in the case of rectangular and Cipolletti weirs. The sides of the V-notch
must be equidistant from an imaginary vertical line drawn through the lower point of the V.
•
The weir crest should be at least 2 mm thick (not sharp).
•
The weir crest must preferably be higher than 2h and in any case never lower than 300 mm above
the channel floor (see Figure 8.7).
•
The distance between the sides of the notch and the channel sides must not be less than 2h and
never less than 300 mm.
•
The nappe should only touch the sharp crest of the notch and not the thicker part of the structure.
•
Air should be able to circulate freely around the nappe.
•
The measuring scale must be fixed at a distance 4h from the structure in a position where it can be
easily read.
•
If the cross-sectional area of the water flowing through the weir is A and the maximum expected
height above the weir is h, the cross-sectional area of the water pool above the restriction must not
be less than 8A for a distance of 20h from the structure.
•
If the water pool above the structure is smaller than prescribed, the approach velocity may be too
high and the measuring scale readings accordingly too low. The approach velocity will then have
to be taken into account when determining Q.
•
The measuring scale must be calibrated to accommodate the maximum expected water level above
the weir.
•
The structure must not let any water pass through the floor or sides.
•
The channel section downstream of the structure must be sufficiently large to prevent high backing
up of water.
•
The accuracy of weirs decreases with a high percentage of silt in the water.
2.4 Equations to determine flow through weirs
Many equations for determining flow through weirs have been developed, the best known being one
by J B Francis dating back to the previous century. Since then observers have continued development
on Francis' work, giving rise to refinement of the original values. A good hydraulics handbook may
be consulted for detailed information on equations that have been developed concerning this subject.
This chapter will deal with imperial as well as metric equations as both are in use.
8.8
Irrigation Design Manual
The Francis equations without approach velocities are as follows:
Table 8.2: Francis equations
Weir type
Metric equations
Imperial equations
Cipolletti
Q = 1,86Lh1, 5
Q = 3,367Lh1,5
90° V-notch
Q = 1,38h2,5
Q = 2,50h2, 5
Rectangular, submerged
Q = 1,84Lh1, 5
Q = 3,33Lh1, 5
Rectangular with end contractions
Q = 1,84(L-0,2h)h1, 5
Q = 3,33(L-0,2h)h1, 5
Units
Q :
h :
L :
Q :
h :
L :
In the above equations:
Q
h
L
[ m³/s]
[metre]
[metre]
[cusec]
[feet]
[feet]
= discharge
= measuring scale reading of water depth
= length of notch
The Francis equations considering approach velocities are as follows:
Table 8.3: Francis equations
Weir type
Metric equations
Cipolletti
Q = 1,86 L(h + 1,5 h a )1,5
90° V-notch
Q = 1,38 (h + h a )2,5 - h a2,5
Rectangular, submerged
Q = 1,84 L (h + h a )1,5 - h1,5
a
Rectangular with end contractions
Q = 1,84 (h + h a )1,5 - h1,5
a (L - 0,2 h)
where: Q
L
h
ha
=
=
=
=
[
]
[
[
discharge [m³/s]
length of notch [m]
measuring scale reading of water depth [m]
velocity head [m]
]
]
Flow measurement
8.9
3 Flow over weirs
Weir crests are mostly rectangular, therefore the following equation applies, where the approach velocity
has little or no effect:
Q = C L h1,5
where Q
C
L
h
=
=
=
=
(8.6)
discharge [m³/s]
discharge coefficient
crest width [m]
height or depth of discharge [m]
The value of C will depend on the depth of overflow – that is the breadth of the weir crest (t) and the
discharge depth over the crest (h). In practice most crests fall between sharp and broad crested and the
following adjustments must be made for a weir with discharge depth (h) and crest breadth (t).
•
•
Sharp crest (h > 3t)
Broad crest (h < 0,3t)
C = 1,822
C = 1,45
Provided that the h/t ratio is between 0,3 and 3,0, the C-value can be interpolated between 1,45 and 1,822.
These refined C-values for rectangular weirs replace the original C-values developed by T B Francis
shown in Tables 8.2 and 8.3.
Figure 8.8: Flow over broad-crested weirs
8.10
Irrigation Design Manual
Figure 8.9: Graph to determine a C-value for a given h/t ratio
For end contractions and approach velocities, the same terminology applies to both sharp-crested and
broad-crested weirs. Discharge under submerged conditions is influenced minimally provided that the
degree of submergence is less than 0,67. Equation 8.5 also applies to broad-crested weirs.
α = hB
(8.5)
h
where α = degree of submergence [fraction]
h = upstream height of water level above crest height [m]
hB = downstream height of water level above crest height [m]
Table 8.4: Reduction factors for different degrees of submergence with broad-crested weirs
α
Reduction in discharge
0,2
0,0
0,4
0,0
0,6
0,0
0,8
0,01
0,9
0,15
Flow measurement
8.11
Example 8.1:
A sharp-crested weir is installed in a river with approximately rectangular section (b = 10,0 m) as shown below:
Section B-B
Section A-A
Determine the flow rate for a discharge height of:
(a) h
(b) h
=
=
0,5 m
1,5 m
Solution:
(a) Considering end contractions:
From equation 8.4:
L'
=
=
=
L - 0,1 nh
5 - 0,1 × 2 × 0,5
4,9 m
From equation 8.6:
Q = CL' h1,5
= 1,822 × 4,9 × 0, 5 1,5
= 3,15 m 3 /s
Determine approach velocity from equation 8.1:
Q
yb
3,15
=
1,5 × 10
= 0,21 m/
va =
Determine velocity head from equation 8.2:
2
va
2g
= 0,002 2 m
ha =
8.12
Irrigation Design Manual
ha is negligibly small, accept Q = 3,15 m3/s
(b) Divide section into 3 parts
No end contractions.
From equation 8.6:
Q1
Q2
=
C L h1,5
=
1,822 × 5 × 1,51,5
=
16,73 m3/s
=
1,822 × 5 × 0,51,5
=
3,22 m3/s
Qtotal = Q1 + Q2 = 19,95 m3/s
Determine approach velocity from equation 8.1:
Q
yb
19,95
=
2,5 × 10
= 0,8 m/s
Determine velocity head from equation 8.2:
va =
v 2a
2g
= 0,03 m
ha =
Recalculate Qtotal:
Q
= 1,822 × 5 × (1,5 + 0,03)1,5
= 17,24 m3/s
Q
= 1,822 × 5 × (0,5 + 0,03)1,5
= 3,51 m3/s
Qtotal
= 20,75 m3/s
Flow measurement
Determine approach velocity:
Q
y b
20,76
=
2,53 × 10
va =
= 0,82 m/s
v 2a
2g
= 0,03 (same as previous calculatio n)
Determine velocity head:
ha =
Therefore the discharge remains constant
= 20,75 m3/s
Qtotal
4 Parshall flumes
8.13
8.14
Irrigation Design Manual
Figure 8.10: Parshall flume
The Parshall flume works on the venturi principle to determine flow in open conduits. The flume consists
of three main parts, namely:
•
•
•
a converging section upstream;
a throat section; and
a diverging section at the end.
The floor of the converging section is level in length and breadth, while the throat section slopes
downwards and the diverging section slopes upwards.
The Parshall flume is named after Ralph L Parshall, an irrigation engineer at the Colorado Agricultural
College in the USA. He began with experiments to design an improved flow measurement device to
replace the known weirs and other devices of the time in approximately 1915.
The Parshall flume has three major advantages as a flow measuring device, namely:
•
An exceptionally high degree of flow measuring accuracy, even under partially submerged conditions
(see Table 8.5).
•
Almost no build-up of silt and sand occurs.
• Due to the small drop in water level, it is suitable for channels with very flat floor slopes. All flumes
should be installed level in all directions to maintain a high measurement accuracy.
The disadvantages of a Parshall flume are the following:
•
Relatively expensive to build as Parshall flumes are normally installed as permanent concrete
structures on water schemes. Portable units of wood, metal, fibre cement and GRP are commercially
available.
•
The smaller the flume, the more important it is to maintain strict construction tolerances, making
construction more difficult.
•
Special care must be taken with installation, particularly on smaller flumes to provide accurate
readings. All flumes must be installed level in all directions.
The size of flume to be used for a particular purpose will be determined by the average maximum flow to
be measured, the permissible head loss through a flume and the normal channel water depth. The final
choice of flume is based on the throat width best suited to the channel dimensions and hydraulic
properties. Generally the throat width of a Parshall flume should be approximately 0,3 - 0,5 times the
upstream width of the water surface during channel design conditions. Metric units cannot be used as
Parshall flumes are experimentally calibrated with imperial units. Dimensions for these flumes will be in
imperial units for some time to come, therefore the same units will be used in this manual.
4.1 Flow characteristics of the Parshall flume
Flow through a Parshall flume can occur in two ways, namely:
•
Free-flow conditions, that is no submergence takes place.
•
Submerged flow conditions where the water level in the diverging section is such that it retards
free flow.
Flow measurement
8.15
Often two measuring plate readings (h en hB) are given to distinguish between submerged and freeflow conditions. Both measuring plate datums are set to the average crest height of the Parshall flume.
The water flow through the throat and diverging sections can occur in two ways:
•
At high velocities it will be a thin layer approximately parallel to the downward sloping section of
the throat (condition Q in Figure 8.10).
•
With the backwater pushing up the water level in the throat section to form a ripple wave
(conditions S in Figure 8.10).
During condition S a marked decrease in outlet velocity occurs, decreasing erosion of the conduit
walls and reducing the drop in water level.
The degree of submergence may also be determined by using equation 8.5. Provided that the ratio
does not exceed certain limits, the flow rate through the flume will not be influenced by a rise in the
tail water level. The permissible degree of submergence for free flow varies with throat width as
shown in Table 8.5
Table 8.5: Permissible levels of submergence for accurate flow determination
Throat width
Free-flow limit
1 - 3 inches
6 - 9 inches
1 - 8 feet
10 - 50 feet
0,50
0,60
0,70
0,80
•
Small Parshall flumes
All flumes smaller than 1 foot are considered small. For submerged flow conditions, Figures 8.12
and 8.13 are used to determine the reduction in flow due to submergence. This reduction is then
subtracted from the free-flow reading (see Table 8.8).
•
Medium Parshall flumes
All flumes with a throat width between 1 and 8 feet, are considered medium.
If submerged flow occurs according to Table 8.5, Figure 8.14 is used to determine flow reduction
due to submergence, which is then subtracted from the free-flow reading. Figure 8.14 applies
only to 1 foot throat width Parshall flumes and the flow reduction (see Figure 8.14) must be
adjusted for larger Parshall flumes with correction factor M (see Table 8.6).
Table 8.6: Correction factors
Throat width [ft]
Factor M
Throat width [ft]
Factor M
1
2
3
4
1,00
1,76
2,45
3,10
5
6
7
8
3,7
4,31
4,9
5,45
8.16
•
Irrigation Design Manual
Large Parshall flumes
All Parshall flumes with throat width larger than 10 feet, are considered large.
Table 8.7: Correction factors
Throat width [ft]
Factor M
Throat width [ft]
Factor M
10
12
15
20
1,0
1,2
1,5
2,0
25
30
40
50
2,5
3,0
4,0
5,0
When submerged conditions occur with large Parshall flumes, the correction factors of Table 8.7
are used for throat widths larger than 10 feet.
4.2 Equations for free flow in Parshall flumes
The following equations are used to determine the discharge of a particular flume.
Table 8.8: Parshall flume equations
Throat width of
Parshall flume
Imperial equations
Metric equations
3 inches
Q = 0,992h1,547
Q = 0,3259h1,547
6 inches
Q = 2,06h1,58
Q = 0,3812h1,58
1 – 8 feet
Q = 4 Wh1,522 W
10 – 50 feet
Units
0,026
Q = 0,3716 W(3,281 h )1,57 W
0,026
Q = (3,6875W + 2,5)h1,6
Q = 0,1895(12,0981W + 2,5)h1,6
Q = discharge [ft3/s]
W = throat width [feet]
h = free-flow depth [feet]
Q = discharge [m³/s]
W = throat width [m]
h = free-flow depth [m]
The equations for submerged flow are more complicated and are not dealt with in this chapter.
Flow measurement
8.17
4.3 Dimensions of Parshall flumes
Table 8.9: Specified dimensions
Description
Lengths
[mm]
Widths
[mm]
Heights
[mm]
Measuring
scale
position
Capacity
[m3/h]
6 inches
9 inches
1 ft
2 ft
3 ft
4 ft
6 ft
8 ft
A
610
864
1 343
1 495
1 645
1 7 94
2 092
2 391
B
305
305
610
610
610
610
610
610
C
610
457
914
914
914
914
914
914
W
152
229
305
610
914
1 219
1 826
2 435
E
394
575
844
1 206
1 571
1 937
2 667
3 397
F
394
381
610
914
1 219
1 524
2 134
2 734
H
114
114
229
229
229
229
229
229
K
76
76
76
76
76
76
76
76
G
457
610
914
914
914
914
914
914
D
414
587
914
1 016
1 118
1 219
1 422
1 616
X
51
51
51
51
51
51
51
51
Y
76
76
76
76
76
76
76
76
Min
5
10
36
67
99
128
268
470
Max
296
520
1 640
3 373
5 136
6 919
10 546
14 215
Figure 8.11: Dimensions of Parshall flumes
8.18
Irrigation Design Manual
Figure 8.12: Flow determination for a 6 inch submerged Parshall flume
Figure 8.13: Flow determination for a 9-inch submerged Parshall flume
Flow measurement
8.19
Figure 8.14: Flow determination for a 1-foot submerged Parshall flume
4.4 Installation of a Parshall flume
The most important factor when installing a Parshall flume is determining the crest height relative to
the floor of the channel in which it is to be placed. With careful planning it is possible to install the
flume so that submerged conditions only occur in isolated cases. It is not always possible with flat
sloped conduits. Whatever happens, the percentage of submergence should always be kept as low as
possible.
With weirs it is advisable to place a flume in a straight section of conduit to avoid the effect of crossflow.
The installation of a Parshall flume as a permanent structure should be done by an expert.
4.5 Examples
Example 8.2:
Determine the flow through a Parshall flume for the following:
1-foot Parshall flume:
h = 0,16 m
hB = 0,1 m
Solution:
Free-flow determination:
hB
h
= 0,625
α=
Free-flow limit:
0,7 (from Table 8.5)
Therefore free-flow conditions occur (0,625 < 0,7)
From Table 8.8 for h = 0,16 m is Q = 0,042 5 m3/s = 153 m3/h
8.20
Irrigation Design Manual
Example 8.3:
Determine the flow through a Parshall flume for the following:
1-foot Parshall flume:
h = 0,16 m
hB = 0,128 m
Solution:
Free-flow determination:
hB
h
= 0,8
α=
Free-flow limit: 0,7 (from Table 8.5)
Therefore submerged conditions occur (0,8 > 0,7)
From Figure 8.14 for h = 0,16 m and α = 0,8, Q = 0,004 2 m3/s
From Table 8.6 M = 1 for a 1-foot Parshall flume
From Table 8.8 for h = 0,16 m Q = 0,042 5 m3/s
Actual flow: Q = 0,042 5 - 0,004 2 = 0,038 3 m3/s = 138 m3/h
Example 8.4:
Determine the flow through a Parshall flume for the following:
2-foot Parshall flume h = 0,671 m and hB = 0,396 m
Solution:
Free-flow determination: α = hB/h = 0,396/0,671 = 0,59
Free-flow limit: 0,7 (from Table 8.5)
0,59 < 0,70, therefore free-flow conditions occur
From Table 8.8 for h = 0,671 m
Q = 0,770 m3/s = 2 772 m3/h
Example 8.5:
Determine the flow through a Parshall flume for the following:
3-foot Parshall flume. h = 0,643 m and hB = 0,566 m
Solution:
Free-flow determination: α = hB/h = 0,566/0,643 = 0,88
Free-flow limit: 0,7 (from Table 8.5)
0,88 > 0,70 therefore submerged conditions occur
From Figure 8.14 for h = 0,643 m and α = 0,88 m,
Q = 0,083 8 m3/s
From Table 8.6 for a 3-foot flume M = 2,45
Total flow reduction is therefore 0,083 8 × 2,45 = 0,205 m3/s
For free-flow conditions: Q = 1,09 m3/s (from Table 8.8)
Actual flow: Q = 1,09 - 0,205 = 0,885 m3/s = 3 186 m3/h
Flow measurement
8.21
5 Crump weir
In the past the Crump did not come to its right in the irrigation industry because it tends to cause a back-up
of water on the upstream side. The most important features of the Crump are as follows:
•
•
•
•
Straightforward structure
High accuracy
Relatively insensitive to submerged conditions
Flow curves can easily be determined for any width
The Crump consists of two parallel walls with a specially shaped overflow wall on the downstream side.
The wall top is sloped at 1:2 on the upstream side and 1:5 on the downstream side. The crest should
preferably be protected by a galvanized steel angle profile. The walls may be of concrete or plastered
brickwork. It is important that the inner distance between the walls remains constant as specified. In the
absence of a solid foundation, the walls are to be founded or the complete structure may be built on a
concrete slab. One disadvantage of the Crump is the straight side walls which lack stability and may fall
over.
A stilling basin is recommended to make readings easier and more accurate. A tube or small hole big
enough to avoid blocking, must be provided between the flume and stilling basin. The best position with
respect to height, is just below the crest of the overflow wall. The distance is specified below and is rather
critical. A tube can also be placed beneath the overflow wall to facilitate drainage if the channel upstream
of the wall needs to be dried out. If the channel is wider than the flume, side walls must be provided to
gradually concentrate the water, the ideal angle being 1:3. This type of flume is very suitable for
rectangular concrete channels because the parallel walls exist and all that remains is the building of the
overflow wall.
•
Dimensions
The width of the Crump will be determined by the minimum and maximum flows to be measured.
The wider the Crump is, the smaller the scale-reading will be for a specific flow. The absolute
minimum reliable reading with a Crump is 50 mm, therefore the width of the Crump should be such
that the minimum flow to be measured gives a reading of at least 50 mm. It is, however, preferable to
choose the width so that the minimum flow will give a reading of 100 mm.
The most generally used scale lengths are 300 mm and 500 mm. The maximum reading and therefore
also the maximum flow measurable by a Crump will be determined by the scale length. Table 8.10
shows the flow for different widths and specific scale readings, thereby allowing determination of a
width (B).
8.22
Irrigation Design Manual
Table 8.10: Flow limits for different Crump widths
Minimum flow [m3/h]
Maximum flow [m3/h]
Reading [mm]
Measuring scale length [mm]
Width [mm]
300
450
600
750
900
1 200
1 500
50
100
300
500
24
36
48
60
72
96
120
68
102
135
169
203
271
338
352
528
703
879
1 055
1 407
1 759
757
1 135
1 514
1 892
2 270
3 027
3 784
Most of the Crump's dimensions are determined by the measuring scale length to be used (see
Table 8.11). This applies to all Crump widths.
Table 8.11: Crump dimensions
Measuring scale length
[mm]
A
[mm]
C
[mm]
D
[mm]
E
[mm]
F
[mm]
I
[mm]
J
[mm]
300
2 800
1 000
900
300
600
150
120
500
4 000
1 000
1 500
500
1 000
250
200
Figure 8.15: Crump weir
Flow measurement
8.23
The other Crump dimensions as determined by the normal flow depth for maximum flow directly
downstream of the proposed position of installation are as follows:
Table 8.12: Crump dimensions depending on maximum flows
Measuring scale
length
[mm]
Maximum
normal flow
depth [mm]
G
L
K
Po
[mm]
[mm]
[mm]
[mm]
300
< 400
<450
<500
650
700
750
50
100
150
80
130
180
200
250
300
500
< 650
< 700
< 750
950
1 000
1 050
50
100
150
100
150
200
300
350
400
•
Equations for flow determination in a Crump weir.
For a horizontal Crump, the discharge equation is as follows:
Q = 7 135 Bh1,5
where Q
B
h
(8.6)
= discharge [m3/h]
= width [m]
= flow depth [m]
The degree of submergence is also determined with equation 8.5:
α =
hB
h
(8.7)
where α = degree of submergence [fraction]
h = upstream height of water level [m]
hB = downstream height of water level [m]
The downstream height begins to influence the upstream height when α > 0,75. Figure 8.16 may
be used to determine the reduction in discharge for a given degree of submergence.
8.24
Irrigation Design Manual
Figure 8.16: Reduction factors for different degrees of submergence for a Crump weir
6 Maintenance of weirs and flumes
Regular maintenance of water measuring devices is required to ensure long, accurate performance and
reduce or avoid costly repairs. The following aspects are important:
Weirs:
• Keep the ponding area free of sediments and plant growth
• Ensure that there is no leakage through or around the device
• Regularly check the position of the weir plate relative to the crest
• Maintain the condition of the crest finish in good order
• Remove rust from steel sections by wire brush and coat with a bituminous paint
Flumes:
• Remove sediments and accretions especially in approach and venturi sections
• If manufactured from steel, remove rust by wire brush and coat with a bituminous paint
• Avoid erosion immediately downstream of the device
• Recast the floor if the existing one is no longer level
• Regularly check the measuring scale position relative to the crest
Flow measurement
8.25
7 Orifices for determining flow in channels
An orifice is an opening where:
•
the dimensions of the opening are small in relation to the water pressure above it; and
•
the water pressure at the centre of the opening, for all practical purposes, is the same as the pressure at
the edge of the opening.
An orifice to be used for flow measurement is usually rectangular or circular in shape and placed
perpendicular to the flow direction in a vertical structure in the channel.
An orifice is under free-flow conditions when the water discharges in an air medium and submerged flow
conditions when it discharges in a water medium. Flow measurement is possible under submerged as well
as free-flow conditions.
As with weirs, orifices have full contraction if the orifice edge is sharp and it is located far from the
channel wall.
One disadvantage of an orifice as a flow measurement device is that it is relatively easily blocked by silt or
sand build up as well as flotsam in the flowing water.
The discharge for a submerged orifice with full contraction as well as for free flow, is determined by the
following general equation:
Q = CA 2 g h
where Q
A
g
h
C
•
=
=
=
=
=
discharge [m³/s]
orifice area [m²]
gravitational acceleration (10 m/s2)
difference in water levels [m]
discharge coefficient (0,61)
C-value
The C-value for short pipes and sluice openings can be determined as follows:
°
Short pipes
Figure 8.17: Short pipes
(8.8)
8.26
Irrigation Design Manual
Table 8.13: Discharge coefficients for flow through short pipes
°
L/D
2
3
5
11
25
50
100
C
0,82
0,82
0,79
0,77
0,71
0,64
0,55
Sluice opening
Figure 8.18: Rectangular sluice opening
Table 8.14: Discharge coefficients for flow through sluices
Wall thickness (T) [m]
C
0,1
0,2
0,4
0,75
1,5
3,0
4,0
0,62
0,64
0,65
0,72
0,77
0,80
0,81
Example 8.6:
Determine the discharge through a sluice opening of 600 mm × 200 mm. The difference in water level
before and after the sluice = 0,35 m. Wall thickness = 0,1 m.
Solution:
Cross sectional area = 0,6 × 0,2
= 0,12 m2
From equation 8.8: Q = CA 2gh
From Table 8.14:
C = 0,62
Q = 0,62 × 0,12 2g × 0,35
= 0,195 m 3 /s
= 702 m 3 /h
Flow measurement
8.27
8 Flow velocity - area methods for flow measurement in channels
8.1 Flowmetering by means of floats
With a lack of suitable measuring devices or where high measurement accuracy is not required, the
flow rate in a channel may easily and quickly be determined, using a float and wrist watch. The
accuracy of measurement will depend on the type of float used. Use something like an orange that
floats quite deep, preventing wind to influence the flow velocity.
The method of flow measurement is as follows:
•
Determine the cross-sectional area of the channel
•
Determine water flow velocity as follows:
° Mark a 10 m straight channel section
° Take the time for the float to travel the 10 m distance
•
Repeat the process 5 times with the float in different flow paths
•
Determine the average flow velocity
v = Cf v f
where v
Cf
vf
(8.9)
= flow velocity [m/s]
= correction factor
= float velocity measured [m/s]
Table 8.15: Correction factors (Cf) to adjust measured float velocity
Average flow
depth [m]
0,3
0,6
0,9
1,2
1,5
1,8
2,7
3,7
4,6
≥6,1
Cf
0,66
0,68
0,70
0,72
0,74
0,76
0,77
0,78
0,79
0,8
The channel discharge may be determined with equation 8.10.
Q = Ak v
(8.10)
where Q = discharge [m3/s]
Ak = cross-sectional area of wetted channel section [m2]
v = flow velocity [m/s]
Example 8.7:
Determine the discharge for a parabolic channel with a flow depth (y) = 400 mm and top width
(W) = 2 m
Time for float to travel 10 m:
Time (1) = 11 s
Time (2) = 12 s
Time (3) = 10 s
8.28
Irrigation Design Manual
Solution:
distance
time
10
=
(11 + 12 + 10)/3
= 0,91 m/s
Float velocity ( v f ) =
From Table 8.15: Cf
= 0,67
From equation 8.9: v
= Cfvf
= 0,67 × 0,91
= 0,61 m/s
2 yW
3
2 × 0,4 × 2
=
3
= 0,54 m 2
Cross sectional area of parabola ( Ak ) =
From equation 8.10:
Q = Akv
= 0,54 × 0,61
= 0,33 m3/s
8.2 Current meters
A current meter is an apparatus with which the flow speed at a specific point in an open channel
(or river course) can be measured. It is used to measure the average flow speed at different
distances from the wall of the channel, so that each measuring point represents a portion of the
cross section area of the channel profile.
Figure 8.19: Flow speed is measured at representative points in the cross section area
Flow measurement
8.29
The flow depths are also registered during the measurement and the collective information is
usually used to determine the flow rate to flow depth relation for measuring structures.
Figure 8.20: Flow depths are measured at the representative points in the cross-section area
The flow rate in the different portions can be calculated by means of the continuity equation.
 vi + vi +1   d i + d i +1 
qi = 

 Li+1 Li
 2  2 
(
)
(8.11)
where qi = the flow rate for the partial cross section areas between measuring points i and i + 1
[m³/s]
vi = average flow speed at point i [m/s]
di = depth of the water at point i [m]
Li = distance of a reference point to point i in the channel [m]
The total flow rate in the channel can be determined by adding the flow rate of the different
portions.
n
Q =∑ q i
(8.12)
i =1
where Q = the total flow rate in the channel [m/s]
9 Other methods
Besides the methods described in this chapter , there are quite a number of other flow measuring methods
which are often used in practice.
9.1 Volumetric flow measurement
Volumetric measurement is one of the most straightforward and accurate methods of flow
measurement. With this method the full flow is discharged into a container of known volume and the
time taken to fill the container recorded. This method is often used to calibrate other measuring
devices.
8.30
Irrigation Design Manual
For flow measurement a stopwatch must measure to ± 0,1 second accuracy, therefore for an accuracy
of ± 1%, it must be possible to fill the container in 20 seconds.
Theoretically a flow of approximately 5 λ/s can be determined with a normal 20 λ bucket. In practice,
however, a maximum flow of 3 λ/s may be determined.
A maximum flow of 30 λ/s can be determined with a 200 litre oil barrel.
Q =
where Q
V
t
V
t
(8.13)
= flow [λ/s]
= container volume [λ]
= time to fill container [s]
Example 8.8:
Determine the flow [λ/h] for the following case:
Container diameter
= 100 mm
Container depth
= 200 mm
Average filling time
= 20 s (five readings)
Solution:
π D2
h
4
0,12
× 0,2
= π×
4
= 0,0016 m 2
Container volume =
From equation 8.11:
V
t
0,0016
=
20
= 0,08 × 10 - 3 m 3 /s
= 288 λ/h
Q=
9.2 Gravimetric flow measurement
One litre of water weighs one kilogram. If the container volume is unknown, a quantity of water is
discharged into a container while the time is recorded. The mass of water is derived by determining
the mass of the full as well as the empty container.
Q =
M
t
where Q = flow [λ/s]
M = water mass [kg water]
t = time to fill container [s]
(8.14)
Flow measurement
8.31
9.3 Co-ordinate methods
9.3.1 Vertically upwards
If a pipe is erected vertically so that the water is ejected straight up, the flow can be determined if
the jet height (h) and the pipe diameter (di) are known (see Figure 8.19). As it is difficult to
measure the jet height above the pipe end, this method is not very accurate and an accuracy of
10% may be expected. This method will therefore only be used to make an estimate of the flow.
Table 8.16 indicates the flow [λ/s] for pipe diameters up to 300 mm and jet heights to 1 m.
Figure 8.19: Dimensions required to determine the flow in vertical pipes
Table 8.16: The flow [λ/s] from vertical pipes
Jet height
[mm]
60
80
100
120
140
160
180
200
250
300
350
400
450
500
600
700
800
900
1 000
Pipe diameter [mm]
50
100
150
225
300
2,7
3,2
3,6
3,9
4,3
4,6
4,9
5,1
5,8
6,4
7,0
7,5
8,0
8,4
9,4
10,3
11,1
11,8
12,4
10,0
12,0
13,9
15,0
16,6
18
19
20
23
26
29
31
33
35
40
44
47
50
53
19,5
23,4
27
30
33
36
39
42
47
53
58
63
68
72
81
89
97
104
112
28
42
56
64
70
77
82
87
101
116
129
140
150
160
180
200
41
62
83
98
111
126
138
150
180
210
240
270
8.32
Irrigation Design Manual
9.3.2 Horizontal
To determine the flow rate of pipes delivering horizontally, both the horizontal distance (x) and
the vertical distance (y) from the same point at the pipe end to the same point on the jet must be
measured. For convenience, the distance from the upper inside edge of the pipe to a point on the
top of the jet is measured (see Fig. 8.20). As in the vertical method, this method is also very
inaccurate. Table 8.17 indicates the flow [λ/s] for pipe diameters of 50, 100 and 150 mm for a
horizontal distance (x) of 150 mm and a vertical distance (y) varying from 6 mm to 200 mm.
Figure 8.20: Dimensions required to determine flow in horizontal pipes
Table 8.17: The flow [λ/s] from horizontal pipes ( x = 150 mm)
Vertical distance (y)
[mm]
6
8
10
15
20
25
30
40
50
60
70
80
100
120
140
160
180
200
Pipe diameter [mm]
50
16,1
14,3
12,7
10,1
8,6
7,6
6,9
5,9
5,2
4,7
4,3
4,0
3,6
3,2
2,9
2,6
2,3
1,9
100
50
47
45
40
35
32
29
24
22
20
19
18
16
14
12
10
7
5
150
108
94
83
76
70
64
58
53
49
46
41
36
31
25
Flow measurement
8.33
10 References
1.
Department of Agriculture and Fisheries. Besproeiing watermeting. Bladskrif nr. 109.
2.
Department of Environmental Affairs. 1984. Handleiding vir die beplanning, ontwerp en bedryf van
riviervloeimeetstasies.
3.
Department of Water Affairs. 1973. Besproeiing. Handleiding vir ingenieurs en tegnici.
4.
Department of Agriculture ARS-57. 1987. Flume: A computer Model for estimating flow through
long-throated measuring flumes. United States.
5.
FAO irrigation and drainage paper 26/2. 1975. Small structures. Rome.
6.
Jensen, M. E. 1983. Design and operation of farm irrigation systems. The American Society of
Agricultural Engineers.
7.
McGraw-Hill Publishing Company. 1959. Open channel hydraulics. Ven te Chow.
8.
Fish River Agriculture Development Centre. Watermeting vir die Visriviervallei-besproeiingsboer.
Cradock.