COURSE OUTCOME #5: Explain operating principles for common flow measuring
instruments.
TOPICS: Nozzles
Weirs
Type of Weirs
LEARNING OUTCOME: Calculate flow rate and other flow properties for the different
flow measuring instrument.
For weir or an orifice meter, estimate uncertainty using the
RMS method.
WEIR
A weir is a small barrier which
is constructed across the open
channel (such as a river) to change its
water flow characteristics and usually
results in a change in the height of the
river level.
Weirs allow water to pool
behind them, while allowing water to
flow steadily over top of the weir.
Additionally, the term weir can be
used to refer to the crest of
a spillway on a large embankment Figure 1. Weir
dam..
Weirs are constructed as an obstruction to flow of water. Commonly, weirs are
used to prevent flooding, measure the volumetric rate of water flow, and help render
rivers more navigable by boat.
Weir Description
`Weirs can be constructed out of several different materials, depending on their
age and purpose. Wood, concrete, or a mixture of rocks, gravel, and boulders can all be
used to construct a weir.
In a weir, the surface over which the water flows is known as the crest. The flow
of water that moves overtop of this crest is known as the nappe, which is simply the
water that makes it overtop the weir. This nappe does not exist with dams, as dams
permit no flow of water over the structure. If this nappe falls a significant distance
through the air - meaning that the weir increases the elevation of the water prior to the
weir - the weir is said to have free discharge. However, if water flows partially
underwater as a result of little elevation increases from the weir it is said to be
submerged or drowned.
Types of Weir
There are many weir designs, but commonly water flows freely over the top of
the weir crest before cascading down to a lower level.
Classification Based on Shape of Opening
Rectangular weir
A weir with a rectangular notch at top for measurement of water flow in open cha-
Figure 2. Parts of the Weir
nnels. It is simple, easy to make, accurate, and popular. It is generally suitable for larger
flowing channels.
Flow over rectangular weir
The flow rate measurement in a rectangular weir is based on the Bernoulli
Equation principles and can be expressed as:
3
2
Q= C d √ 2 g L H 2
3
where
Q = flow rate (m3/s)
H = elevation head on the weir (m)
L = width of the weir (m)
g = 9.81 (m/s2) - gravity
cd = discharge constant for the weir - must be determined
cd must be determined by analysis and calibration tests. For standard weirs - cd - is well
defined or constant for measuring within specified head ranges.
Example - Discharge Over A Rectangular Weir
Problem
A weir of 8m long is to be built across a rectangular channel to discharge a flow
3
of 9m /s. If the maximum depth of water on the upstream side of weir is to be 2m, what
should be the height of the weir ? Adopt Cd = 0.62.
Workings
Given,
L=8m
Q = 9 m3 /s
Depth of water = 2m
Cd = 0.62
Let, H = Height of water above the sill of the weir.
So, the discharge over the weir,
3
2
Q= C d √ 2 gL H 2
3
Therefore, height of weir should be = 2.0 - 0.72 = 1.28 m
Solution
Height of weir = 1.28 m
Triangular weir
A notch weir is any weir where the physical barrier is significantly higher than the
water level except for a specific notch (often V-shaped) cut into the panel. At times of
normal flow all the water must pass through the notch, simplifying flow volume
calculations, and at times of flood the water level can rise and submerge the weir
without any alterations made to the structure. This type of weirs is well suitable for
measuring discharge over small flows with greater accuracy.
Flow over triangular weir
The flow rate measurement in a triangular weir is based on the Bernoulli
Equation principles and can be expressed as:
5
8 θ
Q= C √ 2 g tan H 2
15 d 2
where
Q = flow rate (m3/s)
H = elevation head on the weir (m)
g = 9.81 (m/s2) - gravity
Cd = discharge constant for the weir - must be determined
cd must be determined by analysis and calibration tests. For standard weirs - cd - is well
defined or constant for measuring within specified head ranges.
Example - Discharge through a triangular notch
Problem
A right-angled V-notch was used to measure the discharge of a centrifugal
pump. If the depth of water at V-notch is 200mm, calculate the discharge over the notch
in liters per minute. Assume coefficient of discharge as 0.62.
Workings
Given,
We know that the discharge over the triangular notch,
Solution
Discharge over the notch = 1560 liters/s
Trapezoidal weir
The term 'Cipolletti weir (trapezoidal weir)' as it applies to the area of reclamation
can be defined as ' A contracted weir of trapezoidal shape in which the sides of the
notch are given a slope of 1 horizontal to 4 vertical'.
Flow over cippoletti weir or trapezoidal weir
The flow rate measurement in a triangular weir is based on the Bernoulli
Equation principles and can be expressed as:
3
2
Q= C d L √ 2 g H 2
3
where
Q = flow rate (m3/s)
H = elevation head on the weir (m)
L= length of the weir (m)
g = 9.81 (m/s2) - gravity
cd = discharge constant for the weir - must be determined
cd must be determined by analysis and calibration tests. For standard weirs - cd - is well
defined or constant for measuring within specified head ranges.
Example - Discharge Over A Cippoletti Weir
Problem
Water is flowing over a Cippoletti weir of 4 meters long under a head of 1 meter.
Compute the discharge, if the coefficient of discharge for the weir is 0.6.
Workings
Given,
L = 4m
H = 1m
Cd = 0.62
We know that the discharge over the Cippoletti weir,
Solution
Discharge = 7.32 m3 /s
Classification according to shape of the crest
Sharp-crested weir
The water flowing over the crest comes in contact with the crest line and then
springs up from the crest and falls as a trajectory.
The thickness of weir is kept less than half of the height of water on the weir
The crest of the weir is very sharp such that the water will springs clear of the
crest.
Flow over sharp-crested weir is similar as rectangular weir.
Example - Discharge Over A Sharp-crested Weir
Problem
A rectangular sharp-crested weir is to be constructed in a testing station with small
stream in which the discharge varies from 50 liters/s and 1250 liters/s. Find the suitable
length of the weir, if the minimum head to be measured is 50 mm and the maximum
head on it does not exceed one-third of its length.
Workings
Given,
Qmax = 50 liters/s = 0.05 m3 /s
Qmin = 1250 liters/s = 1.25 m3 /s
Hmin = 50 mm = 0.05 m
Let, H = Length of weir in meters
Maximum head of water, Hmax = L/3
We know that the minimum discharge over the weir (Q min)
(1)
1)
and maximum discharge over the weir (Qmax)
(2)
1)
Dividing equation (2) by (1)
Broad-crested weir
The height of water above the weir crest is not greater than two times of the
width of the crest of weir
These are constructed only in rectangular shape and are suitable for the larger
flows.
Head loss will be small in case of broad crested weir.
Example - Discharge Over A Broad Crested
Weir
Problem
Determine the maximum discharge over a broad-crested weir 60 meters long
having 0.6 m height of water above its crest. Take coefficient of discharge as 0.595.
Also determine the new discharge over the weir, considering the velocity of approach.
The channel at the upstream side of the weir has a cross-sectional area of 45 sq
meters.
Workings
Given,
L = 60 m
H = 0.6 m
Cd = 0.595
A = 45 m2
Maximum Discharge Over The Weir Without Considering The Velocity Of Approach
Maximum Discharge Over The Weir Considering The Velocity Of Approach
and the head due to velocity of approach,
We also know that the maximum discharge over the weir,
Narrow-crested weir
The height of water above the weir crest is greater than two times of the width of
the crest of weir
It is similar to rectangular weir with narrow shaped crest at the top.
The discharge over narrow crested weir is similar to discharge over rectangular
weir.
.
Example -
Discharge Over A Narrow Crested Weir
Problem A narrow-crested weir of 10 meters long is discharging water under a
constant head of 400 mm. Find discharge over the weir in liters/s. Assume coefficient of
discharge as 0.623.
Workings
Given,
L = 10 m
H = 400 m = 0.4 m
Cd = 0.623
We know, the discharge over the weir,
Ogee-shaped weir
Generally ogee shaped weirs are provided for the spillway of a storage dam.
The crest of the ogee weir is slightly rises and falls into parabolic form.
Example - Discharge Over An Ogee Weir
Problem
An ogee weir 4 meters long has 500 mm head of water. Find the discharge over
the weir, if Cd = 0.62.
Workings
Given,
L=4m
H = 500 mm = 0.5 m
Cd = 0.62
The discharge over the weir,
Solution
The discharge over the weir = 2590 liters/s
Classification based on end contractions
Contracted weir
The crest is cut in the form of notch and then it is similar to rectangular weir.
Head loss will occur in this type.
Suppressed weir
The crest is running all the way across the channel so head loss will be
negligible.
Advantages of Weir
Weirs can be built to measure water flow rate, to alter the flow of rivers, or to
prevent flooding. Additionally, small-size weirs can be used in
large hydropower developments as a way to mitigate potential harm that may come about
as a result of dam development. Small weirs can help improve fish numbers, stabilize
water levels, and stabilize effects of river alteration.
Disadvantages of Weir
Weirs do have drawbacks, as they can increase sedimentation and pose
potential migration barriers to fish. To aid in migration, fish ladders are sometimes
incorporated into weirs to aid in fish passage. Sedimentation can occur as the water
slows as it goes over the weir, dropping sediment as it slows. As well, as water passes
over the top of the weir, the motion can alter the dissolved oxygen levels. If the water is
over or under-oxygenated (called hypoxia or anoxia), this can harm the
local ecosystem.
Weirs are particularly dangerous to humans - and are thus commonly called
"drowning machines". Particularly, the circulating "backwash" of water behind the weir is
easy to get trapped within, and if a swimmer or boater is caught within this cycle escape
and rescue is incredibly difficult. Additionally, debris that can be trapped within this cycle
of water can pose harm to anyone trapped behind the weir
