Experiment No.4 Flow measurement by Notched Weirs
Weirs allow hydrologists and engineers a simple method of measuring the volumetric
flow rate in small to medium-sized streams or in industrial discharge locations. Since
the geometry of the top of the weir is known and all water flows over the weir, the
depth of water behind the weir can be converted to a rate of flow. The calculation
relies on the fact that fluid will pass through the critical depth of the flow regime in
the vicinity of the crest of the weir. If water is not carried away from the weir, it can
make flow measurement complicated or even impossible. A weir functions by causing
water to rise above the obstruction in order to flow over it. The height of water above
the obstruction correlates with the flow rate, so that measurement of the height of the
flowing water above the top of the weir can be used to determine the flow rate by the
use of an equation, graph or table. The top of the weir, which is used as the reference
level for the height of water flowing over it, is called the crest of the weir. Weirs are
typically classified as being either sharp-crested or broad-crested. This course is
devoted to the more widely used sharp-crested weir. The major important is on the
calculations used for flow rate over various types of sharp-crested weirs.
1 Objective
In this experiment, two types of Notched weir are used to determine the discharge of
water. The relation of flow rate over the weir to the head is used to figure out the
discharge coefficient, Cd
2 Experiment Apparatus
The experiment apparatus for this experiment consists of a Hydraulic Bench , weir
tank and hook gauge , stop watch , Rectangular notch ( U-Notch ) and Triangular
notch ( V – Notch ).
Figure1 Experiment Apparatus
3 Theory
A weir is a barrier across a river designed to alter the flow characteristics. In most
cases, weirs take the form of a barrier, smaller than most conventional dams, across a
river that causes water to pool behind the structure (not unlike a dam) and allows
water to flow over the top. Weirs are commonly used to alter the flow regime of the
river, prevent flooding, measure discharge and help render a river navigable. Weirs
are structures consisting of an obstruction such as a dam or bulkhead placed across the
open channel with a specially shaped opening or notch. The weir results an increase in
the water level, or head, which is measured upstream of the structure. The flow rate
over a weir is a function of the head on the weir. Common weir constructions are the
rectangular weir, the triangular or v-notch weir, and the broad-crested weir. Weirs are
called sharp-crested if their crests are constructed of thin metal plates, and broadcrested if they are made of wide timber or concrete. Water level-discharge
relationships can be applied and meet accuracy requirements for sharp-crested weirs if
the installation is designed and installed consistent with established ASTM and ISO
standards.
3.1 Common standards and specification for weir flow measurement
Rectangular weirs and triangular or v-notch weirs are often used in water supply,
wastewater and sewage systems. They consist of a sharp edged plate with a
rectangular, triangular or v-notch profile for the water flow. Broad-crested weirs can
be observed in dam spillways where the broad edge is beneath the water surface
across the entire stream. Flow measurement installations with broad-crested weirs will
meet accuracy requirements only if they are calibrated. Other available weirs are the
trapezoidal (Cipolletti) weir, Sutro (proportional) weir and compound weirs
(combination of the previously mentioned weir shapes).There are 2 type of Notched
Weir such as rectangular notched Weir ( U – Notched ) and triangular Notched Weir (
V – Notched ).
Figure2 Type of Notched Weir V-Notched and U-Notched
3.2 Sharp Crested Rectangular Weir Background
Figure3 Sharp Crested Rectangular Weir Background (King, H. W. 1954)
General background on the sharp crested weir is given in the article, "Open Channel
Flow Measurement 4: the V Notch Weir." The diagram at the left summarizes some
terminology and parameters used in connection with sharp crested weirs. The diagram
at the right shows figures of the two types of rectangular weirs to be covered in this
article, a suppressed rectangular weir, which has the weir opening across the entire
channel width, and a contracted rectangular weir, which has a weir opening that is
shorter than the channel width. Equations for calculating the water flow rate over a
suppressed rectangular weir and over a contracted rectangular weir will be covered in
the next two sections.
3.3 Suppressed Rectangular Weir Equation
Figure4 Suppressed Rectangular Weir ( Kindsvater and Carter1957)
The suppressed rectangular weir in the picture at the left is being used to meter flow
of water in an open channel. The equation recommended by the Bureau of
Reclamation in their Water Measurement Manual, for use with a suppressed
rectangular weir is Q = 3.33BH3/2, where Q is the water flow rate in ft3/sec, B is the
length of the weir (and the channel width) in ft, and H is the head over the weir in ft.
Use of this equation is subject to the condition that H/P < 0.33 and H/B < 0.33. Note
from the diagrams above that P is the height of the weir crest above the bottom of the
channel, and B is the channel width. For S.I. units the suppressed rectangular weir
equation becomes Q = 1.84 B H3/2, where Q is the water flow rate in m3/sec, B is the
length of the weir (and the channel width) in m, and H is the head over the weir in m.
The same condition for H/P and H/B apply.
Figure5 Contracted Rectangular Weir (Kindsvater and Carter1957)
Both images in this section show a contracted rectangular weir being used to meter
flow in an open channel. The equation recommended by the Bureau of Reclamation in
their Water Measurement Manual, for use with a fully contracted rectangular weir is
Q = 3.33(L - 0.2H)H3/2, where Q is the water flow rate in ft3/sec and H is the head
over the weir in ft. Use of this fully contracted rectangular weir equation is subject to
the conditions that H/L < 0.33, B - L > 4 Hmax, and P > 2Hmax. L is the weir length,
Hmax is the maximum head over the weir, and H, B, & P are as identified above. For
S.I units the fully contracted rectangular weir equation is: Q = 1.84(L - 0.2H)H3/2,
where Q is the water flow rate in m3/sec, and H is in m. This weir equation is subject
to the same conditions given above. (Kindsvater, C. E. and R. W. Carter. 1959)
Figure6 Rectangular Weir (Replogel, 1998)
The term weir has several meanings. The term rectangular weir refers to a specific
type of weir with a rectangular notch cut in the top edge. This notch can be used by
engineers to calculate the rate of flow of the body of water, providing valuable
information that can be used for environmental management programs, flood
management, further dam construction and civil engineering projects. Generally the
term refers either to a structure consisting of pens or fences in a body of managing
water depth and flow. A weir is different from other types of dam in that water
generally flows over the top rather than through spillways or hydroelectric plants like
in other dams. The flow rate measurement in a rectangular weir is based on the
Bernoulli Equation principles and can be expressed as:
𝑄𝑡ℎ =
2
√2𝑔
3
b𝐻
1
2
(1)
where
Q = flow rate (m3/s)
H = head on the weir (m)
b = 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. The Francis
Formula - Imperial Units. Flow through a rectangular weir can be expressed in
imperial units with the Francis formula
3
Q = 3.33(𝑏 − 0.2)ℎ2
where
q = flow rate (ft3/s)
h = head on the weir (ft)
b = width of the weir (ft)
(2)
Figure7 Graph is shown the relationship between h/p and discharge coefficient
(Kindsvater, C. E. and R. W. Carter. 1959)
Figure8 Graph is shown the relationship between b/B and Kb
(Kindsvater, C. E. and R. W. Carter. 1959)
3.4 Triangular or V-Notch Weir
Figure9 Triangular or V-Notch Weir (Replogel, 1998)
V-Notches or Sharp Crested Weirs are generally used for measuring small discharges
like seepage from drains and gallery of masonry dam or toe drains. V-Notches can
measure discharge from 1 lit/sec to 120 lit/sec maximum. For low discharges, VNotches are superior to Flumes because head over the crest is large and thus flow
remains unaffected by surface tension and viscosity. V-Notches have their own
limitation and not suitable for discharge measurements in field channels due to
obstruction of silt. The Indian Standards Institute (ISI) has drawn specifications for
manufacture of V-Notches. Ni-Plast make V-Notches confirm to Indian Standards IS:
9108-1979. Mechanical and Electronic recorders are available with Ni-Plast VNotches these enable automatic data recording of discharge measurements. Periodic
discharge measurements at preset time intervals are logged in a data logger that is
housed in the electronic recorder unit. The data logger can be connected to a desktop
PC to download the data for further processing and generate reports like water
seepage, water discharge during a given period of time, water accountability etc. For a
triangular or v-notch weir the flow rate can be expressed as:
8
√2𝑔
15
𝑄𝑡ℎ =
tan𝜃2𝐻 2.5
(3)
where
θ = v-notch angle
Formula
Q = 𝐾𝐻 𝑛
𝑸
𝑪𝒅 = 𝑸 𝒂𝒄𝒕𝒖𝒂𝒍
𝒕𝒉𝒆𝒐𝒓𝒚
Cd
= Discharge coefficient
(4)
(5)
Qactual = Discharge from experiment
Qtheory = Derive from Bernoulli’s equation
U – Notched
𝑄𝑡ℎ𝑒𝑜𝑟𝑦 =
2
3
√2𝑔𝑏𝐻1.5
2
𝑄𝑎𝑐𝑡𝑢𝑎𝑙 = 𝑐𝑑 3 √2𝑔𝑏𝐻1.5
2
K = 𝐶𝑑 3 √2𝑔𝑏
(6)
(7)
(8)
V – Notched
𝑄𝑡ℎ𝑒𝑜𝑟𝑦 =
8
15
𝜃
√2𝑔 tan 2 𝐻 2.5
8
𝜃
𝑄𝑡ℎ𝑒𝑜𝑟𝑦 = 𝐶𝑑 15 √2𝑔 tan 2 𝐻 2.5
8
𝜃
K = 𝐶𝑑 15 √2𝑔 tan 2
(9)
(10)
(11)
3.5 Advantages and Disadvantages of weirs
Advantages which are 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 and can be both
portable and adjustable
Disadvantages which are 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.
4. Experiment Procedure
4.1Measure the size of each weir, thoroughly.
4.2Insert the weir into the hydraulic bench and fit it tightly.
4.3Turn on the pump and open the valve, wait until water discharge over a weir.
Then, close the valve and turn the pump off and allow water to drops until water flow
over the weir stops.
4.4Be sure that the water surface is in the same level as the weir crest (for U-notch) or
the lower tip of weir (for V-notch). Adjust the Hook gauge to touch the water surface.
Set and record the reading to be the zero gauge reading, so that the bottom of the
notch is taken as the datum.
4.5Turn on the pump and open the valve again.
4.6Adjust the Hook gauge to touch water surface. Read the scale as the Gauge reading
and minus it by the Zero gauge reading to get the water height, H. Record H in your
data sheet.
4.7Measure the discharge by the Weight time measurement method. Record Q in your
data sheet.
4.8Adjust the valve again to get totally 8 points of data for each type