H6
Discharge Over a Notch
User Guide
© TecQuipment Ltd 2016
Do not reproduce or transmit this document in any form or by
any means, electronic or mechanical, including photocopy,
recording or any information storage and retrieval system
without the express permission of TecQuipment Limited.
TecQuipment has taken care to make the contents of this
manual accurate and up to date. However, if you find any
errors, please let us know so we can rectify the problem.
TecQuipment supply a Packing Contents List (PCL) with the
equipment. Carefully check the contents of the package(s)
against the list. If any items are missing or damaged, contact
TecQuipment or the local agent.
DB/0816
:
User Guide
TecQuipment Ltd
H6 Discharge Over a Notch
Contents
Introduction
Description
.................................................................. 1
................................................................... 3
Technical Details
............................................................ 5
Noise Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Installation and Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Background to Weirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Theory of Flow over Sharp-Edge Notch Weirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Finding the Mean Coefficient of Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Predicting Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
The Cipoletti (Trapezoidal) Weir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
The Linear Head/Flow (Proportional) Weir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Alternative Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
Useful Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Experiment 1 - Flow and Head Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Experiment 2 - Predicting Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Typical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
Experiment 1 - Flow and Head Relationship. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Experiment 2 - Predicting Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Maintenance, Spare Parts and Customer Care . . . . . . . . . . . . . . . . . . . . . . .
33
Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Spare Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Customer Care . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
TecQuipment Ltd
User Guide
H6
Flow Over a Notch
User Guide
Introduction
Figure 1 H6 Flow Over a Notch
Often, engineers use weirs to simply raise the level of upstream water in a river or canal system.
Alternatively, weirs can help to retain fish stocks in a section of river. However, engineers often use weirs
to regulate flow in rivers and other open channels. In some applications engineers have designed and
calibrated the weir with its surrounding water levels, so that they only need to know the upstream water
level to find the flow over the weir.
Weirs have different shapes and designs, which work better for different applications. The most common
include; broad-crested, sharp-edged (or sharp-crested) or weirs that have a shaped ‘notch’.
The TecQuipment Flow Over a Notch apparatus (H6) fits onto TecQuipment’s Digital Hydraulic Bench
(H1F) or an existing Gravimetric Hydraulic Bench (H1). It works over a range of flow to allow
experiments that show the relationship between flow and head and how you can use the weirs to
measure flow. The apparatus includes three standard weirs, one rectangular and two V-notch. It also
includes an advanced set of two weirs, Cipoletti (trapezoidal) and a linear head/flow weir for more
experiments.
TecQuipment Ltd
1
User Guide
H6 Flow Over a Notch
User Guide
2
TecQuipment Ltd
H6 Flow Over a Notch
Description
Depth or
Height Gauge
Downstream
Open Channel
section
Rectangular
Weir (fitted)
Upstream
V-Notch Weirs
Trapezoidal
(Cipoletti) Weir
Linear
Head/Flow
Weir
Figure 2 Main Parts
Figure 2 shows the main parts of the equipment. The drawing of Figure 3 shows more detail. The main
part of the apparatus is a moulded tank in three sections. It has an enlarged upstream section and a
thinner but deeper downstream section. The ‘open channel’ between the two sections has a slot for the
weirs and a fixing point for the depth (or height) gauge.
The unit fits onto TecQuipment’s Digital Hydraulic Bench (H1F) or an existing Gravimetric Hydraulic
Bench (H1). The benches work as the water supply and external flow measurement system.
The bench supply pipe connects to the bottom of the upstream end of the apparatus. The outlet of the
downstream end drains into the large central hole in the lid of the Bench. The enlarged upstream section
and special disc at the inlet help to stabilize the inlet (upstream) flow conditions for better results.
TecQuipment Ltd
3
User Guide
H6 Flow Over a Notch
Inlet
pipe
Weir
Depth gauge
Outlet to
Gravimetric Bench
Inlet pipe
Disc
Figure 3 Details of the Equipment
User Guide
4
TecQuipment Ltd
H6 Flow Over a Notch
Technical Details
Item
NOTE
Details
Nett dimensions and
weight
920 mm x 620 mm x 520 mm and 12 kg
Open channel
(nominal dimensions)
228 mm x 178 mm x 305 mm
Rectangular Notch
Weir
(nominal dimensions)
Depth 100 mm, width 30 mm
(Measure accurately before use)
V Notch Weirs
(nominal dimensions)
One of depth 100 mm, total notch angle 30º (θ = 15°)
One of depth 100 mm, total notch angle 90º (θ = 45°)
(Check before use)
Linear Head/Flow
(nominal dimensions)
Height of cut-out 77 mm.
Base 50 mm.
Cipoletti
(nominal dimensions)
Depth 100 mm, width at top 75 mm, width at bottom
25 mm.
Slope ratio of 4 units vertical to one unit horizontal.
Check all nominal dimensions accurately before use.
Noise Levels
The noise levels recorded at this apparatus are lower than 70 dB (A).
TecQuipment Ltd
5
User Guide
H6 Flow Over a Notch
User Guide
6
TecQuipment Ltd
H6 Flow Over a Notch
Installation and Assembly
The terms left, right, front and rear of the apparatus refer to the operators’ position, facing the unit.
NOTE
• A wax coating may have been applied to parts of this apparatus to
prevent corrosion during transport. Remove the wax coating by using
paraffin or white spirit, applied with either a soft brush or a cloth.
• Follow any regulations that affect the installation, operation and
maintenance of this apparatus in the country where it is to be used.
TecQuipment supply the apparatus disassembled for transport. To reassemble:
1. TecQuipment may remove the depth gauge assembly for transport. Use the fixings supplied to refit
it to the open channel section.
2. The inlet pipe may have been removed for transport. Refit it to the channel. You may use some of
the silicon grease (supplied) to help create a good seal if needed.
3. Put the equipment onto the top of the Hydraulic Bench and use its adjustable feet to make it level.
4. Connect the bench supply hose to the upstream inlet connection.
5. Put the downstream end over the large hole in the lid of the Hydraulic Bench. You may need to use
a short piece of pipe to help direct the flow into the hole.
6. Wear suitable gloves and smear some of the grease (supplied) around the slot in the open channel
or around the edge of the weir that you are to test. This helps to create a good seal.
TecQuipment Ltd
7
User Guide
H6 Flow Over a Notch
User Guide
8
TecQuipment Ltd
H6 Flow Over a Notch
Theory
Notation
Symbol
Meaning
Units
u
Velocity of flow
m.s-1
H
Total Head
m
h
height (or depth)
m
Q
Flow or discharge
m3.s-1
A
Area
m2
B
Breadth (Width) of weir base
m
b
Breadth (Width) at a point on the V
notch weir
m
p
Pressure
Pa or N.m-2
kc
kR
kV
kL
Constants for Cipoletti, rectangular,
V and Linear notch weirs
-
g
Acceleration due to gravity
m.s-2
x
Distance
m
w
Specific weight (water)
9810 N.m-3
z
Elevation (above a datum or given
level)
m
θ
Angle
degrees
Cd
Coefficient of discharge
-
CdR
Coefficient of discharge (rectangular
notch weir)
-
CdV
Coefficient of discharge (V notch
weir)
-
CdL
Coefficient of discharge (Linear weir)
-
Table 1 Notation
Unit Conversions
Gravimetric Flow: 1 m3.s-1 = approximately 1000 kg.s-1 for clean water at room temperature.
TecQuipment Ltd
9
User Guide
H6 Flow Over a Notch
Background to Weirs
In many cases, the upstream water level determines the rate of flow over a weir. Engineers often call this
relationship between flow rate and water level the “rating curve”. However, the water level downstream
of a weir may reach a height that affects the conditions of flow. In this case, the flow rate now becomes
a function not only of the upstream water level but also of the water level downstream. The weir is then
called “suppressed” or “drowned”.
As mentioned earlier, weirs have many different designs, but generally, local conditions affect the design
of weir needed for any application.
In many applications the weir has a round or broad crest as shown in Figures 4 and 5. On these weirs,
the flow usually remains attached to the downstream surface.
However, in the case of the sharp crested weir shown in Figures 6, the flow separates at the crest to form
a curved jet that plunges into the downstream pool. In plan view, the weir may be straight or curved to
suit local conditions. In some applications, the crest level is not uniform along the whole of the length.
For example, part of the whole length may carry normal flow, the rest of the length may have a higher
crest, so that it comes into use only at higher flow rates.
Figure 4 Round Crested Weir
Figure 5 Broad Crest Weir
Figure 6 Sharp Crest Weir
User Guide
10
TecQuipment Ltd
H6 Flow Over a Notch
One type of weir good for flow measurement, is the “notch” weir. It has this name because it has a sharp
edged notch cut out of a plate. The cut out may be of any shape, but the most common shapes are
rectangular and V, as shown in Figure 7.
Rectangular
V Notch
Figure 7 Rectangular and V Notches
TecQuipment Ltd
11
User Guide
H6 Flow Over a Notch
Theory of Flow over Sharp-Edge Notch Weirs
h
h
N
H
M
dh
zN
zM
B
q
q
h
h
N
H
M
zN
zM
dh
b = 2(H - h)tanq
Figure 8 Flow Over Sharp Edge Notch Weirs
Figure 8 shows the main features of flow over rectangular and V notches. The approaching (upstream)
flow is assumed to be uniform, with total head H measured with respect to the crest level of the notch.
If the cross-sectional area of the upstream open channel is much larger than that of the area of flow over
the notch, then the velocity head in the upstream flow will be negligible, and the water level there will
represent the total head H.
Throughout the undisturbed flow upstream, conditions are effectively hydrostatic, the total head H at a
typical point M being given by:
pM
H = --------------w + zM
(1)
Consider a typical streamline of the flow, from the typical point M in the upstream section to the point
N in the plane of the notch. In the absence of any loss of total head, according to Bernoulli's equation:
2
p
u
p
H = -----M- + z M = -----N- + -----N + z N
w
2g w
(2)
The static pressure pN at N is now assumed to be atmospheric (pN = 0), so that:
User Guide
12
TecQuipment Ltd
H6 Flow Over a Notch
2
u
H = -----N- + z N
2g
(3)
H – zN = h
(4)
Using the substitution:
Where h is the depth of the point N below the upstream undisturbed surface level.
Using equations 3 and 4 with Figure 8, we can find the velocity of flow at point N, so that:
uN =
(5)
2gh
The flow velocity at N is the velocity of a particle falling freely (due to gravity) from the level of the
undisturbed upstream surface.
The discharge rate over any notch may now be found by integration. If b is the width of the notch at
depth h below the upstream surface level, then for an element of height δh, the element of area δA is:
δA = bδh
(6)
so the element of discharge δQ is
δQ = u N δA =
2gh ⋅ bδh
(7)
The total flow rate Q, obtained by integration from zero to H, is then:
Q =

H
2gh ⋅ bδh
(8)
0
This result applies to a notch of any shape, and can be easily applied to the rectangular and V shaped
notches.
For the rectangular notch of breadth B, equation 8 becomes:
H
Q = B

2gh ⋅ bδh
0
which integrates immediately to give:
3
---
2
Q = 2--- 2g ⋅ BH
3
(9)
For the V notch of total angle 2θ, the width b is given by:
b = 2 ( H – h )tanθ
TecQuipment Ltd
13
User Guide
H6 Flow Over a Notch
The total flow rate is therefore given by Equation (8) as:
Q =
H

2gh ⋅ 2 ( H – h )tanθδh
0
The result of integration is:
5
---
8- 2g ⋅ tanθH 2
Q = ----15
(10)
Coefficient of Discharge
Each of the theoretical results given in Equations 9 and 10 ignore the contraction of the flow as it passes
through the notch. During your experiments you will see this contraction:
• In the vertical plane - you will see the upper surface drawn downwards over the notch and
how the lower surface springs from the crest in an upward direction;
• In the horizontal plane - you will see where the water springs from the edges of the notch in
a curve which reduces the width of the stream.
The contraction is similar to that caused by a sharp edged orifice, and has the same effect of reducing
the discharge rate. The coefficient of discharge allows for this reduction, as it is a measure of how the
actual flow compares with ideal flow. Therefore, as with an orifice, the equations must be rewritten to
include the coefficient of discharge.
So, for the rectangular notch:
3
---
2
Q = C dR 2--- 2g ⋅ BH
3
(11)
Inserting known values:
Q = C dR × 2.95 × BH
3
--2
(12)
and for the V notch:
5
---
8- 2g ⋅ tanθH 2
Q = C dV ----15
(13)
Inserting known values:
Q = C dV × 2.36 × tan θH
5
--2
(14)
Textbooks give typical values of coefficient of discharge for orifices and weirs. Also, designer’s reference
books will give the values for given weir dimensions. However, where possible, engineers should try to
calibrate the weir to find an accurate value. This should also give them an idea of how it changes
throughout the weir’s flow range.
User Guide
14
TecQuipment Ltd
H6 Flow Over a Notch
Finding the Mean Coefficient of Discharge
Rectangular Notch
For the Rectangular Notch, a rearrangement of Equation 11 gives:
Q
C dR = ---------------------------3
--2--- 2g BH 2
⋅
3
(15)
Or alternatively:
kR
C dR = --------------------2--- 2g ⋅ B
3
Where kR is a constant found from the ratio of flow over Head3/2:
Qk R = ----3
H
(16)
--2
and inserting known values:
kR
C dR = ------------------2.95 × B
(17)
From this, a plot of Q against H3/2 from actual results should give a straight line (see Figure 9). Its
gradient will be the mean value of kR, which you can use with Equation 17 to find the mean value of
CdR for the rectangular notch.
For the Rectangular Notch
For the V Notch
Flow
Q
Flow
Q
Slope = Q/H
Head
3/2
= kR
Slope = Q/H
3/2
Head
5/2
= kV
5/2
Figure 9 Finding the Mean Value of Coefficient
TecQuipment Ltd
15
User Guide
H6 Flow Over a Notch
V Notch
For the V Notch, a rearrangement of Equation 13 gives:
Q
C dV = ---------------------------------------5
--2
8
------ 2g ⋅ tanθH
15
(18)
Or alternatively:
kV
C dV = -------------------------------8
------ 2g ⋅ tanθ
15
Where kV is a constant found from the ratio of flow over Head5/2:
Q
k V = -----5H
(19)
--2
and inserting known values:
kV
C dV = ---------------------------2.36 × tanθ
(20)
From this, a plot of Q against H5/2 from actual results should give a straight line (see Figure 9). Its
gradient will be the mean value of kV, which you can use with Equation 20 to find the mean value of
CdV for the V notch.
Predicting Flow
For the Rectangular Notch, once you have found its constant (kR), you can re-arrange Equation 16 to
predict the flow simply by using the upstream head.
Q = kR × H
3
--2
(21)
For the V Notch, once you have found its constant (kV), you can re-arrange Equation 19 to predict the
flow simply by using the upstream head.
Q = kV × H
User Guide
16
5
--2
(22)
TecQuipment Ltd
H6 Flow Over a Notch
The Cipoletti (Trapezoidal) Weir
H
B
Figure 10 The Cipoletti Weir
For flow measurement, the most popular sharp-edged notched weirs are rectangular and V-shaped.
However, an Italian engineer - Cipoletti developed an alternative shape (see Figure 10). This slight
variation of a rectangular profile produces a constant value of discharge coefficient over a wide range of
heads.
Experiments on rectangular notches should show that the value of the discharge coefficient falls slightly
with increasing head, and therefore ratio H/B. The sloped sides of the Cipoletti weir gives a width that
increases with head, providing compensation for the reduction in discharge coefficient.
The best way to check this is to test Cipoletti notch in the same manner as a rectangular notch, and
compare the head-discharge (H and Q) characteristics on a logarithmic basis.
For this weir:
Q = kc H
TecQuipment Ltd
17
3
--2
(23)
User Guide
H6 Flow Over a Notch
The Linear Head/Flow (Proportional) Weir
Top of Weir Plate
Shaped
Orifice
b
H
H
y
x
H0
Q
B
Figure 11 The Linear Head/Flow Weir
The linear head/flow (proportional) weir (sometimes called a Sutro Weir) is an ingenious design for
producing a flow rate Q which is linearly proportional to Head H. Therefore, in the expression:
n
Q = kL H n = 1
Earlier equations show that for a rectangular notch, n = 3/2, and for a V notch, where the width
increases with head, n = 5/2. So, for n = 1, the notch width would need to decrease with increasing
head, exactly as shown in the Linear Head weir shown in Figure 11.
For low values of head and flow, the water passes through the lower rectangular section and the notch
works exactly like a simple rectangular one.
For higher head and flow rates, the water passes through the rectangular section and the curved section,
so:
Q = kL ( H – Ho )
(24)
Where:
Ho ≈ H
---3
and
k L = C dL B 2gx
User Guide
18
(25)
TecQuipment Ltd
H6 Flow Over a Notch
Accurate values for CdL and Ho can be found from experiment.
Figure 11 also shows the head-flow relationship for this weir, which should give a straight line. Extending
this line should give a value for H0. The gradient should give kL and using this with a rearranged
Equation 25 will give a value for CdL.
TecQuipment Ltd
19
User Guide
H6 Flow Over a Notch
Alternative Theory
Equation 26 gives an alternative and general way of expressing the flow for both rectangular and Vnotch weirs:
Q = kH
n
(26)
This can be expressed in logarithmic terms as:
logQ = log k + n logH
So, if you create a chart of log Q against log H for your actual results (see Figure 10), it should produce
a straight line. You can then find its slope to confirm the value for n and find its intercept to give log k.
This should help prove the values given in the theory and possibly give you more accurate calibration
constants (kV, kR and 3/2 or 5/2) for your weir.
Log Q
X
X
X
X
Gradient = n
X
Intercept = log k
X
X
Log H
X
Figure 12 Log-Log Results
User Guide
20
TecQuipment Ltd
H6 Flow Over a Notch
Experiments
Useful Notes
Two People
This equipment is safe to use, but TecQuipment recommend that at least two people do the
experiments. One person to take weir readings and the other to check flow rates.
Splashes of Water
This apparatus uses water and may splash some onto the top of the Hydraulic Bench. Be prepared for
small splashes of water.
Setting up Initial Water Level (Datum of Head)
Steel rule
Level too low
Level too high
Level correct
(a) Rectangular Notch
V-notch
Reflection
in water
surface
Level too low
Level too high
Level correct
(b) V-notch
Figure 13 Water Level
TecQuipment Ltd
21
User Guide
H6 Flow Over a Notch
Before each experiment, you must set a datum point for the upstream head of water, then all other
measurements of head during the tests will be with respect to this value. To do this, start the pump of
the hydraulic bench until the upstream water level just starts to pour over the bottom of the notch of
the weir, then stop the pump.
Now, wait for the level to stabilize and use a rule or flat edge to make sure the water upstream of the
weir is exactly level with the bottom of the notch (see Figure 13). This is easiest with the rectangular
notch. For the V notch, try to use the weir reflection in the water to help you see how the water level
matches with the bottom of the V.
If necessary, use a small cup or beaker (not supplied) to add or remove some water to or from the
upstream section.
Now carefully adjust the depth gauge so that its tip touches the surface of the water. This is the datum
Head value.
User Guide
22
TecQuipment Ltd
H6 Flow Over a Notch
Experiment 1 - Flow and Head Relationship
Aims
To show how flow varies with Head.
To show how the coefficient of discharge changes slightly with flow.
To find the mean coefficient of discharge for the weir and therefore its ‘constant’ for calibration.
Procedure 1 - Rectangular Weir
Datum Value of Head:
Width of notch (B):
Water
Quantity
(kg)
Time
(seconds)
Flow (Q)
(m3.s-1)
Gauge
Reading
(mm)
Head (H)
(m)
H3/2
(m)
CdR
Table 2 Blank Results Table
1. Create a blank results table similar to Table 2.
2. Use the given nominal values or carefully measure the notch width (B) and record it.
3. Set up the equipment as described in Installation and Assembly on page 7.
4. Set up the initial water level as shown in Setting up Initial Water Level (Datum of Head) on
page 21.
5. Start the pump of the hydraulic bench and adjust for the highest flow rate (around 1 kg per second
or 60 kg in one minute).
6. Wait for the flow rate and the upstream level to stabilize and note the water quantity you collect
and the time taken. Convert this into volume flow (m3.s-1).
TecQuipment Ltd
23
User Guide
H6 Flow Over a Notch
7. Use the gauge to measure the new water height. Subtract the datum value from your reading to
get the true value of Head and convert this into metres.
8. Repeat for at least seven more lower flow rates that give equal decreases in head (roughly 10 mm
steps should work).
9. Watch carefully the water as it leaves the weir. At some point as the flow gets lower, the water does
not spring clear of the weir and starts to run down the downstream side of the weir. Stop taking
results when this happens.
Procedure 2 - V Notch Weirs
Datum Value of Head:
Angle of notch (θ):
Tan θ:
Water
Quantity
(kg)
Time
(seconds)
Gauge
Reading
(mm)
Flow (Q)
(m3.s-1)
Head (H)
(m)
H5/2
(m)
CdV
Table 3 Blank Results Table
1. Create a blank results table similar to Table 3.
2. Use the nominal values given or carefully measure the notch angle to find θ and record the angle
and the tan value of the angle.
3. Repeat the experiment just as in procedure 1.
4. Repeat for the other V notch.
User Guide
24
TecQuipment Ltd
H6 Flow Over a Notch
Procedure 3 - Cipoletti and Linear Head/Flow Weir
Datum Value of Head:
Width at base (B):
Water
Quantity
(L)
Time
(seconds)
Flow (Q)
(m3.s-1)
Gauge
Reading
(mm)
Head (H)
(m)
Log Q
Log H
Table 4 Blank Results Table
1. Create a blank results table similar to Table 4.
2. Repeat the experiment just as in procedure 1.
Results Analysis - Rectangular and V Notch Weirs
For the rectangular notch weir, calculate H3/2 and use Equation 15 to calculate the coefficient of
discharge for each line of your results.
For the V notch weirs, calculate H5/2 and use Equation 18 to calculate the coefficient of discharge for
each line of your results.
For each of your notch weirs, plot a chart of coefficient of discharge (vertical axis) against flow to see
how it changes with flow.
For the rectangular and both V notches, plot charts of Flow (vertical axis) against Head. Note the nonlinearity of the results and how the head changes with flow.
Add to your rectangular notch chart the values of H3/2, then find its slope to calculate the mean value
of coefficient of discharge (using Equation 17).
Add to your V notch charts the values of H5/2, then find its slope to calculate the mean value of
coefficient of discharge (using Equation 20).
TecQuipment Ltd
25
User Guide
H6 Flow Over a Notch
Results Analysis - Cipoletti and Linear Head/Flow Weir
From your results, find Log Q and Log H, then use these to create a chart of Log Q (vertical axis) against
Log H. Find the gradient and intercept to confirm the values of k and n.
User Guide
26
TecQuipment Ltd
H6 Flow Over a Notch
Experiment 2 - Predicting Flow
Aims
To show how to calculate flow from the upstream head using the constants found from the earlier
procedures.
To show that you can use the constants found from experiment to accurately predict flow.
Procedure
Weir:
Datum Value of Head:
Constant k:
H3/2
or
H5/2
or
Water
Quantity
(L)
Time
(seconds)
Actual
Flow (Q)
(m3.s-1)
Gauge
Reading
(mm)
Head (H)
(m)
H1
(m)
Calculated
Flow
(m3.s-1)
Error
(%)
Table 5 Blank Results Table
1. For each weir, create a blank results table similar to Table 5.
2. Repeat head and actual flow measurement, as in experiment 1.
3. Repeat for the other weirs.
TecQuipment Ltd
27
User Guide
H6 Flow Over a Notch
Results Analysis
For each line of your results, calculate H1, H3/2 or H5/2 (determined by your weir).
Use the Equations in the theory to calculate the flow based on the head and your constant.
Subtract the actual flow from the calculated flow, divide by the actual flow and multiply by 100 to find
the error in percent.
Explain the cause of any significant errors.
User Guide
28
TecQuipment Ltd
H6 Flow Over a Notch
Typical Results
All results are for reference only. Actual results may differ slightly.
Experiment 1 - Flow and Head Relationship
Rectangular Notch Weir
0.68
Coefficient of Discharge
0.66
0.64
0.62
0.6
0.58
0.56
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
Flow (m 3.s-1)
Figure 14 Typical Results for the Rectangular Notch Weir
Figure 14 shows that for the rectangular notch weir, ignoring any obviously inaccurate results, the trend
for the coefficient of discharge generally increases slightly to towards the middle of the flow range and
decreases at each end of the flow rate.
Figure 15 shows that for the rectangular notch weir, flow increases with head in a non-linear way.
However, flow against Head3/2 produces linear results, giving a gradient (kR) of 0.0539.
Where the weir notch width (B) is 30 mm (0.030 m), from Equation 17, this gives:
0.0539 C dR = ----------------------------2.95 × 0.030
Which gives a mean coefficient of discharge for the rectangular notch (CdR) of 0.61.
TecQuipment Ltd
29
User Guide
H6 Flow Over a Notch
Rectangular Notch Weir
Head3/2 (m 3/2)
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.0009
0.0008
Head
Head^3/2
Flow (m 3.s-1)
0.0007
0.0006
0.0005
y = 0.054x + 5E-06
0.0004
0.0003
0.0002
0.0001
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Head (m)
Figure 15 Typical Results for the Rectangular Notch Weir
Figure 16 shows that for the 30° V notch weir, ignoring any obviously inaccurate results, the trend for
the coefficient of discharge generally decreases slightly with increasing flow.
Figure 17 shows that for the 30° V notch weir, flow increases with head in a non-linear way. However,
flow against Head5/2 produces linear results, giving a gradient (kV) of 0.395.
Where notch total angle is 30° giving θ = 15°, from Equation 20, this gives:
0.395 C dV = ----------------------------2.36 × 0.268
Which gives a mean coefficient of discharge for the 30° V notch (CdV) of 0.625.
User Guide
30
TecQuipment Ltd
H6 Flow Over a Notch
V Notch Weir ( total angle = 30° theta = 15°)
0.68
Coefficient of Discharge
0.66
0.64
0.62
0.6
0.58
0.56
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
Flow (m 3.s-1)
Figure 16 Typical Results for the 30° V Notch Weir
V Notch Weir ( total angle = 30° theta = 15°)
Head5/2 (m 5/2)
0
0.0005
0.001
0.0015
0.002
0.0025
0.0009
0.0008
Head
Head^5/2
0.0007
Flow (m 3.s-1)
0.0006
y = 0.3952x + 9E-07
0.0005
0.0004
0.0003
0.0002
0.0001
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Head (m)
Figure 17 Typical Results for the 30° V Notch Weir
TecQuipment Ltd
31
User Guide
H6 Flow Over a Notch
Experiment 2 - Predicting Flow
A typical line of results from the rectangular notch weir gives:
Actual Flow
0.0003676 m3.s-1
Head
0.03541 m
Head3/2
0.00666329
Constant kR
0.0539
From Equation 21,
calculated flow
= 0.0539 x 0.00666329 =
0.0003591 m3.s-1
% error
= [(3591-3676)/3676] x 100
= -2.3%
Table 6 Typical Results for the Rectangular Notch Weir
A typical line of results from the 30° V notch weir gives:
Actual Flow
0.00021008 m3.s-1
Head
0.04889 m
Head5/2
0.000528506
Constant kV
0.395
From Equation 22,
calculated flow
= 0.395 x 0.000528506 =
0.00020876 m3.s-1
% error
= [(20876-21008)/21008] x 100
= -0.63%
Table 7 Typical Results for the 30° V notch Weir
Expect flow prediction accuracies of better than 3% for each weir over most of the flow range. Note that
the accuracy reduces (error increases) when the flow rate becomes low. At low flow rates, any errors in
measurement become more significant, also the water does not pass over the weir’s edge cleanly, so the
contraction is no longer present. This means that the theoretical equations that include the coefficient
of discharge are no longer correct.
The results should prove that the theory works accurately to help define the constants and predict the
flow over rectangular and V notch weirs, but only over a given (normal) range of flow for the weir.
User Guide
32
TecQuipment Ltd
H6 Flow Over a Notch
Maintenance, Spare Parts and Customer Care
Maintenance
Regularly check all parts of the apparatus for damage, renew if necessary.
When not in use, store the apparatus in a dry, dust-free area, covered with a plastic sheet. If the
apparatus becomes dirty, wipe the surfaces with a damp, clean cloth. Do not use abrasive cleaners.
Regularly check all fixings and fastenings for tightness, adjust where necessary.
NOTE
Renew faulty or damaged parts with an equivalent item of the same type or
rating.
Spare Parts
Check the Packing Contents List to see what spare parts we send with the apparatus.
If you need technical help or spares, please contact your local TecQuipment agent, or contact
TecQuipment direct.
When you ask for spares, please tell us:
• Your name
• The full name and address of your college, company or institution
• Your email address
• The TecQuipment product name and product reference
• The TecQuipment part number (if you know it)
• The serial number
• The year it was bought (if you know it)
Please give us as much detail as possible about the parts you need and check the details carefully before
you contact us.
If the product is out of warranty, TecQuipment will let you know the price of the spare parts.
Customer Care
We hope you like our products and manuals. If you have any questions, please contact our Customer
Care department:
Telephone: +44 115 954 0155
Fax: +44 115 973 1520
Email: customercare@tecquipment.com
For information about all TecQuipment products visit: www.tecquipment.com
TecQuipment Ltd
33
User Guide
H6 Flow Over a Notch
User Guide
34
TecQuipment Ltd