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Executive Summary
Use this space to complete the executive summary, or abstract, for the piece of work
you have conducted.
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A summary of the essential aspects of the report.
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Abstracts are hard to write.
ii
Contents
Executive Summary ....................................................................................................ii
Nomenclature .............................................................................................................iv
1
Introduction ......................................................................................................... 1
2
Background Theory ............................................................................................. 5
3
4
2.1
Conservation of Mass ................................................................................... 5
2.2
Conservation of Energy ................................................................................. 6
2.3
Flow measurement ........................................................................................ 6
2.4
Coefficient of discharge ................................................................................. 7
Experimental Procedure ...................................................................................... 8
3.1
Equipment ..................................................................................................... 8
3.2
Procedure...................................................................................................... 9
3.3
Your reflection ............................................................................................. 11
3.4
Procedure Mark Scheme ............................................................................ 11
Results .............................................................................................................. 12
4.1
Your reflection ............................................................................................. 12
4.2
Results Mark Scheme ................................................................................. 12
5
Discussion ......................................................................................................... 13
6
Conclusions ...................................................................................................... 13
6.1
Your reflection ............................................................................................. 14
6.2
Discussion Mark Scheme ............................................................................ 14
7
Further Work ..................................................................................................... 14
8
References ........................................................................................................ 15
iii
Nomenclature
Area of the pipe
Area of the constriction
Discharge Coefficient
Diameter of the pipe
Diameter of the constriction
Mass
Mass flow rate
Pressure
Average velocity
Time
Ratio of diameters
Density
iv
1 Introduction
The aim of the investigation is to experimentally determine the coefficient of
discharge of a specific Venturi meter and compare the result to previously obtained
empirical results.
A Venturi meter is an invasive, full bore flow measurement device that employs a
combination of the conservation of mass and energy to determine the flowrate of
internal flows in within pipes. The device was invented by Clemens Herschel in 1819
and is named in honour of Italian physicist Giovanni Venturi (1746-1822). The
principle design consists of a Venturi meter is to introduce a constriction into a pipe
and measure the drop in pressure of fluid in the pipe of original diameter and that in
the constriction, as shown in figure 5.1, where A1represents the area of the original
pipe and A2 represents the area of the constriction, known as the "throat".
Figure 1.1 The control volume used in the conservation analysis of the Venturi meter
The pressure difference measurement in figure 1.1 is illustrated using a U tube
manometer, where the difference in height difference, h, in the manometer fluid can
be measured and converted into a pressure difference using Pascal's Law. Other
pressure measuring devices, such as digital pressure gauges or piezometers, can
also be used to recorder the pressure difference in the fluid in the pipe and the
constriction.
Venturi meters are used in a wide variety of industrial engineering applications over
a range of size scales. One such installation of is shown in figure 1.2. Advantages
over other flow meters, for example an orifice plate, include their robust operation
1
due to simple design and lack of moving parts, and, once installed, they do not
require interruption of the flow to measure the flow rate.
Figure 1.2 Industrial Venturi meter with digital readout [1]
If the gradient of the contracting (nozzle) and diverging (diffuser) section of the
Venturi meter is shallow, the pressure loss due to friction is minimal and the
relationship between measure pressure drop and flow rate can be determined using
analytical means. Regardless of the design of a Venturi meter, friction will reduce
recoverable pressure within the fluid and create a discrepancy between the
theoretical and actual flow rate recorded. This discrepancy is characterised by the
quantity referred to as the coefficient of discharge, , which can only be determined
though empirical means. In the theoretical idealized example of no friction existing
and all pressure being recoverable, the coefficient of discharge for a flow meter
would be unity. The coefficient of discharge of Venturi meters is typically higher than
other full bore flow measurement devices, resulting in less running cost from
pumping systems required to overcome the non-recoverable pressure loss. However,
the capital cost of Venturi meters is typically higher than simpler flower measurement
devices.
The original Herschel Venturi meter, as illustrated in figure 1.3,consisted of a
21oconical contraction,constant diameter throat of length equal to diameter and a
conical expansion of 7 to 15o. The coefficient of discharge of the Herschel Venturi
meter varies is independent of the ratio of throat to pipe diameter ( ), but varies with
Reynolds number, as shown in figure 1.4.
2
Figure 1.3 Herschel Venturi meter
Figure 1.4Variation of coefficient of discharge with Reynolds for Herschel type
Venturi meters (In this image, Red and ReD refer to the Reynolds number in the
throat and pipe, respectively) [2]
The modern standard for measurement of fluid flow by means of orifice plates,
nozzles, and Venturi meters is given byISO 5167-3 2003 [3]. These standards
dictate a Venturi meter should contain an ISA 1932 nozzle entrance and conical
expansion of no more than 15o, as illustrated in figure 1.5. When operated within a
Reynolds number range of between 1.5×105 and 2×106, based on the pipe rather
than throat diameter, the coefficient of discharge for the Venturi meter should be
given by equation 2.0.1.
3
(1.0.1)
The empirical correlation in equation 1.0.1 is valid for value of
0.775 and is independent of Reynolds number.
between 0.316 and
Figure 1.5 International standard (ISO 5167-3 3003) shapes for Venturi meter [3]
4
2 Background Theory
The physical principles underlying the operation of a Venturi meter are those of the
conservation of mass, also referred to as the continuity, and the conservation of
energy though the Bernoulli equation. When analysing conservation in engineering
systems a theoretical boundary in physical space, referred to as a control volume, is
utilised to balance the flows of the conserved property. The control volume use in the
conservation analysis of the Venturi meter is illustrated in figure 2.1.
Figure 2.1The control volume used in the conservation analysis of the Venturi meter
2.1
Conservation of Mass
Conservation of mass dictates that, with the exception of the existence of nuclear
reactions, the difference between the mass entering a control volume and the mass
leaving a control volume must equal the accumulation of mass within the control
volume. This relationship, in rate quantities, is given in equation 2.1.1,
(2.1.1)
where subscript and
represent the quantity into and out of the control volume,
respectively. It is assumed that, as the flow is incompressible and running for a
significant period of time that the operation of the Venturi meter will be steady state
and the transient term in equation 2.1.1 ( ) will become zero, leading to the mass
flow rate out being equal to the mass flow rate in.
The velocity of the fluid within the pipe will vary across the cross section due to the
no slip boundary condition at the wall. However, for the purposes of analysis, an
5
average velocity, , can be defined based on the mass flow rate using the
relationship shown in equation 2.1.2.
(2.1.2)
In steady state the mass flow rate into and out of the control volume shown in figure
2.1 must be equal and for incompressible flow the density will remain constant,
giving rise to equation 2.1.3.
(2.1.3)
The physical manifestation of continuity equation 2.1.3 is that the fluid must
accelerate as the area of the pipe decrease.
2.2
Conservation of Energy
The conservation of energy, also referred to as the first law of thermodynamics,
dictates that the difference between the energy entering a control volume and the
energy leaving a control volume must equal the accumulation of energy within the
control volume, as energy can neither be created nor destroyed. Under the same
assumption that the Venturi meter is operating in steady state, the energy that is
transported by the fluid into the control volume must also leave the control volume.
Bernoulli's equation describes the conservation of energy within a fluid stream and
assumes that all the energy is accounted for by a combination of static ( ) and
dynamic (
) pressure, and that there is no change in the fluid's internal energy,
no change in elevation and no energy is lost due to friction. If it is assumed that all
the energy that leaves the control volume is transported out by the fluid leaving the
control volume, Bernoulli's equation can be applied to the control volume in figure 6.1
as shown in equation 2.2.1.
(2.2.1)
2.3
Flow measurement
Substituting equation 2.1.3 into 2.2.1 and rearranging yieldthe result shown in
equation 2.3.1
(2.3.1)
Rearranging equation 2.3.1 and substituting in equation 2.1.3 produces a
relationship for the mass flow rate though the control volume based on the pressure
drop between the inlet and outlet, as shown in equation 2.3.2,
6
(2.3.2)
where is the ratio of outlet and inlet pipe diameters. Therefore by measuring the
pressure drop across any section of a converging or diverging section of a Venturi
meter where the area is known, the theoretical mass flow rate can be determined,
under the following assumptions
1. The Venturi meter is operating in steady state
2. There is no change in elevation
3. There is no change in temperature of the fluid and hence no change in
internal energy
4. The fluid is incompressible
5. There is no recoverable pressure loss due to friction.
2.4
Coefficient of discharge
The theoretical relationship between mass flow rate and pressure drop across a
control volume of a Ventrui meter will not be achieved in practices due to the
presence of friction. In order to account for this discrepancy, the coefficient of
discharge, , is defined for Venturi meters using equation 2.4.1,
(2.4.1)
where the subscript
is the predicted mass flow rate determined by
analytical means, though measurement of the pressure drop,
, and
applying it toequation 2.3.2.The subscript
is the actual mass flow rate passing
though the control volume of the Venturi meter, which can be measure directly.
Coefficients of discharge can only be established though experimental methods. An
empirical relationship for Herschel type Venturi meters is given in figure 1.4 and for
an ISO 5167-3 standard [3] Venturi meter in equation 1.0.1.
7
3 Experimental Procedure
3.1
Equipment

Venturimeter fitted across a pipeline leading to a collecting tank

Stop Watch

U-Tube
manometer
connected
across
8
entry
and
throat
sections
3.2
Procedure
Close the valve on the outlet side of the venturi, then switch the pump on, making
sure that the valve on the inlet side of the venturi is fully open. Slowly open the outlet
side valve until the air is cleared from the connecting pipes and tubes. Then reclose
the outlet side valve. This may have already been done.
As the pressure level observed from the manometer tubes can be seen to be lower
when the outlet valve is open, i.e. water is flowing, then we have to adjust the static
pressure such that we can get maximum use from the manometer range.
With the outlet side valve closed, very carefully release air pressure from the
manometer system by means of pressing in the valve located on the top RHS of the
arrangement. By means of this valve adjust the static level in the manometer tubes
until it is 90% of full scale (reading about 21-22cm). Again this will probably have
been done. Note the levels in the individual tubes in the chart given with this
instruction sheet.
Now, open the outlet side valve and adjust the flow so that the lowest pressure in the
manometer tubes is as near to zero as you can obtain (without going lower than
zero). Note all the manometer readings on the chart provided.
Next measure the actual mass flow rate of water. Close the drain on the weighing
tank underneath the apparatus by turning the handle on the front. Water will now
start to fill the tank until it causes the balance to tip. At this instance start timing with
the stop watch provided and place on the end of the balance arm a weight
representing 15Kg (or weights) which will tip the balance back. As the tank fills up
further the balance will again tip over. At this instance stop the watch and note down
the time. The actual mass flow rate is this weight divided by the time recorded.
Record this value on the sheet provided.
Repeat for 2 other lower mass flow rates, one of which should be when the pressure
difference between the inlet and throat is approximately 2cm.
Calculate the theoretical mass flow rate for the three sets of measurements and
determine the value of C_D.
9
OR
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







Note the pipe diameter (d1) and throat diameter (d2) of Venturimeter.
Note the density of manometric liquid i.e. mercury (ρm) and that of fluid
flowing through pipeline i.e. water (ρw ).
Check all the clamps for tightness.
Check whether the water level in the tank is sufficient such that the suction
pipe of pump is completely immersed.
For measurement through venturi, open the outlet valve of the venturi meter
and
For a good amount of variation in discharge also close the by-pass valve of
pump.
Now switch on the pump.
Open the gate valve and start the flow.
If any air bubbles exist in U-tube manometer remove them through air cock
valve.
Operate the air cock valve slowly and cautiously to avoid mercury run away
through water.
Wait for a while for stabilization of flow.
Close the gate valve of measuring tank and measure the time for discharge of
five liters of water and the manometer difference. Before taking any
measurements, make sure the flow is stable.
Repeat the procedure by changing the discharge by slowly opening the bypass valve and take the five readings.
Determine the coefficient of discharge (Cd) for each flow rate and find the
mean value of coefficient of discharge (Cd) mean.
SAFETY NOTES
1. Safety Glasses with side shields shall be worn during the running of this
experiment.
2.Tap water is used in this experiment. As stated, it is possible for hoses or
tubing to pop off and spray water.
3. Be careful of the outlet hose position and the position of the bench and flow
control valves when starting the pump. It is easy for the outlet hose to spray
water. It is also possible to blow off the pressure tap hoses and spray water all
over.
10
3.3
Your reflection
The images for each equipment was provided so that all the equipments may be
easily identified. Further the procedure was written carefully and in detail so that
anyone would be able to replicate the process.
Marks: 14/20
3.4
Procedure Mark Scheme
20-14
14-12
12-10
10-8
8-0
Procedure is written in
prose and contains
enough information to
be repeatable by
anybody else at a later
date, without including
superfluous
information. Use of
images enhances the
readers understanding
of the experiment.
Equipment is fully
described (such as
including model
numbers) and the
precision and/or
accuracy is
detailed.Reflection is
mature and professional,
illustrating both
strengths and weakness.
The procedure is
written in prose and
contains enough
information to make
the experiment
repeatable by a
anybody else at a later
date. Images have
been included to aid
understanding of the
procedure adopted.
Equipment is well
described (such as
including model
numbers).
The procedure is
written in prose, but
misses information to
fully describe the
procedure undertaken
during the laboratory.
Images are not
included or are not
sufficiently labelled or
discussed to make
them helpful for the
reader. Equipment
used during the
experiment is listed.
Procedure consists of
bullet points with of
tasks that were
completed. Information
is missing that would
prevent a reader from
being able to repeat
the experiment. The
equipment used is not
listed.
None or very little
procedure given.
Procedure may be
written in such a way
that it makes it
impossible for the
reader to understand
what happened during
the experiment. The
equipment used is not
listed.
Appropriate mark
awarded and reasonable
supporting comments
given.
Reflection contains
unjustified mark and
some relevant
comments.
11
Reflection consists only
of an unjustified mark.
No reflection has taken
place
4 Results
Table 1: Observations
m (Kg)
Time
(sec)
mass flow
rate 𝑚̇
(Kg/sec)
𝑃1
𝑃4
𝑃11
Pressure
Loss
100(𝑃1 − 𝑃11 )
𝑃1
(%)
15
15
15
15
15
35
53
65
115
45
0.429
0.283
0.231
0.130
0.333
0.245
0.216
0.216
0.250
0.089
0.004
0.122
0.155
0.230
0.089
0.201
0.200
0.205
0.246
0.197
17.95
7.47
5.09
1.60
10.45
Table 2: Calculations
4.1
m (Kg)
Time
(sec)
mass flow
rate 𝑚̇
(Kg/sec)
K2
∆p
Theoretical
Mass Flow
Rate
(Kg/sec)
Cd
15
15
15
15
15
35
53
65
115
45
0.429
0.283
0.231
0.130
0.333
0.143
0.143
0.143
0.143
0.143
2364
922
598
196
1285
0.47
0.30
0.24
0.14
0.35
0.907
0.959
0.971
0.958
0.957
Your reflection
The results are as expected for the experiment. The coefficient of discharge values
are in line with expected values for a Venturi meter.
Marks Obtained: 16/20
4.2
Results Mark Scheme
20-14
14-12
12-10
10-8
8-0
Data presented in
alogical manner
usingthe most
appropriate methods.
Data ispresented in a
stylethat clearly
displaysthe points
beingreferred to in the
text.
Any raw or superfluous
Data is presented in a
suitable manner. It may
be displayed so it cannot
be compared to other
results or so trends
cannot be seen.
Discussion of results is
presented but displays
limited understanding of
the experiment.
The method of data
presentation is not
appropriate. Raw data
may not be processed or
not properly processed
or there is limited
discussion of how raw
data has been converted
into experimental
results.
Raw data is presented
without processing or
calculations being
shown. Very little
discussion of results or
the discussion of results
is limited to basic
description with little
context.
Little or no data has
been presented. The data
presented may consist of
a table of raw data or a
graph that is not
discussed. No points are
raised in the text to
illustrate why data is
displayed.
12
data in appendix.
Reflection is mature and
professional, illustrating
both strengths and
weakness.
Appropriate mark
awarded and reasonable
supporting comments
given.
Reflection contains
unjustified mark and
some relevant
comments.
Reflection consists only
of an unjustified mark.
No reflection has taken
place
5 Discussion
In the calculation table, the Cd for was calculated for each time the experiment was
repeated. The average value from the 5 readings give the coefficient of discharge as
0.950. The expected value of coefficient of discharge for an venturi meter is between
0.95 - 0.98.
There were sources of error in this experiment. One source of error was due to the
measurement of the head loss, Δh, from the manometer board. Due to nonsteady
flow in the testing apparatus, the air over water manometer did not give a steady
reading. Inorder to compensate for this discrepancy, the lowest value the fluctuating
fluid took wasthe recorded value. Another source of error was present due to the
neglecting of frictionin the theoretical flow rate calculation. This discrepancy explains
the difference of values plotted in Because friction was neglected, the theoretical
values of the flow rateappear to be higher than the experimental values. In reality,
the viscous forces of the fluid and the pipe cause the flow rate to be lower than the
calculated values.
6 Conclusions
The actual flow rate will be different from the theoretical flow rate due to frictional and
turbulence effects. In order to take this into account the coefficient of discharge is
introduced into the equations. The coefficient of discharge Cd is the ratio of the
actual mass flow rate to the theoretical mass flow rate.
The actual mass flow rate of water was measured by dividing the mass of the
balance by the time taken for the tank to fill before it tipped over. On the other hand
the theoretical mass flow rate was calculated using this formula
𝑚̇ = 𝐴2 √
2∆𝑝𝜌
[1− 𝜅2 ]
Thus dividing the actual mass flow rate by the theoretical value one calculated the C d.
In this experiment, the value of Cd (0.95) was along the expected value of a Venturi
meter. Hence the experiment was a success.
13
6.1
Your reflection
Marks: 25/30
6.2
Discussion Mark Scheme
Use this marking grid to assign yourself the mark you think you deserve for the
discussion and conclusion section.
30-21
21-18
18-15
15-12
12-0
Discussion displays
solid understanding of
the physics of the
experiment. Points
raised about results
relate back to the
introduction section.
Error in the experiment
have been identified and
an attempt has been
made to quantify.
Repeatability is
discussed. Conclusions
contain brief summary
of points raised in
discussion.
Discussion displays
good understanding of
the physics of the
experiment. Points
raised about results
relate back to the
introduction section.
Errors in the experiment
have been identified and
an attempt has been
made to indicate their
impact on the results.
Conclusions contain
brief summary of points
raised in discussion.
Discussion displays
some understanding of
the physics of the
experiment. The points
raised in the discussion
do not relate to the aims
and objectives set out in
the introduction. Errors
are listed and
qualitatively discussed.
Conclusions are given,
but either do not
correctly summarise
points in the discussion
or includes new
information.
Discussion displays
limited understanding of
the physics of
theexperiment. Results
are not discussed or with
little understanding or
reference to why
experiment was
conducted. Errors are
listed only, without
attempt to suggest
importance. Conclusions
are not attempted.
The discussion
illustrates that student
has no or little
understanding of the
experiment or the physic
of the system. Presented
results not discussed, or
discussion is a
reiteration of the results
presented. There is little
indication that
experimental errors have
been considered.
Reflection consists only
of an unjustified mark.
No reflection has taken
place
Reflection is mature and
professional, illustrating
both strengths and
weakness.
Appropriate mark
awarded and reasonable
supporting comments
given.
Reflection contains
unjustified mark and
some relevant
comments.
7 Further Work
You may attempt to complete this section, about what further work you would do if
you have the resources, to improve the experiment you have conducted.
14
8 References
1. Paras Engineers, Company Product Catauouge 24th January 2012.
http://52168.in.all.biz/goods_venturi-meter_383220 (last accessed 7th August 2012)
2. White, F. M., Fluid Mechanics. Sixth Edition, McGraw Hill, 2008.
3. Int. Organ. Stand. “Measurement of Fluid Flow by Means of Orifice Plates,
Nozzles, and Venturi Tubes Inserted in Circular Cross Section Conduits Running
Full,” Rep. DIS-5167, Geneva, April 1976.
15
Presentation mark scheme
Use this marking grid to assign yourself the mark you think you deserve for the
presentation of your report
20-14
14-12
12-10
10-8
8-0
Professionally
presented. All standards
in marking proforma
adhered to. Use of
English is concise,
technically correct and
precise. Clear and
consistent referencing is
used.
Document is well
presented. One or two
standards in marking
proforma not adhered to.
Use of English is
technically correct.
Clear and consistent
referencing is used.
Document is well
presented but a few
minor standards in the
marking proforma not
adhered to. The standard
of English is reasonable,
but the use of colloquial
terms or journalistic
styles is present.
Document is visually
well presented, but fails
to conform to many
standards in the marking
proforma. Poor use of
English. Sourced
material is referencing,
but style not consistent
or lacks enough detail.
Document is poorly
presented or hand
written. Many of the
important standards in
the proforma not
adhered to. Standard of
English is poor. Sourced
material is not cited.
Appropriate marking
has been awarded by
student.
Mark not appropriate for
work submitted.
Appropriate marking
has been awarded by
student.
Appropriate marking
has been awarded by
student.
Mark not appropriate for
work submitted
Laboratory Mark Breakdown
Record of work in during lab time
/10
Procedure
/20
Presentation of results
/20
Discussion and conclusions
/30
Presentation of document
/20
Total
/100
16