H10
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@TecQuipment Ltd 1999
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Educational
PRODUCTS
CONTENTS
J
T
r
1
INTRODUCTION
1.1
2
DESCRIPTION OF THE APPARATUS
Installation
Preparation
Routine Care and Maintenance
2-1
3
THEORY
3-1
4
EXPERIMENTAL PROCEDURE
4-1
5
RESULTS AND CALCULATIONS
Calculations of Discharge
Venturi Meter
Orifice Meter
Rotameter
5-1
5-1
5-1
5-1
5-2
5-3
5-3
5-3
5-3
5-4
5-4
5-4
5-5
Calculations of Head Loss
Venturi Meter
Orifice Meter
Rotameter
Wide-Angled Diffuser
Right-Angled Bend
Discussion of Meter Characteristics
Conclusion
r
2-1
2-2
2-2
SECTION 1 INTRODUCTION
I
Figure 1.1 TecQuipment flow measurement apparatus
The TecQuipment
010
l'1ow Measurement
apparatus is designed to familiarise students with the
typical methods of measuring the discharge of an
essentially incompressible fluid,
whilst
giving
applications of the Steady-Aow Energy Equation and
Bernoulli's Equation. The discharge is determined
using a venturi meter, an orifice plate meter and a
rotameter. Head losses associated with each meter are
detennined and compared as well as those arising in a
rapid enlargement and a 90° elbow.
The unit is designed for use with the TecQuipment
HI or HID Hydraulic Bench, which provides the
necessary liquid service and evaluation of flow rate.
SECTION 2 DESCRIPTION OF APPARATUS
Rotameter
outlet tube
/
The apparatusis shown in Figure 2.1. Water from the
Hydraulic Benchentersthe equipmentthrough a venturi
meter, which consists of a gradually-converging
section, followed by a throat. and a long graduallydiverging section. After a change in cross-section
through a rapidly diverging section.the flow continues
along a settling length and through an orifice plate
meter. This is manufactured in accordance with
BSI042. from a plate with a hole of reduceddiameter
through which the fluid flows.
TecQuipmentFlow Measurement
Following a further settling length and a right-angled
bend, the flow enters the rotameter. This consistsof a
transparenttube in which a float takesup an equilibrium
position. The position of this float is a measureof the
flow rate.
After the rotameter the water returns via a control
valve to the Hydraulic Bench, where the flow rate can
be evaluated.The equipmenthas nine pressuretappings
(A to I) as detailed in Figure 2.2, each of which is
connectedto its own manometerfor immediatereadout.
Installation
SeaI~
clip
R~meter
outlet tube
direct its free end into the bench measuringdevice.
Before continuing, refer to the hydraulic bench
manualto find the methodof flow evaluation.
2. With the air purge-valve closed, close the main
valve fully then open it by approximately 1/3.
Switch on the bench and slowly open the bench
valve until water startsto flow. Allow the HIO to fill
with water then openthe benchvalve fully, and then
close the main HIO valve. Couple the handpump to
the purge valve and pump down until alr the
manometersread approximately 330 mm. Dislodge
any entrappedair from the manometersby gentle
tappingwith the fingers. Check that the water levels
are constant.A steadyrise in levels will be seenif
the purgevalve is leaking.
3. Check that the tube ferrulesand the top manifold are
free from water blockage, which will suppressthe
manometerlevel. Ferrules blockage can be cleared
by a sharpburst of pressurefrom the hand pump.
Routine Care and Maintenance
Manometer
tapping tube
Do not allow water to stand in the apparatusfor long
periods. After use fully drain the apparatusand dry
externallywith a lint-free cloth.
The control valve is a commercial gate valve. the
internal detailsof which are shown in Figure 2.4. Slight
gland leakagecan be rectified as follows:
s..Ig
'-,
---"
,
:, ~
I. Remove the handwheel retaining nut and the
handwheel.
2. Slacken the nut and remove. The gland packing
ferrule will now be exposed.The headof the ferrule
should be about 2 mm clear of the thread. If this is
not the case, the leak may be rectified by refitting
and tightening nut.
Figure 2.3 Rotameter connection diagram
Figure 2.3 showsthe layout of the rotameterassembly.
To fit the rotameter and float, push one of the short
piecesof hoseover the elbow outlet and drop over two
hose clips. Push the rotameterinto the hose, and then
carefully drop the float into the rotameter.Pusha short
piece of hose over the top of the rotameter and drop
over two hoseclips. Then pushthe outlet pipe assembly
into the top of this hose. Tighten all four pipe clips
ensuringthat the hoseis securedto the elbow, rotameter
and outlet tube. Finally attach the clear outlet tube,
securing with the pipe clip, and manometer tapping
tube,securingwith a cabletie.
Preparation
Connectthe supplyhosefrom the hydraulic benchto
the inlet of the venturi meter and securewith a hose
clip. Connecta hose to the control valve outlet and
If the ferrule is flush with the thread,then the gland
requiresrepacking.To do this:
TecQuipment Flow Measurement
1. Remove the existing packingand repackwith either
replacementnylon '0' rings or asbestoscord.
2. Refit the gland ferrule and nut, ensuring that the
gland ferrule has sufficient clearanceto tighten the
packing when the nut is refitted.
If the plastic manometertubes becomediscoloured a
stain and deposit remover is availablefor usewithin the
benchsupply.
~
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SECTION 3 THEORY
~
The head loss MI2 may be assumedto arise as a
consequenceof vorticity in the stream. Becausethe
flow is viscousa wall shearstressexists and a pressure
force must be applied to overcomeit. The consequent
increasein flow work appearsas an increasein internal
energy, and becausethe flow is viscous, the velocity
profile at any sectionis non-uniform.
The kinetic energy per unit massat any section is
then greater than y2/2g and Bernoulli's Equation
incorrectly assessesthis term. The fluid mechanics
entailed in all but the very simplest internal flow
problemsare too complex to permit the headloss M to
be determinedby any other meansthan experimental.
Sincea contractionof streamboundariescan be shown
(with incompressiblefluids) to increaseflow uniformity
and a divergencecorrespondinglydecreasesit, M is
typically negligibly small between the ends of a
contracting duct but is normally significant when the
duct walls diverge.
Figure 3. 1 The steady-flow energy equation
(3-1)
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SECTION 4 EXPERIMENTAL PROCEDURE
When the equipment has been set up as in Section 2,
measurementscan be takenin the following manner:
Open the apparatusvalve until the rotametershows
a reading of approximately 10 mrn. When a steady
flow is maintained measure the flow with the
Hydraulic Bench as outlined in its manual. During
r
Test number
1
1:
:Manometric
levels
..
D
~
G
"
Rotameter
Water, W
Time, T
Mass flow rate
in (kg/S)
(cm)
(kg)
(..~)
Venturi (8)
Orifice (11)
Rotameter
Wel~ tank
Venturi (13)
DH/ Inlet
kinetic head
Or~
(14)
Rotameter
O~ser
(16)
Elbow J:!!)J
Table 4.1 Form of results
2
3
this period.recordthe readingsof the manometersin
Table 4.1.
2. Repeatthis procedurefor a number of equidistant
valuesof rotameterreadingsup to the point in which
the maximumpressuresvaluescan be recordedfrom
the manometer.
4
5
6
7
8
9
10
SECTION 5 RESULTS AND CALCULATIONS
Calculations of Discharge
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r
The venturi meter, the orifice plate meter and the
rotameterare all dependentupon Bernoulli's Equation
for their principle of operation. The following have
been preparedfrom a typical set of results to show the
form of the calculations.
Venturi Meter
Since LlHI2 is negligibly small betweenthe ends of a
contracting duct it, along with the Z tenns, can be
omitted from Equation (3-1) betweenstations (A) and
(B).
Orifice Meter
Between tappings (E) and (F) ~12 in Equation (3-1) is
by no means negligible. Rewriting the equation with the
appropriate symbols:
-2
-2
VF
VE-I
~-2";l'
h..-PL
pg pg,
(5-4)
such that the effect of the head loss is to make the
difference in manometricheight (hE - hF) less than it
would otherwisebe. An alternativeexpressionis:
From continuity:
(5-5)
pVAAA = pVsAB
(5-1)
The discharge,
2g
Q = AsVB = ~
P..6.._fi
-=(AB / AJ2
pg
pg
where the coefficient of discharge K is given by
previous experience in B51042 (1943)1 for the
particular geometry of the orifice meter. For the
apparatusprovidedK is given as 0.601.
Reducingthe expressionin exactly the sameway as
for the venturi meter,
(5-2)
r
Q = AF~ = kAc
With the apparatusprovided, the bores of the meter at
(A) and (B) are26 rom and 16 rom respectively,so:
~A
= 0.38 andAB =
(5-6)
2.01 x 10-4 m2
With the apparatusprovided, the bore at (E) is 51.9 mrn
and at (F) is 20 mrn, then:
AA
Since g = 9.81 m/s2 and
are the respective
.&.,fi
pg
=
Q
pg
heightsof the manometrictubesA and B in metres,we
havefrom Equation(5-2):
Q
9.62X IO-4(hA- hsf2
r
o.962(hA -
hs)l/2 kgjs
hF=40mrn
then
=
0.58
and
hB = IIOmrn
m
then
=
kg/S
hE=372 mrn
(hE- ~f2
hA = 375 mrn
m3/s
For exampleif
For exampleif
(hA - he)1/2
8.46X lO-4(~ - hFf2
m = O.846(~- hp)1/2
Taking the density of water as 1<XX>
kg/m3, the mass
flow will be:
=
=
Thus
m3/s
(5-3)
ni
;
t:<'A;'i"A;Y.
2g
0.51
= 0.846x 0.58 = 0.49 kg/s
(The correspondingHydraulic Flow Bench assessment
was0.48 kg/s.)
and
ni
=
0.962x 0.51 = 0.49kg/s
(The correspondingHydraulic Flow Bench assessment
was0.48 kg/s).
t
The value of C is given in the 1943 BS1042publication. Figures
given in later editions may vary.
TecQuipment Flow Measurement
Rotameter
Observationof the recordings for the pressure drop
acrossthe rotameter(H) - (I) showsthat this difference
is largeand virtually independentof discharge.There is
a term which arisesbecauseof wall shearstressesand
which is therefore velocity dependent,but since the
rotameteris of largebore this term is small. Most of the
observedpressuredifferenceis required to maintain the
float in equilibrium and since the float is of constant
weight. this pressure difference is independent of
discharge.
The causeof this pressuredifferenceis the headloss
associatedwith the high velocity of water around the
float periphery.Sincethis headloss is constantthen the
peripheralvelocity is constant.To maintain a constant
velocity with varying dischargerate, the cross-sectional
areathrough which this high velocity occursmust vary.
This variation of cross-sectionalarea will arise as the
float movesup and down the taperedrotametertube.
From Figure 5.1, if the float radius is Rf and the
local bore of the rotametertube is 2Rtthen:
Jt(Rt" R;
art
Discharge
Constantperipheralvelocity
.,
=
= 2xRlS = Cross-sectional
~,-~
Now 0 = Ie. where I is the distancefrom datum to the
cross-sectionat which the local bore is Rt and e is the
semi-angleof tube taper. Hence I is proportional to
discharge. An approximately linear calibration
characteristicwould be anticipatedfor the rotameter.
Figure 5. 1 Principle of the rotameter
Figure 5.2 Typical rotameter calibration curve
TecQulDmentFlow Measurement
~
Calculations of Head Loss
By referenceto Equation (3-1) the headloss associated
with eachmetercan be evaluated.
Venturi Meter
Applying the equation betweenpressuretappings (A)
and (C).
pg
i.e.
hA
Therefore:
- hc = L\HAC
AHEF
This can be made dimensionlessby dividing it by the
-2
inlet kinetic head ~.
2g
Now,
v.~.
n7:
2g
~~
Orifice Meter
Applying Equation (3-1) between (E) and (F) by
substitutingkinetic and hydrostaticheadswould give an
elevated value to the head loss for the meter. This is
becauseat an obstructionsuchas an orifice plate, there
is a small increasein pressureon the pipe wall due to
part of the impact pressureon the plate being conveyed
to the pipe wall. BS1042 (Section 1.1 1981) gives an
approximateexpressionfor finding the head loss and
generally this can be taken as 0.83 times the measured
headdifference.
(l:A.-.rk.
kJ.'\~"'+
'
= 0.83 (hE -
hF) mm
=0.83 (372 - 40) mm = 275 mm
The orifice plate diameter (51.9 mm) is approximately
twice the venturi inlet diameter(26 mm), thereforethe
orifice inlet kinetic head is approximately 1/16 that of
the venturi, thus:
r
'
44.26 = 276
16
1-(As/AA)2 Ptf1awP8
and
Therefore.
-2
VA
= VB (AB/A~ )2
Head loss = ifs
-2
= 99.6 inlet kinetic
276
thus
Rotameter
With the apparatusprovided (Ao/AA)
(
=0.38. therefore
the inlet kinetic headis:
'\72
~
?
(r-g
.
= 0.144 x 116 EA._.&.
pg
pg.
= O.167(hA-~)
For exampleif:
hA = 375 rom
hB = 110rom
hc = 350 mm
then:
AHAC = hA-hc = 25 mm
-2
VA
:f'd1'67(~A -hB)
= 0.167)(26-'
2g
= 44.26mm
Therefore,
Headloss = ~ 2S
= 0.565inlet kinetic heads
Figure 5.3 Rotameter head loss
heads
TecQuipment Flow Measurement
For this meter, applicationof Equation(3-1) gives:
.!!l+zJ)
f&~
P8 t:i!I)
=
Right-Angled Bend
The inlet to the bend is at (G) where the pipe bore is
51.9 mIn and outlet is at (H) where the bore is 40 mIn.
Applying Equation(3-1):
AHHI
pg
-2
Then as illustrated in Figure 5.3:
"ti:"2
.P.Q.+-Y9--=.P1i.+-1L+L\HGH
pg
hH - hI = AHHI
Inspection of the table of experimentalresults shows
that this head loss is virtually independentof discharge
and has a constant value of approximately100rom of
water. As has already been shown, this is a
characteristic property of the rotameter. For
comparativepurposesit could be expressedin terms of
the inlet kinetic head. However, when the velocity is
very low the head loss remains the same and so
becomesmany, many times the kinetic head.
It is instructive to compare the head losses
associatedwith the three meters with those associated
with the rapidly diverging section, or wide-angled
diffuser, and with the right-angled bend or elbow. The
sameprocedureis adoptedto evaluatetheselosses.
Wide-Angled Diffuser
The inlet to the diffuser may be consideredto be at (C)
and the outlet at (D). Applying Equation(3-1):
-2
Sincethe arearatio, inlet to outlet, of the diffuser is 1:4,
the outlet kinetic headis 1/16of the inlet kinetic head.
For exampleif:
hA = 375 rnm
hB= Il0rnm
hc = 350 rnm
hD = 360 rnm
then
Inlet kinetic head = 44.26mrn
44.26 - 28 mm
-16
and
Mm
= (350-360)+(44.26-28)
= 3 L46 mm of water
Therefore,
Headloss is
i~L46
4275
= 0.71 inlet kinetic heads
pg
The
2$". :J
The outlet kinetic headis now 2.8 timesthe inlet kinetic
head.For exampleif:
hA =
hB =
hG =
hH =
375 mm
110 mm
98 mm
88mm
and
Inlet kinetic head = 2.76 mrn
Outlet kinetic head = 7.73 mrn
then
MlGH
= (98-88) + (21'f!'it73)
= 5.03mID of water
Therefore,
Headloss = 103
276
-2
E£.+~=.E!2.+.YP.-+AHCD
pg
2g
pg
2g
(See venturi meter head loss calculations).
correspondingoutlet kinetic headis:
2g
= 182inlet kinetic heads
Discussion of the Meter Characteristics
There is little to choose in the accuracyof discharge
measurementbetween the venturi meter, the orifice
meter and the rotameter- all are dependentupon the
sameprinciple. Dischargecoefficientsand the rotameter
calibration are largely dependenton the way the streain
from a 'vena contracta'or actualthroat of smallercrosssectional area than that of the containing tube. This
effect is negligibly small where a controlled contraction
takes place in a venturi meter but is significant in the
orifice meter. The orifice meter dischargecoefficient is
also dependenton the precise location of the pressure
tappings (E) and (F). Such data is given in BSI042
which also emphasisesthe dependenceof the meters
behaviour on the uniformity of the flow upstreamand
downstreamof the meter.
In order to keep the apparatus as compact as
possible the dimensions of the equipment in the
neighbourhoodof the orifice meter have been reduced
to their limit, consequently some inaccuracy in the
assumedvalue of its dischargemay be anticipated.
The considerabledifference in head loss between
the orifice meter and the venturi meter should be noted.
The orifice meter is much simpler to make and use, for
it is comparatively easy to manufacture a suitable
orifice plate and insert it between two existing pipe
flanges which have been appropriatelypressure-tapped
for the purpose. In contrast the venturi meter is large,
comparatively difficult to manufactureand complicated
to fit into an existing flow system.But the low headloss
TecQuiomentFlow Measurement
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associatedwith the controlled expansionoccurring in
the venturi meter gives it an obvious superiority in
applicationswhere power to overcomeflow lossesmay
be limiting.
Rotametersand other flow measuringinstruments
which dependon the displacementof floats in tapered
tubes may be selected from a very wide range of
specifications.They are unlikely to be comparablewith
the venturi meter from the standpointof head loss but,
provided the dischargerangeis not extreme,the easeof
reading the instrument may well compensatefor the
somewhathigher headloss associatedwith it.
The head losses associatedwith the wide-angled
diffuser and the right-angled bend are not untypical.
Both could be reducedif it were desirableto do so. The
diffuser head loss would be minimised if the total
expansion angle of about 50 degreeswere reduced to
about 10 degrees.The right-angledbend loss would be
substantially reduced if the channel, through which
water flows, was shapedin the arc of a circle having a
large radius compared with the bore of the tube
containingthe fluid.
Large lossesin internal flow systemsare associated
with uncontrollableexpansionof the stream.Attention
should always be paid to increasesin cross-sectional
area and changesof direction of the stream as these
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parts of the system are most responsive,in tenns of
associatedheadloss, to small improvementin design.
Discussion of Results
If the massflow results are plotted against massflow
ratesfrom the weighing tank methodthe accuracyof the
variousmethodscan be compared.Since all arederived
from Equation (1) similar results would be expected
from the three methods. The differential mass flow
measurement(mmeter
- mweightank)could be plotted
againstthe weighing tank massflow resultsfor a better
appraisalof accuracy.
Some overestimation in the venturi meter
termination can be anticipated because its vena
contracta has been assumedto be negligibly small.
Similarly, the rotameter determination may well be
sensitive to the proximity of the elbow and the
associatedinlet velocity distribution. The orifice meter
is likely to be sensitive to the inlet flow which is
associatedwith the separationinducedin the wide-angle
diffuser upstreamof it. Thus both the rotameterand the
orifice metercalibrationswould be likely to changeif a
longer length of straight pipe were introducedupstream
of them.
Inlet kinetic head: scale B
.
(J
~
ii
~
0(
"'i
~
.
-c
.
."c"
:
~
u
~
.
c
~
~
.c
~
=
~
~
~
'"
:E
i
:5
r
Inlet kinetic head: scale D (mm)
Figure 5.4 Typical head loss graph
TecQulpment Flow Measurement
In the calculationsthe head lossesassociatedwith the
various meters and flow componentshave been made
dimensionless by dividing by the appropriate inlet
kinetic heads.The advantageof the venturi meter over
the orifice meterand rotameteris evident althoughover
a considerablerange of inlet kinetic heads the loss
associatedwith the rotameter is sufficiently small to
considerthat it would be more thancompensatedby the
relative ease in evaluation of mass flow from this
instrument.
It should also be noted from Figure 5.1 that the
dimensionlesshead lossesof the venturi meter and the
orifice meter are Reynolds number dependent.This
effect is also noticeable with the dimensionlesshead
loss of the elbow.
Conclusions
The most direct measurementof fluid dischargeis by
the weightank principle. In installations where this is
impracticable(e.g. on account of size of installation or
gaseousfluid flow), one of the three dischargemeters
describedmay be usedinstead.
The venturi meteroffers the bestcontrol to the fluid.
Its dischargecoefficient is little different from unity and
the head loss it offers is minimal. But it is relatively
expensive to manufacture and could be difficult to
install in existingpipework.
The orifice meter is easiest to install between
existing pipe flanges and provided it is manufactured
and erected in accordancewith BS1042, will give
accuratemeasurement.
The head loss associatedwith it
is very largecomparedwith that of the venturi meter.
The rotameter gives the easiest derivation of
discharge,dependentonly on sighting the float and
reading a calibration curve. It needs to be chosen
judiciously, however,so that the associatedheadloss is
not excessive.