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~@TecQuipment Ltd 1999No part of this publication may be reproduced or transmitted inany form or by any means, electronic or mechanical, includingphotocopy, recording or any information storage and retrievalsystem without the express permission of TecQuipment limited.

All due care has been taken to ensure that the contents of thismanual are accurate and up to date. However, if any errors arediscovered please inform TecQuipment so the problem may berectified.

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EducationalPRODUCTS

CONTENTS

JINTRODUCTION1 1.1

2 2-1

2-1

2-2

2-2

DESCRIPTION OF THE APPARATUSInstallationPreparationRoutine Care and Maintenance

THEORY3 3-1

EXPERIMENTAL PROCEDURE4 4-1

5 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

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RESULTS AND CALCULATIONSCalculations of Discharge

Venturi MeterOrifice MeterRotameter

Calculations of Head LossVenturi MeterOrifice MeterRotameterWide-Angled DiffuserRight-Angled Bend

Discussion of Meter CharacteristicsConclusion

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SECTION 1 INTRODUCTION

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Figure 1.1 TecQuipment flow measurement apparatus

The TecQuipment 010 l'1ow Measurementapparatus is designed to familiarise students with thetypical methods of measuring the discharge of anessentially incompressible fluid, whilst givingapplications of the Steady-Aow Energy Equation andBernoulli's Equation. The discharge is determinedusing a venturi meter, an orifice plate meter and arotameter. Head losses associated with each meter aredetennined and compared as well as those arising in arapid enlargement and a 90° elbow.

The unit is designed for use with the TecQuipmentHI or HID Hydraulic Bench, which provides thenecessary liquid service and evaluation of flow rate.

SECTION 2 DESCRIPTION OF APPARATUS

Rotameteroutlet tube

/

through a rapidly diverging section. the flow continuesalong a settling length and through an orifice platemeter. This is manufactured in accordance withBSI042. from a plate with a hole of reduced diameterthrough which the fluid flows.

The apparatus is shown in Figure 2.1. Water from theHydraulic Bench enters the equipment through a venturimeter, which consists of a gradually-convergingsection, followed by a throat. and a long gradually-diverging section. After a change in cross-section

TecQuipment Flow Measurement

Following a further settling length and a right-angledbend, the flow enters the rotameter. This consists of atransparent tube in which a float takes up an equilibriumposition. The position of this float is a measure of theflow rate.

After the rotameter the water returns via a controlvalve to the Hydraulic Bench, where the flow rate canbe evaluated. The equipment has nine pressure tappings(A to I) as detailed in Figure 2.2, each of which isconnected to its own manometer for immediate read out.

Installation

SeaI~ clipR~meteroutlet tube

direct its free end into the bench measuring device.Before continuing, refer to the hydraulic benchmanual to find the method of flow evaluation.

2. With the air purge-valve closed, close the mainvalve fully then open it by approximately 1/3.Switch on the bench and slowly open the benchvalve until water starts to flow. Allow the HIO to fillwith water then open the bench valve fully, and thenclose the main HIO valve. Couple the hand pump tothe purge valve and pump down until alr themanometers read approximately 330 mm. Dislodgeany entrapped air from the manometers by gentletapping with the fingers. Check that the water levelsare constant. A steady rise in levels will be seen ifthe purge valve is leaking.

3. Check that the tube ferrules and the top manifold arefree from water blockage, which will suppress themanometer level. Ferrules blockage can be clearedby a sharp burst of pressure from the hand pump.

Routine Care and MaintenanceManometer

tapping tube

Do not allow water to stand in the apparatus for longperiods. After use fully drain the apparatus and dryexternally with a lint-free cloth.

The control valve is a commercial gate valve. theinternal details of which are shown in Figure 2.4. Slightgland leakage can 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 head of the ferruleshould be about 2 mm clear of the thread. If this isnot the case, the leak may be rectified by refittingand tightening nut.

Figure 2.3 Rotameter connection diagram

Figure 2.3 shows the layout of the rotameter assembly.To fit the rotameter and float, push one of the shortpieces of hose over the elbow outlet and drop over twohose clips. Push the rotameter into the hose, and thencarefully drop the float into the rotameter. Push a shortpiece of hose over the top of the rotameter and dropover two hose clips. Then push the outlet pipe assemblyinto the top of this hose. Tighten all four pipe clipsensuring that the hose is secured to the elbow, rotameterand outlet tube. Finally attach the clear outlet tube,securing with the pipe clip, and manometer tappingtube, securing with a cable tie.

Preparation

Connect the supply hose from the hydraulic bench tothe inlet of the venturi meter and secure with a hoseclip. Connect a hose to the control valve outlet and

If the ferrule is flush with the thread, then the glandrequires repacking. To do this:

TecQuipment Flow Measurement

1. Remove the existing packing and repack with eitherreplacement nylon '0' rings or asbestos cord.

2. Refit the gland ferrule and nut, ensuring that thegland ferrule has sufficient clearance to tighten thepacking when the nut is refitted.

If the plastic manometer tubes become discoloured astain and deposit remover is available for use within thebench supply.

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SECTION 3 THEORY

~ The head loss MI2 may be assumed to arise as aconsequence of vorticity in the stream. Because theflow is viscous a wall shear stress exists and a pressureforce must be applied to overcome it. The consequentincrease in flow work appears as an increase in internalenergy, and because the flow is viscous, the velocityprofile at any section is non-uniform.

The kinetic energy per unit mass at any section isthen greater than y2/2g and Bernoulli's Equationincorrectly assesses this term. The fluid mechanicsentailed in all but the very simplest internal flowproblems are too complex to permit the head loss M tobe determined by any other means than experimental.Since a contraction of stream boundaries can be shown(with incompressible fluids) to increase flow uniformityand a divergence correspondingly decreases it, M istypically negligibly small between the ends of acontracting duct but is normally significant when theduct 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,measurements can be taken in the following manner:

this period. record the readings of the manometers inTable 4.1.

2. Repeat this procedure for a number of equidistantvalues of rotameter readings up to the point in whichthe maximum pressures values can be recorded fromthe manometer.

Open the apparatus valve until the rotameter showsa reading of approximately 10 mrn. When a steadyflow is maintained measure the flow with theHydraulic Bench as outlined in its manual. During

Test number

1:

1 2 3 4 5 6 7 8 9 10r..D~: Manometric levels

G"

RotameterWater, WTime, T

(cm)(kg)(..~)Venturi (8)Orifice (11)Rotameter

Wel~ tankVenturi (13)

Or~ (14)Rotameter

O~ser (16)Elbow J:!

Mass flow rate

in (kg/S)

DH/ Inlet

kinetic head

Table 4.1 Form of results

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SECTION 5 RESULTS AND CALCULATIONS

Calculations of Discharge Orifice Meter

Between tappings (E) and (F) ~12 in Equation (3-1) isby no means negligible. Rewriting the equation with the

appropriate symbols:

-2 -2VF VE-I

~-2";l'

The venturi meter, the orifice plate meter and therotameter are all dependent upon Bernoulli's Equationfor their principle of operation. The following havebeen prepared from a typical set of results to show theform of the calculations.

rh..-PLpg pg,

(5-4)

r such that the effect of the head loss is to make thedifference in manometric height (hE - hF) less than itwould otherwise be. An alternative expression is:

Venturi MeterSince LlHI2 is negligibly small between the ends of acontracting duct it, along with the Z tenns, can beomitted from Equation (3-1) between stations (A) and(B).

From continuity:(5-5)

pVAAA = pVsABwhere the coefficient of discharge K is given byprevious experience in B51042 (1943)1 for theparticular geometry of the orifice meter. For theapparatus provided K is given as 0.60 1.

Reducing the expression in exactly the same way asfor the venturi meter,

(5-1)

The discharge,

2g P..6.._fipg pg

Q = As VB = ~-=(AB / AJ2

2g ;t:<'A;'i"A;Y.

Q = AF~ = kAc

r (5-6)

With the apparatus provided, the bore at (E) is 51.9 mrnand at (F) is 20 mrn, then:

(5-2)

With the apparatus provided, the bores of the meter at(A) and (B) are 26 rom and 16 rom respectively, so:

A -4 2~ = 0.38 andAB = 2.01 x 10 mAA

Q = 8.46 X lO-4(~ - hF f2 m3/sSince g = 9.81 m/s2 and .&.,fi are the respective

pg pgheights of the manometric tubes A and B in metres, wehave from Equation (5-2): Thus

m = O.846(~ - hp )1/2Q = 9.62 X IO-4(hA - hsf2 kg/Sm3/s

(5-3) For example if

hE = 372 mrn

hF=40mrn

Taking the density of water as 1<XX> kg/m3, the massflow will be:

ni = o.962(hA - hs)l/2 kgjs then

For example if (hE - ~f2 = 0.58r hA = 375 mrn

hB = IIOmrnand

thenm = 0.846 x 0.58 = 0.49 kg/s

(The corresponding Hydraulic Flow Bench assessmentwas 0.48 kg/s.)(hA - he)1/2 = 0.51

and

ni = 0. 962 x 0.51 = 0.49 kg/s

(The corresponding Hydraulic Flow Bench assessmentwas 0.48 kg/s).

t The value of C is given in the 1943 BS1042 publication. Figures

given in later editions may vary.

TecQuipment Flow Measurement

Rotameter Observation of the recordings for the pressure dropacross the rotameter (H) - (I) shows that this differenceis large and virtually independent of discharge. There isa term which arises because of wall shear stresses andwhich is therefore velocity dependent, but since therotameter is of large bore this term is small. Most of theobserved pressure difference is required to maintain thefloat in equilibrium and since the float is of constantweight. this pressure difference is independent ofdischarge.

The cause of this pressure difference is the head lossassociated with the high velocity of water around thefloat periphery. Since this head loss is constant then theperipheral velocity is constant. To maintain a constantvelocity with varying discharge rate, the cross-sectionalarea through which this high velocity occurs must vary.This variation of cross-sectional area will arise as thefloat moves up and down the tapered rotameter tube.

From Figure 5.1, if the float radius is Rf and thelocal bore of the rotameter tube is 2Rt then:

Jt(Rt" R; = 2xRlS = Cross-sectional art

., ~,-~=

DischargeConstant peripheral velocity

Now 0 = Ie. where I is the distance from datum to thecross-section at which the local bore is Rt and e is thesemi-angle of tube taper. Hence I is proportional todischarge. An approximately linear calibrationcharacteristic would be anticipated for the rotameter.

Figure 5. 1 Principle of the rotameter

Figure 5.2 Typical rotameter calibration curve

TecQulDment Flow Measurement

~ Calculations of Head Loss Orifice MeterApplying Equation (3-1) between (E) and (F) bysubstituting kinetic and hydrostatic heads would give anelevated value to the head loss for the meter. This isbecause at an obstruction such as an orifice plate, thereis a small increase in pressure on the pipe wall due topart of the impact pressure on the plate being conveyedto the pipe wall. BS 1042 (Section 1.1 1981) gives anapproximate expression for finding the head loss andgenerally this can be taken as 0.83 times the measuredhead difference.

By reference to Equation (3-1) the head loss associatedwith each meter can be evaluated.

Venturi MeterApplying the equation between pressure tappings (A)and (C).

pg

i.e.Therefore:

hA - hc = L\HAC

This can be made dimensionless by dividing it by the-2

inlet kinetic head ~.2g

AHEF = 0.83 (hE - hF) mm

= 0.83 (372 - 40) mm = 275 mm

The orifice plate diameter (51.9 mm) is approximatelytwice the venturi inlet diameter (26 mm), therefore theorifice inlet kinetic head is approximately 1/16 that ofthe venturi, thus:

44.26 = 276

Now,n7: 2g ' (kJ.'\~"'+ r' v.~. ~~ l:A.-.rk.

1-(As/AA)2 Ptf1awP8 16

Therefore.and

ifs

276

-2 -2 ( )2VA = VB AB/A~ Head loss = = 99.6 inlet kinetic heads

thus

Rotameter

With the apparatus provided (Ao/AA) = 0.38. therefore

the inlet kinetic head is:

'\72( .

~ = 0.144 x 116 EA._.&.pg pg.

= O.167(hA -~)?(r-g

For example if:

hA = 375 romhB = 110 romhc = 350 mm

then:

AHAC = hA-hc = 25 mm

-2

VA

2g

:f'd1'67(~A -hB) = 0.167 )(26-'

= 44.26mm

Therefore,

Head loss = ~ = 0.565 inlet kinetic heads2S

Figure 5.3 Rotameter head loss

TecQuipment Flow Measurement

For this meter, application of Equation (3-1) gives:

f&~ t:i!I).!!l+zJ) = AHHI

pgP8

Then as illustrated in Figure 5.3: -2 "ti:"2

.P.Q.+-Y9--=.P1i.+-1L+L\HGHpg 2g pg 2$". :JhH - hI = AHHI

The outlet kinetic head is now 2.8 times the inlet kinetichead. For example if:

hA = 375 mmhB = 110 mmhG = 98 mmhH = 88 mm

and

Inlet kinetic head = 2.76 mrnOutlet kinetic head = 7.73 mrn

Inspection of the table of experimental results showsthat this head loss is virtually independent of dischargeand has a constant value of approximately 100 rom ofwater. As has already been shown, this is acharacteristic property of the rotameter. Forcomparative purposes it could be expressed in terms ofthe inlet kinetic head. However, when the velocity isvery low the head loss remains the same and sobecomes many, many times the kinetic head.

It is instructive to compare the head lossesassociated with the three meters with those associatedwith the rapidly diverging section, or wide-angleddiffuser, and with the right-angled bend or elbow. Thesame procedure is adopted to evaluate these losses.

then

MlGH = (98-88) + (21'f!'it73)

= 5.03 mID of water

Therefore,

103276

Head loss = = 182 inlet kinetic heads

Wide-Angled DiffuserThe inlet to the diffuser may be considered to be at (C)and the outlet at (D). Applying Equation (3-1):

-2 -2

E£.+~=.E!2.+.YP.-+AHCDpg 2g pg 2g

Since the area ratio, inlet to outlet, of the diffuser is 1 :4,the outlet kinetic head is 1/16 of the inlet kinetic head.

Discussion of the Meter Characteristics

For example if:

hA = 375 rnm

hB= Il0rnmhc = 350 rnm

hD = 360 rnm

then

Inlet kinetic head = 44.26 mrn

The(See venturi meter head loss calculations).corresponding outlet kinetic head is:

44.26 - 28-- mm16

There is little to choose in the accuracy of dischargemeasurement between the venturi meter, the orificemeter and the rotameter - all are dependent upon thesame principle. Discharge coefficients and the rotametercalibration are largely dependent on the way the streainfrom a 'vena contracta' or actual throat of smaller cross-sectional area than that of the containing tube. Thiseffect is negligibly small where a controlled contractiontakes place in a venturi meter but is significant in theorifice meter. The orifice meter discharge coefficient isalso dependent on the precise location of the pressuretappings (E) and (F). Such data is given in BSI042which also emphasises the dependence of the metersbehaviour on the uniformity of the flow upstream anddownstream of the meter.

In order to keep the apparatus as compact aspossible the dimensions of the equipment in theneighbourhood of the orifice meter have been reducedto their limit, consequently some inaccuracy in theassumed value of its discharge may be anticipated.

The considerable difference in head loss betweenthe orifice meter and the venturi meter should be noted.The orifice meter is much simpler to make and use, forit is comparatively easy to manufacture a suitableorifice plate and insert it between two existing pipeflanges which have been appropriately pressure-tappedfor the purpose. In contrast the venturi meter is large,comparatively difficult to manufacture and complicatedto fit into an existing flow system. But the low head loss

and

Mm = (350-360)+(44.26-28)

= 3 L46 mm of water

Therefore,

i~L464275

Head loss is = 0.71 inlet kinetic heads

Right-Angled BendThe inlet to the bend is at (G) where the pipe bore is51.9 mIn and outlet is at (H) where the bore is 40 mIn.Applying Equation (3-1 ):

TecQuioment Flow Measurement

parts of the system are most responsive, in tenns ofassociated head loss, to small improvement in design.

Discussion of Results

r If the mass flow results are plotted against mass flowrates from the weighing tank method the accuracy of thevarious methods can be compared. Since all are derivedfrom Equation (1) similar results would be expectedfrom the three methods. The differential mass flowmeasurement (mmeter - mweightank) could be plotted

against the weighing tank mass flow results for a betterappraisal of accuracy.

Some overestimation in the venturi metertermination can be anticipated because its venacontracta has been assumed to be negligibly small.Similarly, the rotameter determination may well besensitive to the proximity of the elbow and theassociated inlet velocity distribution. The orifice meteris likely to be sensitive to the inlet flow which isassociated with the separation induced in the wide-anglediffuser upstream of it. Thus both the rotameter and theorifice meter calibrations would be likely to change if alonger length of straight pipe were introduced upstreamof them.

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associated with the controlled expansion occurring inthe venturi meter gives it an obvious superiority inapplications where power to overcome flow losses maybe limiting.

Rotameters and other flow measuring instrumentswhich depend on the displacement of floats in taperedtubes may be selected from a very wide range ofspecifications. They are unlikely to be comparable withthe venturi meter from the standpoint of head loss but,provided the discharge range is not extreme, the ease ofreading the instrument may well compensate for thesomewhat higher head loss associated with it.

The head losses associated with the wide-angleddiffuser and the right-angled bend are not untypical.Both could be reduced if it were desirable to do so. Thediffuser head loss would be minimised if the totalexpansion angle of about 50 degrees were reduced toabout 10 degrees. The right-angled bend loss would besubstantially reduced if the channel, through whichwater flows, was shaped in the arc of a circle having alarge radius compared with the bore of the tubecontaining the fluid.

Large losses in internal flow systems are associatedwith uncontrollable expansion of the stream. Attentionshould always be paid to increases in cross-sectionalarea and changes of direction of the stream as these

Inlet kinetic head: scale Brr

0(."'i~

."c"

:~u

~.c

~

i

:5

(J~ii~.-c.~

.c

~=~~

~

'":E

rInlet kinetic head: scale D (mm)

Figure 5.4 Typical head loss graph

TecQulpment Flow Measurement

In the calculations the head losses associated with thevarious meters and flow components have been madedimensionless by dividing by the appropriate inletkinetic heads. The advantage of the venturi meter overthe orifice meter and rotameter is evident although overa considerable range of inlet kinetic heads the lossassociated with the rotameter is sufficiently small toconsider that it would be more than compensated by therelative ease in evaluation of mass flow from thisinstrument.

It should also be noted from Figure 5.1 that thedimensionless head losses of the venturi meter and theorifice meter are Reynolds number dependent. Thiseffect is also noticeable with the dimensionless headloss of the elbow.

The venturi meter offers the best control to the fluid.Its discharge coefficient is little different from unity andthe head loss it offers is minimal. But it is relativelyexpensive to manufacture and could be difficult toinstall in existing pipework.

The orifice meter is easiest to install betweenexisting pipe flanges and provided it is manufacturedand erected in accordance with BS 1042, will giveaccurate measurement. The head loss associated with itis very large compared with that of the venturi meter.

The rotameter gives the easiest derivation ofdischarge, dependent only on sighting the float andreading a calibration curve. It needs to be chosenjudiciously, however, so that the associated head loss isnot excessive.

Conclusions

The most direct measurement of fluid discharge is bythe weightank principle. In installations where this isimpracticable (e.g. on account of size of installation orgaseous fluid flow), one of the three discharge metersdescribed may be used instead.