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FLOW
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Over the past 60 years, the importance offlow measurement has grown, not onlybecause of its widespread use for accountingpurposes, such as the custody transfer offluid from supplier to consumer, but alsobecause of its application in manufacturingprocesses.
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Food & beverage Medical
Mining & metallurgical
Oil & gas transport Petrochemical
Power generation
Distribution
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Velocity it is a measure of speed & directionof an object or when related to fluids, it issimply the rate of flow of fluid particles in apipe.
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Laminar flow of a liquid occurs when itsaverage velocity is comparatively low & thefluid particles tend to move smoothly inlayers
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Turbulent flow occurs when the flowvelocity is high & the particles no longer flowsmoothly in layers & turbulence or a rollingeffect occurs.
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Viscosity is a property of a gas or liquid thatis a measure of its resistance to motion orflow.
Dynamic viscosity measured in poise orcentipoise
Kinematic viscosity measured in stokes orcentistokes
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Early flow measurement was centred roundthe question of disputation: how much hashe got versus how much have I got. Asearly as 5000 BC flow measurement was used
to control the distribution of water throughthe ancient aqueducts of the early Sumeriancivilisations from the Tigris and Euphratesrivers. Such systems were very crude, basedon volume per time: e.g. diverting flow in onedirection from dawn to noon, and diverting itin another direction from noon to dusk.
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The first major milestone in the field of flowtechnology occurred in 1738 when the Swissphysicist Daniel Bernoulli published hisHydrodynamica in which he outlined theprinciples of the conservation of energy for flow.In it he produced an equation showing that anincrease in the velocity of a flowing fluidincreases its kinetic energy while decreasing itsstatic energy. In this manner a flow restriction
causes an increase in the flowing velocity and afall in the static pressure the basis of todaysdifferential pressure flow measurement.
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The word turbine is derived from the Latinspinning top and although the ancient Greeksground flour using horizontal turbine wheels,the idea of using a spinning rotor or turbine
to measure flow did not come about until1790 when the German engineer, ReinhardWoltman, developed the first vane-typeturbine meter for measuring flow velocities inrivers and canals.
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Other types of turbine meter followed. In thelate 1800sLester Pelton built the first Peltonwater wheel that turned as a result of water
jets impinging on buckets attached around
the outside of the wheel. And in 1916Forrest Nagler designed the first fixed- bladepropeller turbine.
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A third milestone occurred in 1832 when MichaelFaraday attempted an experiment to use his lawsof electromagnetic induction to measure flow.With the aim of measuring the water flow of theRiver Thames, Faraday lowered two metalelectrodes, connected to a galvanometer, into theriver from Waterloo Bridge. The intent was tomeasure the induced voltage produced by theflow of water through the earthsmagnetic field.
The failure of Faraday to obtain any meaningfulresults was probably due to electrochemicalinterference and polarization of the electrodes.
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The last milestone occurred only three yearsafter Faraday conducted his originalexperiment when, in 1835, Gaspar Gustav deCoriolis, made the discovery of what is now
termed the Coriolis effect, which led, nearly acentury and a half later, to the developmentof the highly accurate direct measurementmass flow Coriolis meter.
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The cost of many liquids & gases are basedon the measured flow through a pipelinemaking it necessary to accurately measure &control the rate of flow for accounting
purposes.
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One of the most important primary propertiesof a fluid (liquid or gas) is its viscosity itsresistance to flow or to objects passingthrough it.
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The viscosity of a fluid also depends onpressure but, surprisingly, pressure has lesseffect on the viscosity of gases than onliquids.
A pressure increase from 0 to 70 bar (in air)results in only an approximate 5% increase inviscosity. However, with methanol, forexample, a 0 to 15 bar increase results in a10-fold increase in viscosity.
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In a frictionless pipe in which there is noretardation at the pipe walls, a flat idealvelocity profile would result in which all thefluid particles move at the same velocity
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At low flow rates the fluid particles move instraight lines in a laminar manner witheach fluid layer flowing smoothly pastadjacent layers with no mixing between the
fluid particles in the various layers. As aresult the flow velocity increases from zero,at the pipe walls, to a maximum value at thecentre of the pipe and a velocity gradient
exists across the pipe.
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The shape of a fully developed velocity profilefor such a laminar flow is parabolic, with thevelocity at the centre equal to twice the meanflow velocity. Clearly, if not corrected for,
this concentration of velocity at the centre ofthe pipe can compromise the flowcomputation.
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As the velocity increases further theindividual paths start to intertwine and crosseach other in a disorderly manner so thatthorough mixing of the fluid takes place.
This is termed turbulent flow.
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Obstructions in a pipe, such as bends,elbows, reducers, expanders, strainers,control valves, and T-pieces, can all affect theflow profile in a manner that can severely
affect measurement accuracy. Such disturbedflow, which should not be confused withturbulent flow, gives rise to a number ofeffects that include:
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Swirl fluid rotation about the pipe axis.
Vortices areas of swirling motion with highlocal velocity which are often caused byseparation or a sudden enlargement in pipe
area.
Asymmetrical profile
Symmetrical profile with high core velocity
caused by a sudden reduction in pipe area.
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The onset of turbulence is often abrupt andto be able to predict the type of flow presentin a pipe, for any application, use is made ofthe Reynolds number, Re a dimensionless
number given by:
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Irrespective of the pipe diameter, type offluid, or velocity, Reynoldsshowed that theflow is:
Laminar: Re < 2000
Transitional: Re = 2000 - 5000
Turbulent: Re > 4000
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Volumetric flow rate The volumetric flow rate, Q,represents the total volume of fluid flowingthrough a pipe per unit of time and is usuallyexpressed in litres per second (l/s) or cubicmetres per hour (m3/h). The measurement of
volumetric flow rate is most frequently achievedby measuring the mean velocity of a fluid as ittravels through a pipe of known cross sectionalarea A.
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The term velocity is often used very loosely todescribe the speed at which the fluid passes apoint along the pipe. In reality, most modernflowmeters measure either the point velocity
or the mean velocity.
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The point velocity is the flow velocity in alocalised region or point, in the fluid and is,generally of little use in practice. It is usedmainly in research to determine, for example,
velocity profiles or flow patterns.
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The mean flow velocity, can be obtained bymeasuring the volumetric flowrate, Q, anddividing it by the cross-sectional area of thepipe, A:
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If we want to measure the rate at which wateris flowing along a pipe. A very simple way ofdoing this is to catch all the water coming outof the pipe in a bucket over a fixed time
period. Measuring the weight of the water inthe bucket and dividing this by the time takento collect this water gives a rate ofaccumulation of mass. This is know as the
mass flow rate.
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More commonly we need to know the volumeflow rate - this is more commonly know asdischarge. (It is also commonly, butinaccurately, simply called flow rate). The
symbol normally used for discharge is Q. Thedischarge is the volume of fluid flowing perunit time.
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Flow rate is the volume of fluid passing agiven point in a given amount of time & istypically measured in gpm, cfm, or lpm.
Total flow is the volume of liquid flowing
over a period of time & is measured ingallons, cubic feet, liters, and so on.
Energy loses in flowing fluids are caused byfriction bet. the fluid & containment walls &by fluid impacting an object
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The continuity equation states that if theoverall flow rate in a system is not changingwith time, the flow rate in any part of thesystem is constant.
Q=AVWhere: Q flow rate
V average velocity
A cross-sectional area of pipe
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If liquids are flowing in a tube with differentcross section areas, i.e., A1 and A2, as isshown in Fig. 7.2b, the continuity equationgives:
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The Bernoulli equation gives the relationbetween pressure, fluid velocity, andelevation in a flow system. The equation isaccredited to Bernoulli (1738).
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Losses are accounted for by pressure lossesand fall into two categories. Firstly, thoseassociated with viscosityand the frictionbetween the constriction walls and the
flowing fluid, and secondly, those associatedwith fittings, such as valves, elbows, tees, andso forth.
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Frictional losses. They are losses from liquidflow in a pipe due to friction between theflowing liquid and the restraining walls of thecontainer. These frictional losses are given
by:
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Fitting losses are losses due to couplings andfittings, which are normally less than thoseassociated with friction and are given by:
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Differential pressure measurements can bemade for flow rate determination when a fluidflows through a restriction. The restrictionproduces and increase in pressure which can
be directly related to flow rate.
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Differential pressure flow rate meters arebased on a physical phenomenon in which arestriction in the flow line creates a pressuredrop that bears a relationship to the flow
rate. This physical phenomenon is based on two
well-known equations: the equation ofcontinuity and Bernoullis equation.
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Orifice plate Venturi tube
Flow nozzle
Dall tube
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The orifice plate is the simplest and mostwidely used differential pressure flowmeasuring element and generally comprises ametal plate with a concentric round hole
(orifice) through which the liquid flows.
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The orifice is offset from the centre and isusually set at the bottom of the pipe bore.This configuration is mainly used inapplications where the fluid contains heavy
solids that might become trapped andaccumulate on the back of the plate. With theorifice set at the bottom, these solids areallowed to pass. A small vent hole is usuallydrilled in the top of the plate to allow gas,
which is often associated with liquid flow, topass.
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It should be noted, however, that the vent holeadds an unknown flow error and runs the risk ofplugging.
Eccentric plates are also used to measure theflow of vapours or gases that carry smallamounts of liquids (condensed vapours), sincethe liquids will carry through the opening at thebottom of the pipe.
The coefficients for eccentric plates are not as
reproducible as those for concentric plates, andin general, the error can be 3 to 5 times greaterthan on concentric plates.
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The opening in a segmental orifice plate is acircular segment comparable to a partiallyopened gate valve. This plate is generallyemployed for measuring liquids or gases that
carry non-abrasive impurities, which arenormally heavier than the flowing media suchas light slurries, or exceptionally dirty gases.
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The measurement of differential pressurerequires that the pipe is tapped at suitableupstream (high pressure) and downstream(low pressure) points. The exact positioning
of these taps is largely determined by theapplication and desired accuracy.
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Pipe taps are a compromise solution and arelocated 2 pipe diameters upstream and 8pipe diameters downstream. Whilst notproducing the maximum available differential
pressure, pipe taps are far less dependent onflow rate and orifice size.
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Simple construction. Inexpensive.
Robust
Easily fitted between flanges.
No moving parts. Large range of sizes and opening ratios.
Suitable for most gases and liquids as well assteam.
Price does not increase dramatically with size.
Well understood and proven.
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Permanent pressure loss of head is quite high. Inaccuracy, typically 2 to 3%. Low turndown ratio, typically from 3 to 4:1. Accuracy is affected by density, pressure and
viscosity fluctuations.
Erosion and physical damage to the restriction affectsmeasurement accuracy. Viscosity limits measuring range. Requires straight pipe runs to ensure accuracy is
maintained. Pipeline must be full (typically for liquids). Output is not linearly related to flowrate. Multiple potential leakage points
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The venturi flow meter, while considered anobstruction flow meter, is less of anobstruction than the orifice type. It still doeshave a certain amount of pressure drop, but
it is significantly less than the orifice typemeter.
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Less significant pressure drop acrossrestrictions
Less unrecoverable pressure loss
Requires less straight pipe up & downstream
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More expensive Bulky requires large section for installation
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The flow nozzle is used mainly in highvelocity applications or where fluids are beingdischarged into the atmosphere. It differsfrom the nozzle venturi in that it retains the
'nozzle' inlet but has no exit section.
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A flow nozzle consists of a restriction with anelliptical contour approach section thatterminates in a cylindrical throat section.Pressure drop between the locations one pipediameter upstream and one-half pipediameter downstream is measured. Flownozzles provide an intermediate pressuredrop between orifice plates and venturi tubes;also, they are applicable to some slurry
systems that would be otherwise difficult tomeasure.
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The main disadvantage of the flow nozzle isthat the permanent pressure loss is increasedto between 30 to 80% of the measureddifferential pressure depending on its
design.
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Accuracy is only slightly less than for theventuri tube ( 1 to 1.5 %) and it is usuallyonly half the cost of the standard venturi. Inaddition it requires far less space for
installation and, because the nozzle can bemounted between flanges or in a carrier,installation and maintenance are much easierthan for the venturi.
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Although many variations of low-loss metershave appeared on the market, the best-known and most commercially successful isthe Dall tube.
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The Dall tube is virtually throatless and has a
short steep converging cone that starts at astepped buttress whose diameter is somewhatless than the pipe diameter. Following anannular space at the 'throat', there is a diverging
cone that again finishes at a step.
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The Dall tube has the lowest insertion lossbut is not suitable for use with slurries.
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The orifice is the simplest, cheapest, easiest toreplace, least accurate, more subject to damageand erosion, and has the highest loss.
The Venturi tube is more difficult to replace,most expensive, most accurate, has high toler-
ance to damage and erosion, and the lowestlosses of all the three tubes.
The flow nozzle is intermediate between theother two and offers a good compromise.
The Dall tube has the advantage of having thelowest insertion loss but cannot be used withslurries.
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The elbow can be used as a differential flowmeter. Figure 7.6a shows the cross section of anelbow. When a fluid is flowing, there is adifferential pressure between the inside andoutside of the elbow due to the change in
direction of the fluid. The pressure difference isproportional to the flow rate of the fluid.
The elbow meter is good for handling particulatesin solution, with good wear and erosion resistancecharacteristics but has low sensitivity.
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A number of factors contribute to the differentialpressure that is produced and, subsequently, it isdifficult to predict the exact flow rate accurately.Some of these factors are:
force of the flow onto the outer tapping
turbulence generated due to cross-axial flow atthe bend
differing velocities between outer and innerradius of flow
pipe texture relationship between elbow radius and pipe
diameter.
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The pilot static tube shown is an alternativemethod of measuring the flow rate, but hassome disadvantages in measuring flow, inthat it really measures the fluid velocity at the
nozzle.
Because the velocity varies over the crosssection of the pipe, the Pilot static tubeshould be moved across the pipe toestablish an average velocity, or the tubeshould be calibrated for one area.
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Other disadvantages are that the tube canbecome clogged with particulates and thedifferential pressure between the impact andstatic pressures for low flow rates may not be
enough to give the required accuracy.
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The variable area flowmeter is a reversedifferential pressure meter used to measurethe flow rate of liquids and gases.
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The instrument generally comprises avertical, tapered glass tube and a weightedfloat whose diameter is approximately thesame as the tube base.
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In operation, the fluid or gas flows throughthe inverted conical tube from the bottom tothe top, carrying the float upwards. Since thediameter of the tube increases in the upward
direction the float rises to a point where theupward force on the float created bydifferential pressure across the annular gap,between the float and the tube, equals the
weight of the float.
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The simplest method of measuring the
rotor speed is by means of a magnet,fitted within the rotor assembly, thatinduces a single pulse per revolution inan externally mounted pick-up coil.
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The Woltman meter, used primarily as a watermeter, is very similar in basic design to theturbine meter. The essential difference is thatthe measurement of rotation is carried out
mechanically using a low friction gear trainconnecting the axle to the totalizer.
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Electromagnetic flowmeters, also known asMagflows or Magmeters, have now been inwidespread use throughout industry for morethan 40 years and were the first of modern
meters to exhibit no moving parts and zeropressure drop.
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The principle of the EM flowmeter is based onFaraday's law of induction that states that if aconductor is moved through a magnetic field avoltage will be induced in it that is proportionalto the velocity of the conductor.
Electromagnetic flow meters can only beused in conductive liquids
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used in conductive liquids. The device consists of two electrodes
mounted in the liquid on opposite sides of
the pipe. A magnetic field is generatedacross the pipe perpendicular to theelectrodes. The conducting fluid flowingthrough the magnetic field generates avoltage between the electrodes, which can
be measured to give the rate of flow. Themeter gives an accurate linear outputvoltage with flow rate. There is noinsertion loss and the readings areindependent of the fluid characteristics,
but it is a relatively expensive instrument.
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no pressure drop short inlet/outlet sections (5D/2D) insensitive to flow profile changes (laminar to turbulent) rangeability of 30:1 or better inaccuracy of better than 0.2% of actual flow over full
range
no recalibration requirements bi-directional measurement no taps or cavities no obstruction to flow not limited to clean fluids
high temperature capabilities, high pressure capabilities; volumetric flow can be installed between flanges andcan be made from corrosion resistance materials at lowcost.
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Vortex flowmeters for industrial flowmeasurement were first introduced in themid-1970s but the technology was poorlyapplied by several suppliers. As a result, the
technology developed a bad reputation andseveral manufacturers dropped thetechnology. However, since the mid-1980smany of the original limitations have been
overcome and vortex flowmetering hasbecome a fast growing flow technology.
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Vortex meters are based on the phenomenon knownas vortex shedding that takes place when a fluid (gas,steam or liquid) meets a non-streamlined obstacle termed a bluff body. Because the flow is unable tofollow the defined contours of the obstacle, theperipheral layers of the fluid separate from itssurfaces to form vortices in the low pressure area
behind the body.
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These vortices are swept downstream to form aso-called Karman Vortex Street. Vortices areshed alternately from either side of the bluffbody at a frequency that, within a given Reynoldsnumber range, is proportional to the mean flow
velocity in the pipe.
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Vortices formed can be measuredultrasonically
Vortex flow meters are mostly applied to highflow rates.
At low flow rates, the vortex frequency tendsto be unstable.
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Includes devices used to measure the totalquantity of fluid flowing or the volume ofliquid in a flow
Positive displacement meters use containers
of known size, which are filled and emptiedfor a known number of times in a given timeperiod to give the total flow volume.
Common instruments are Piston flow meter &
nutating disc flow meter.
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The oscillating or rotating piston meterconsists of a stainless steel housing and arotating piston. The only moving part in themeasuring chamber is the oscillation piston
which moves in a circular motion.
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The number of times the piston traverses thecylinder in a given time frame gives the totalflow.
The meter has high accuracy but is expensive
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The term nutation is derived from the action of aspinning top whose axis starts to wobble anddescribe a circular path as the top slows down.
In a nutating disc type meter the displacementelement is a disc that is pivoted in the centre of a
circular measuring chamber. The lower face ofthe disc is always in contact with the bottom ofthe chamber on one side, and the upper face ofthe disc is always in contact with the top of thechamber on the opposite side. The chamber istherefore divided into separate compartments ofknown volume.
Liquid enters through the inlet connection on
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Liquid enters through the inlet connection onone side of the meter and leaves through an
outlet on the other side successively fillingand emptying the compartments and movingthe disc in a nutating motion around a centrepivot. A pin attached to the disc's pivot point
drives the counter gear train.
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Although there are inherently more leakagepaths in this design, the nutating disk meteris also characterised by its simplicity andlow-cost.
It tends to be used where longer meter life,rather than high performance, is required, forexample, domestic water service. The meteris also suitable for use under high
temperatures and pressures.
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By measuring the flow and knowing thedensity of a fluid, the mass of the flow can bemeasured. Mass flow instruments includeconstant speed impeller turbine wheel-spring
combinations that relate the spring force tomass flow and devices that relate heattransfer to mass flow.
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A mass flow meter, also known as an inertialflow meter is a device that measures massflow rate of a fluid traveling through a tube.The mass flow rate is the mass of the fluid
traveling past a fixed point per unit time.
The mass flow meter does not measure thevolume per unit time (e g cubic meters per
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volume per unit time (e.g., cubic meters persecond) passing through the device; it
measures the mass per unit time (e.g.,kilograms per second) flowing through thedevice.
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Dry particulate flow rate can be measured asthe particulate are being carried on aconveyer belt with the use of a load cell. Tomeasure flow rate it is only necessary to
measure the weight of material on a fixedlength of the conveyer belt.
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A weir is essentially a dam mounted at rightangles to the direction of flow, over which theliquid flows.
For the associated equation to hold true andaccurate flow measurement determined, thestream of water leaving the crest (the nappe)
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stream of water leaving the crest (the nappe),should have sufficient fall. This is called free
or critical flow, with air flowing freely beneaththe nappe so that it is aerated. Should thelevel of the downstream water rise to a pointwhere the nappe is not ventilated, the
discharge rate may be inaccurate anddependable measurements cannot beexpected.
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The discharge equation (head vs. flow rate),without end contractions, is:
where:
q = flow rate; k = constant; L = length ofcrest; and h = the head.
Generally, this means that for a 1 % change inflow, there will be a 0.7 % change in the level.
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Many different types of sensors can be usedfor flow measurements. The choice of anyparticular device for a specific applicationdepends on a number of factors such as-
reliability, cost, accuracy, pressure range,temperature, wear and erosion, energy loss,ease of replacement, particulates, viscosity,and so forth.
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