flow fundamentals

8/20/2019 Flow Fundamentals

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Flow is the study of fluids in motion—a fluid is any substance that can flow, andthus the term applies both to liquids and to gases. Precise measurement andcontrol of fluid flow through pipes can be difficult, but is extremely important inalmost all process industries.

ACCURACY Accuracy is typically specified either as “% of flow rate” or as “% of full scale”. Theuser should be careful when defining accuracy since “% of flow rate” and “% of fullscale” are not the same. In “% of flow rate”, the accuracy is the same for low flowsas it is for high flows. For example, a device with 0-100 L/m range and ±1% flowrate accuracy, will have, at 100 L/m, an error of ±1 L/m and at a flow of 20 L/m, the

error will be ±0.2 L/m (i.e., 1% of measurement in both cases).

On the other hand, a “% of full scale” device has different measuring accuracies atdifferent flow rates. For example, a device with 0-100 L/m range and ±1% full scaleaccuracy will have, at 100 L/m, an error of ±1 L/m and at a flow of 20 L/m, the errorwill still be ±1 L/m (i.e., 5% of measurement). This is a much larger error than theflow of 20 L/m under “% of flow rate”.

Different process industries measure flow for different reasons, and one flowmetermay be used for more than one application even within one industry.

REPEATABILITYRepeatability is the ability of a flowmeter to produce the same measurement eachtime it measures a flow. High repeatability does not ensure accuracy. Dependingon the application, repeatability of a flowmeter may be more important thanaccuracy. For example, in a flow control loop, if a flowmeter gives a stable,repetitive reading, the true accuracy of the measurement is not necessarilyimportant.



Why Measure Flow?

CUSTODY TRANSFERThe measurement of fluid passing from a supplier to a customer —is one of the

most important flow measurement applications. In custody transfer applications,flowmeters are essentially the cash register of the system. For example, aflowmeter at your local gas station measures how much gas you pump into yourvehicle and bills you accordingly. Given the economic implications, custodytransfer applications require high measurement accuracy.

PRODUCT CONSISTENCY Accurate flow measurement ensures product integrity. Flow is used as an input toprocess control systems so that the product produced is the same. As a consumer,you expect processed food you eat or the gasoline you use in your car to be thesame each and every time you purchase these products.

EFFICIENCYPrecise flow measurement can also provide indications of process efficiency basedon the amount of inputs used and the amount of product produced.

For example, in a boiler, combustion efficiency is an indication of the burner’sability to burn fuel. The amount of unburned fuel and excess air in the exhaust areused to assess a burner’s combustion efficiency. Burners resulting in low levels ofunburned fuel while operating at low excess air levels are considered efficient.Well-designed burners firing gaseous and liquid fuels operate at excess air levelsof 15% and result in negligible unburned fuel. By operating at only 15% excess air,

less heat from the combustion process is being used to heat excess air, whichincreases the available heat for the load. Combustion efficiency is not the same forall fuels and, generally, gaseous and liquid fuels burn more efficiently than solidfuels.

PROCESS VARIABLE CONTROLFlow rate is measured and controlled during applications. For example, during heatexchange, fluid temperature can be controlled by changing the flow rate of steamthrough the heat exchanger. Other process applications use flow rate control tomanipulate such variables as pressure, level in a vessel, chemical composition,and weight.

SAFETYRegulation of flow is often essential for safety reasons. Flow rates outside thedesired range can be an indication that something else in the process is in anupset condition, such as a compressor or a pump or even a valve.



Terminology

FLOW RATEFlow rate refers to the velocity of the fluid being measured. Velocity is generallymeasured in feet or meters per second. Flow rate answers the question: How fast

is the fluid moving?

Flow can be defined as a volume of fluid in a pipe passing a given point per unit oftime. This can be expressed by

Q = v x A

Where A is the cross-sectional area of the pipe, and v is the average fluid velocity.

VOLUMETRIC FLOW RATEMore often the question is: How much fluid is passing through the pipeline or

system? One way to describe a quantity of fluid is by giving the volumetric flowrate; the volume of fluid that is transported over some period of time such asgallons per minute, liters per hour, and so forth. Volumetric flow rate can bedetermined from the velocity of the fluid if the area of the pipeline is known. Theequation that describes the relationship between velocity and volumetric flow rateis:

Q = v x A

Where:Q = the flow rate in units of volume per unit of timev = the velocity of the fluid

A = the cross-sectional area of the pipe

Flow rate is not measured directly. Instead, some other variable (in this instance,velocity) is measured and translated into a flow rate based on the cross-sectionalarea of the pipeline.



Limitations of volumetric measurement

There are a few limitations inherent to volumetric flow. For example, volumetricflow measurement devices usually do not account for changes in fluid density ,which is especially important when measuring gases or vapors. As the temperature

of a gas increases, the molecules move further apart. This means there is asmaller amount by weight of the measured fluid in a given volume than there wouldbe at some lower temperature. Similarly, increases in pressure will cause themolecules to move closer together, resulting in more of the measured fluid byweight in a given volume. One solution to this problem is to use devices thatprovide temperature and pressure compensation. Another solution is to use massflow measurement. These concepts will be discussed later.

MASS FLOW RATE

When very precise flow rate measurements must be made, mass flowmeters areoften preferred. Mass flow measurements give the actual weight of the fluid that isbeing transported per unit of time, such as pounds per hour, kilograms per second,and so forth.

The mass flow may then be defined as

volumetric flow × density

TOTALIZED FLOW

Totalized flow gives an ongoing measurement of the total amount of fluid passingby the point of measurement. Everyday examples of totalized flow measurementare the measurements made by the gas and water meters attached to homes andbusinesses.



Fluid Properties

The following fluid properties are often used in process industries both as variablesin flow equations and separately to evaluate and predict process efficiency andsafety:

Density

Viscosity

Fluid type

Flow profile

DENSITY

Density (ρ), one of the most commonly used measures, is the mass per unitvolume of a fluid, typically given at a reference temperature and pressure. Table

3.1 shows how density is affected by temperature and pressure both for liquids andfor gases. In general, density is proportional to pressure and inversely proportionalto temperature.

Density = Mass / Volume

The density of the process fluid is important to flowmeter selection andperformance.

Gravedad específica en gases

SG = MW de gas

MW de aire

SG (Oxígeno) = 32 / 28.8 = 1.11



FLUID TYPE

A wide variety of process fluid types can be measured. Often, the fluids containsuspended solids or other particulate matter that may affect flowmeter function or

measurement accuracy:

Clean fluid— A fluid that is free from solid particles (e.g., water)

Dirty fluid— A fluid containing solid particles (e.g., muddy water)

Slurry— A liquid with a suspension of fine solids that can flow freely througha pipe (e.g., pulp and paper, oatmeal)

Steam

The condition of the fluid (i.e., clean or dirty) also presents limitations. Somemeasuring devices may become plugged or eroded if dirty fluids are used. Forexample, differential-pressure devices would normally not be applied where dirty or

corrosive fluids are used (though flow nozzles may handle such applications undercertain conditions). On the other hand, magnetic meters are capable of accuratelymeasuring dirty, viscous, corrosive, abrasive, and fibrous liquids.

Flow of SolidsThe flow measurement of solids typically involves using a weighing device or aradioactive (radiation) device. For example, a batch in a hopper could be measuredwith load cells and then discharged. For a continuous process, isolated weighingconveyors provide the weight measurement. Such measurements are not providedin this handbook since in many cases they fall under the responsibility ofmechanical engineering activities.

VISCOSITY

Viscosity can be thought of as fluid thickness. Viscosity is a measure of a fluid’stendency to resist a shearing force or to resist flow (Figure 3.3). The higher a fluid’sviscosity, the greater the force required to shear the fluid and the slower the fluid’sflow rate. For example, honey has a higher viscosity than water, so water flowsfaster and more easily around obstructions in its flow path than honey. Typicalunits used to represent viscosity are poise (cm/g/sec) and centipoise (cP).



In simple terms. Viscosity is:

The resistance of fluid to flow

The internal friction generated by one layer of liquid flowing over anothero In a Newtonian Fluid the friction (viscosity) is constanto

In a Non-Newtonian Fluid the friction (viscosity) is a function of theshear rate - hence viscosity is not constant

Generally, fluid viscosity is inversely proportional to temperature—as temperatureincreases, fluid viscosity decreases. Gas viscosity is an exception. Gas viscosity isproportional to temperature—as temperature increases, gas viscosity increases.

Viscosity Values of Selected Substances @ 20°C (64°F):

Substance Dynamic Viscosity (cP) Gases 0.01 to 0.02Liquid Hydrogen 0.01

Air 0.018 Acetone 0.32Water 1.0

Mercury 1.55Blood plasma 1.77Full blood 5 to 120Sugar solution 57Engine oil 100 to 500Castor oil 1000Honey 10,000Molten plastic 10e4 to 10e8Tar 1-e5 to 10e8Earth Crust 10e24



Environmental Conditions

Although pressure is an absolute quantity, everyday pressure measurements, suchas pipeline pressure, are usually made relative to ambient air pressure. In somecases, measurements are made relative to absolute pressure or vacuum.



FLOW PROFILE

Flow profile characterizes the behavior of a fluid as it flows through a pipe (e.g.,smooth or turbulent, symmetrical or asymmetrical). A fluid may change profilesseveral times before it reaches its destination point. Generally, at a given point in

time, a fluid will have one of the following three flow profiles:

Laminar

Turbulent

Transition

Laminar

In laminar flow, fluid flows in smooth, ordered layers. As a result, there is very littlemixing of fluid across the pipe cross section. The layers in the center of the pipehave the highest velocity, while friction between the fluid and the pipe wall causes

a lower velocity near the pipe wall (Figure 3.5). Laminar flow profiles occur whenviscous (restraining) forces have more influence in the flow stream than do inertial(driving) forces. Laminar flow streams may be symmetrical or non-symmetrical.

Turbulent

Turbulent flow profiles often occur with low-viscosity fluids, when inertial forceshave more influence in the flow stream than do viscous forces. The low viscosity

enables turbulent eddies (whirlpools) to form, which occur randomly in the fluidstream (Figure 3.6). In turbulent flow, the fluid velocity is nearly constant across thepipe cross section (uniform flow), with significantly lower velocity occurring onlyvery near the pipe wall. Because of the turbulence, considerable mixing takesplace across the pipe cross section.



Transition

Transition flow profiles mark the change from laminar to turbulent flows. Transitionflow varies depending on the pipe radius and may have characteristics of laminar

flow, turbulent flow, or both.

REYNOLDS NUMBER

The effects of the most important factors affecting fluid flow can be combined andexpressed with a dimensionless, numerical value called the Reynolds number(RD). The Reynolds number can be thought of as the ratio of the inertial force tothe viscous force in the flow stream. The basic equation for the Reynolds numberis:

Where:

ρ = Fluid densityv = Fluid velocityD = Pipe inside diameterμ = Fluid viscosity



Because the Reynolds number expresses the characteristics of a flow stream, it isuseful when determining whether a particular flowmeter is appropriate for anapplication. The Reynolds number is especially helpful in predicting the flow profile:

Laminar —RD <2,000

Transition—RD 2,000 –4,000 Turbulent—RD >4,000

STANDARD VS. ACTUAL VOLUMETRIC FLOW RATE

For gases, pressure and temperature must be compensated for, if the measuredvalues differ from the ones used for calculations. Unlike gases, liquids areincompressible but they may require temperature compensation since their densitymay vary significantly after a large change in temperature.

To standardize expressions of gas flow, process measurement professionals oftenrefer to the gas flow at operating conditions to standard pressure and temperatureconditions. Standard conditions are presumed to be 14.696 psia (101.325 kPaabsolute) for pressure and 59°F (or 15°C) for temperature. However, such“standard” conditions may vary from industry to industry, so it is good practice todefine these conditions to avoid errors.

Gas flow expressed in standard units is the amount of gas at standard conditionsthat is required to effect the same mass flow. The reasoning behind this approachis to relate the volumetric flow to mass flow at given operating conditions, since themass flow at 100 psig is quite different from the mass flow at 5000 psig due to

density change.

Standard volumetric flow rate is the volumetric flow rate that would occur if theprocess pipe conditions were set at a reference temperature and pressure. Thestandard volumetric flow rate is multiplied by the density of the fluid to determinethe mass flow rate. Actual volumetric flow rate is the volumetric flow rate at theactual pressure and temperature conditions within the process pipe.



Figure 3.7 shows the difference between actual and standard volumetric flow rates.The pipe flow conditions of Pipe 1 are at the standard reference conditions, so oneactual cubic meter (Am

3) equals one normal cubic meter (Nm

3). Most process

pipes do not operate at standard conditions.

More often, the conditions are like those in Pipe 2, where the pressure in the pipeis higher than the standard reference pressure. The same mass of gas that was in

5 m3 in Pipe 1 is compressed into 1 m3 in Pipe 2, where the pressure is five timeshigher. In Pipe 2, one Am3 is equal to five Nm3 of the process gas.

Ley de Avogadro:“El número de moléculas integrales en cualquier gas; a iguales condiciones de

presión y temperatura es siempre el mismo en volúmenes iguales. La masa de un

gas es directamente proporcional a su peso molecular”. Amadeo Avogadro 1776-1856

1 mol contiene 6.02 x 1023 átomos (No. De Avogadro)



The base reference conditions used to describe a standard cubic foot (SCF) orNm

3 vary. There are actually several different base pressures used to define an

SCF (Table 3.2):



Name of Gas Chemical

Formula

Approx

Mol.

Wei ht

Specific

Gravity

Acetylene (ethyne) C2H2 26.0 0.0682 1.0930 0.907

Air ~ 29.0 0.0752 1.2052 1.000Ammonia NH3 17.0 0.0448 0.7180 0.596

Argon Ar 39.9 0.1037 1.6619 1.379

Butane C4H10 58.1 0.1554 2.4904 2.067

Carbon dioxide CO2 44.0 0.1150 1.8430 1.529

Carbon monoxide CO 28.0 0.0727 1.1651 0.967

Chlorine Cl2 70.9 0.1869 2.9953 2.486

Ethane C2H6 30.0 0.0789 1.2645 1.049

Ethylene C2H4 28.0 0.0733 1.1747 0.975

Helium He 4.0 0.0104 0.1665 0.138

Hydrogen chloride HCl 36.5 0.0954 1.5289 1.268

Hydrogen H2 2.0 0.0052 0.0838 0.0695Hydrogen sulphide H2S 34.1 0.0895 1.4343 1.190

Methane CH4 16.0 0.0417 0.6683 0.554

Methyl chloride CH3Cl 50.5 0.1342 2.1507 1.785

Natural Gas ~ 19.5 0.0502 0.8045 0.667

Nitric oxide NO 30.0 0.0780 1.2500 1.037

Nitrogen N2 28.0 0.0727 1.1651 0.967

Nitrous oxide N2O 44.0 0.1151 1.8446 1.530

Oxygen O2 32.0 0.0831 1.3318 1.105

Propane C3H8 44.1 0.1175 1.8831 1.562

Propene (propylene) C3H6 42.1 0.1091 1.7484 1.451

Sulphur dioxide SO

2 64.1 0.1703 2.7292 2.264

Standard Density

lb/ft3 kg/m3

Table 3.3: Standard densities

STEAM – PRESSURE AND TEMPERATURE

Process pressure and temperature of the fluid inside the pipe are also keyelements in flow equations. Changes in pressure and temperature are especiallyimportant when measuring steam, which is one of the most commonly measuredfluids in the process industry. As water transits into steam, transition from the liquidphase to the gaseous state occurs.

RELACION CALOR-TEMPERATURA

La temperatura no es indicador de la cantidad de calor: El calor es la causa yla temperatura es la consecuencia. La relación entre el calor y la temperatura paralas sustancias se enuncian en las Leyes de cambio de Estado:

1. A Presión constante una sustancia cambia de estado a una temperaturadefinida llamada Punto de Transformación.



2. Mientras ocurre el cambio de estado, el Punto de Transformación de la

sustancia permanece constante.

3. El Punto de Transformación no cambia, cualquiera que sea el sentido de latransformación, por ejemplo, a presión atmosférica a nivel del mar, el agua

se congela a 0°C y se funde a 0°C y también hierve a 100 °C y se condensa a100 °C.

Esto puede explicarse mejor en con ayuda del gráfico siguiente:

Líquido Saturado:Es una condición de un fluido, a una Presión dada en la cual su calidad de

vapor es 0, es decir, es completamente líquido y si recibe una cantidad infinitesimal

de energía, empieza su cambio de fase hacia vapor.

Vapor Saturado:Es vapor a la temperatura de ebullición del líquido. Es la condición de un

fluido a la misma Presión y Temperatura que su Líquido Saturado, en la cual sucalidad de vapor es 100% y si pierde infinitesimalmente una cantidad de energía,empezará a cambiar su fase hacia líquido.

Vapor Sobrecalentado:Es vapor a una temperatura mayor a la de ebullición del líquido. Siempre su

calidad de vapor es 100% y sólo si pierde grandes cantidades de energía, seaproximará a la condición de saturación.

Calidad de Vapor o vapor húmedo:Es la masa en fase vapor que existe en cada unidad de masa de un fluido. Se

expresa en forma adimensional o bien como porcentaje:

x = masa en fase vaporunidad de masa

Agua a760



Saturation Point

Saturation point is the point under a specific set of conditions at which a liquid turnsto vapor. Saturation pressure and temperature vary according to a well-definedrelationship called the vapor-pressure curve. Water at its saturation point may be

saturated liquid (all liquid), saturated steam (all vapor), or a mixture of water liquidand vapor.

Diagrama de Mollier:



STATES OF STEAM

Pressure and temperature in the pipeline determine the state of the steam.Saturated steam is steam in the process pipe that is exactly at its saturation point.If the pressure drops or the temperature rises, superheated steam (steam heated

beyond its saturation point) results. For example, at 350 psia (pounds per squareinch absolute), the saturation temperature for water is 432 °F (222 °C). Thus,steam at 350 psia and 532 °F (278 °C) includes 100 °F (56 °C) of superheat. If thepressure rises or the temperature drops, the steam will start to condense andbecome saturated (the steam won’t condense until the superheat is removed at432 °F or 222 °C). Most flowmeters will measure steam well. However, almost allflowmeters have some additional error when measuring saturated steam. The errorusually becomes greater as steam quality decreases because of the difficulty indetermining the density of the liquid/vapor mixture.

Pipe Geometry and ConditionsPipe geometry (design) and conditions are the third key component in flowequations. Pipe geometry can cause changes in the flow profile. Process pipeconditions, such as roughness of the inner wall, can also affect the flow. Forexample, the texture of the inner pipe wall can cause a slight increase (smoothwall) or decrease (rough wall) in fluid velocity.

Not all measuring devices cover all line sizes. For example, the maximum size ofmost vortex meters is eight inches. Therefore, the question is whether the selectedflow device can handle the line size (and required flow).

PIPE INSIDE DIAMETER

In most industries, the inside diameter of a process pipe does not remain constantthroughout the entire process. Fluctuations in pipe inside diameter affect severalfactors (e.g., Reynolds number). For example, doubling the diameter of a processpipe can increase the flow rate by as much as four times if the velocity remainsunchanged.

(See size-sch.xls file)

CAVITACIÓNOcurre cuando la presión de operación se reduce por debajo de la presión devapor del fluido. Esto causa que el vapor cavite o burbujee. Si la presión seincrementa rápidamente por encima del punto de vapor, las burbujas colapsan congran fuerza.



FLOW PROFILE DISTURBANCES

A uniform, symmetrical, turbulent flow profile is desirable for most flowmeters.Factors that cause the flow profile to change are called flow profile disturbances.Most flow profile disturbances are caused by pipe geometry. Flow profile

disturbances can affect flowmeter accuracy, although to what degree depends onthe sensitivity of the flowmeter. There are three types of flow profile disturbances:

Symmetrical profile disturbance

Asymmetrical profile disturbance

Swirl

Symmetrical Profile Disturbance

In a symmetrical flow profile disturbance, the velocity profile of the fluid remainssymmetrical about the process pipe axis, but it is no longer uniform. Symmetrical

profile with a higher core velocity may be caused by either a reducer (pipe sectioninserted to decrease the cross-sectional area) or an expander (pipe sectioninserted to increase the cross-sectional area) (Figure 3.9). Reducers andexpanders may also cause a symmetrical profile velocity to become asymmetrical.

Asymmetrical Profile Disturbance

In an asymmetrical flow profile disturbance, the velocity profile of a fluid is notsymmetrical about the process pipe axis. Asymmetrical profile can be caused byanything that tends to push the flow to one side of the pipe. Elbows (Figure 3.10),valves, and tees are common sources of this disturbance.



Swirl

Swirl occurs when the velocity profile of a fluid moves in a circular motion as itflows forward. Swirl can be caused by pumps, compressors, or two pipe elbows indifferent planes (Figure 3.10). Swirl causes fluids to flow across the diameter of the

process pipe rather than parallel to the pipe. Such flow characteristics can takemore or less time to pass by the point of measurement, which can produceerroneous readings in flowmeters that measure velocity.

Eliminating the Effects of Flow Profile Disturbances

Some flowmeters are more sensitive to flow irregularities than others—mostflowmeters require a specific length of straight piping between disturbances toensure a uniform flow profile at the flowmeter. For each flowmeter, industry ormanufacturer’s standards specify the required length of straight pipe. The standardis referred to as an upstream or downstream straight piping requirement. Straightpiping length is usually specified in pipe diameters.

Knowing the cause of the disturbance can also help determine how much straightpiping is required. For example, swirl may take 100 or more pipe diameters todissipate, and a reducer requires significantly less straight piping to dissipate thana double elbow. Flow conditioners can be disks with circular holes in them orbundled tubes that are inserted in the process pipe to eliminate swirl (Figure 3.11).Flow conditioners create a turbulent, uniform (constant across the pipe crosssection), flow profile and can be used to decrease the length of the straight pipingrequirement.

Many types of flowmeters use a minimum number of upstream and downstreamstraight pipe runs because irregular velocity profiles affect the accuracy of themeasurement. This requirement has a direct effect on the piping and maysometimes be a problem (especially on existing installations). For example, for



orifice plates, typically a straight run of 10 to 20 upstream pipe diameters isrequired, with five pipe diameters for the downstream side. On the other hand, aPitot tube requires 40 upstream and 10 downstream pipe runs respectively,depending on the fluid dynamic disturbance. Major vendors offer tables to guidethe user in determining the recommended upstream and downstream straight pipe

runs. For Coriolis and variable area flowmeters, no upstream and downstream piperuns are required. There are many applications where appropriate upstream anddownstream pipe lengths are not available to provide accurate measurement. Inthese applications, straightening vanes or flow conditioners (consisting, forexample, of tube bundles) can be used. The length of these tubes should be morethan ten times the diameter of the tubes, with the inside diameter of the tubes lessthan 1/4 the inside pipe diameter.

Flowmeter Selection

There are several devices and instruments available for measuring fluid flow. Eachis designed to measure accurately and efficiently in a variety of applications,although some flowmeter designs perform better with certain applications.

Of the many flowmeters available for measuring fluid flow, the type of flowmeterused often depends on the nature of the fluid and the process conditions underwhich the fluid is measured. Each type of flowmeter has benefits and limitations

that depend partly on the flowmeter design and partly on the application. You willneed to be familiar with flowmeter specifications in order to select the bestflowmeter for a particular application.



Classes of Flowmeters

Flowmeters operate according to many different principles of measurement. Theycan be broadly classified into four categories:

1. Flowmeters that have wetted moving parts (such as positive displacement,turbine, and variable area). These meters utilize high-tolerance machinedmoving parts, which determine the meter’s performance. These parts aresubject to mechanical wear and thus are practical for clean fluids only.

2. Flowmeters that have wetted non-moving parts (such as vortex, differentialpressure, target, and thermal). The lack of moving parts gives these metersan advantage. However, excessive wear, plugged impulse tubing, andexcessively dirty fluids may cause problems for these meters.

3. Obstructionless flowmeters (such as coriolis and magnetic). These metersallow the fluid to pass undisturbed and thus maintain their performancewhen handling dirty and abrasive fluids.

4. Flowmeters with sensors mounted externally (such as clamp-on ultrasonicand weir flow measurements). These meters offer no obstruction to the fluidand have no wetted parts. However, their limitations prevent them frombeing used in all applications.



Flowmeters are grouped into four classes:

DP flowmeters

Velocity flowmeters

Mass flowmeters Positive displacement flowmeters (also called volumetric flowmeters)

Which class a flowmeter belongs to is important when deciding which flowmeter touse for a specific application. The classes are delineated based upon how eachmeasures fluid flow. With most classes of flowmeters, flow is first measuredindirectly by measuring differential pressure or a quantity proportional to fluidvelocity. Volumetric flow rate is then determined electronically from this firstmeasurement.

HOW DP FLOWMETERS WORK

DP flowmeters, also called differential producers, are the most common type offlowmeter used and account for just over half of all industrial flow measurements.Flowmeters in this class measure the differential pressure ( ΔP) caused by anobstruction in the flow stream. The differential pressure is the difference inpressure between a point before the obstruction and a point after the obstruction.DP flowmeters work because of the equation of continuity and Bernoulli’s equation.The equation of continuity shows that for a steady, uniform flow, a decrease in pipediameter (A) results in an increase in fluid velocity (V):

Bernoulli’s equation states that the total of kinetic, potential, and pressure energywithin a fluid stream remains constant. If velocity increases, there must be acorresponding decrease in either pressure energy or potential energy. If weassume a horizontal pipeline, we can ignore the potential energy consideration.Therefore, according to Bernoulli’s equation, an increase in fluid velocity at therestriction will produce a corresponding decrease in pressure. The flow equationused for DP flowmeters is based on Bernoulli’s equation. Volumetric flow rate (Q)is proportional (α) to the square root of differential pressure:

DP flowmeters consist of two parts: a primary device and a secondary device. Theprimary device is placed in the process pipe to restrict the flow and create apressure drop. The secondary device measures the differential pressure andtransmits the result to a control system.



Some of the most common DP flowmeters are:

Orifice plate

Pitot tube

Flow nozzle

Venturi tube

Wedge V-cone

Rotameter

HOW VELOCITY FLOWMETERS WORK

Velocity flowmeters work by producing an output based upon fluid velocity that isproportional to the volumetric flow rate. Velocity is the speed of a fluid flowing pasta stationary point ina process pipe. Typical units used to represent velocity are ft/ sand m/s. Some of the most common velocity flowmeters are:

Magnetic flowmeter

Vortex flowmeter

Turbine meter

Ultrasonic flowmeter

Velocity flowmeters also have a primary device and a secondary device. Theprimary device generates a signal proportional to fluid velocity, while the secondarydevice interprets and transmits this signal to a control system.

HOW MASS FLOWMETERS WORK

Mass flow rate is the mass (actual weight) of a fluid that is transported through aprocess pipe per unit of time. Typical units used to represent mass flow rate arelb/hr and kg/sec.

The two most common mass flowmeters are: Coriolis mass flowmeter and Thermalmass flowmeter. True mass flowmeters measure mass flow rate directly, withoutan intermediate calculation from volume or density.

HOW POSITIVE DISPLACEMENT FLOWMETERS WORK

Volumetric flow rate is the volume of fluid that is transported through a processpipe per unit of time. Typical units used to represent volumetric flow rate aregallons per minute (gpm) and liters per hour (L/hr). Volumetric flow rate can bedetermined from the velocity of the fluid if the cross-sectional area of the processpipe is known. Positive displacement flowmeters measure the volumetric flow ratedirectly by repeatedly trapping and measuring a sample of the process fluid. The



total volume of the fluid passing through the flowmeter in a given period of time isthe product of the volume of each sample and the number of samples taken.

FLOWMETER MARKET

Just over half of all industrial flow measurements are made by DP flowmeters.Velocity flowmeters hold the second largest market share, at about 28%. Mass andpositive displacement meters are least used for industrial flow measurements.Figure 3.12 shows more specifically the percentages of industrial flowmeasurements made by each type of flowmeter.

DP Flowmeters



Orifice Plate

An orifice plate is a thin disk placed in the path of fluid flow with a sharp-edgedopening (orifice) in it. The orifice plate acts as the primary element of a DPflowmeter. Fluid velocity increases and pressure decreases as a fluid passes

through the orifice, which creates a pressure drop. The value of the pressure dropis determined by measuring the pressure before the plate at a high pressure tapand after the plate at a low pressure tap (Figure 3.13). The pressure drop istypically measured with a DP or multi-variable transmitter.



BENEFITS AND LIMITATIONS

Reliability

Industry standards, such as AGA Report No. 3, ISO 5167, and ASME MFC 3M,ensure industry-accepted measurement performance without the need for flow labcalibration. In addition, extensive research and data are available concerning theperformance of orifice plates with various process fluids and in various industries.

Accuracy

Because the discharge coefficient varies over the flow range, the accuracy of anorifice plate varies with the type of measurement device used. Dischargecoefficient is a laboratory-determined factor for a DP flow primary element. If onlydifferential pressure is measured, an accurate measurement can be expected overa 3:1 to 5:1 range. With multi-variable measurement, an accuracy of 1% of rate canbe achieved over a much wider range (6:1 to 12:1 depending on the application).

Compatibility

Orifice plates can accommodate virtually all clean fluids, although abrasive orsticky fluids may reduce accuracy and increase maintenance costs because ofclogged pressure taps or particulate matter buildup near the orifice plate. Orificeplates are compatible with most pipe sizes.

CostInitially, orifice plates are inexpensive (instrument cost only), but because theyrequire impulse lines, a three-valve manifold, and a pipe stand, the installation costis high. While orifice plates are relatively easy to maintain, maintenance costs canincrease as well because the orifice edge must be clean and sharp for optimalmeter performance. In addition, orifice plates may cause a high relative pressureloss that consumes energy and may result in higher costs.

In comparison to some velocity flowmeters, orifice plates will provide an outputover a very wide operating range.

Pitot Tube

A common pitot tube design for flow measurement consists of a cylindrical probeinserted into the process pipe. The probe is bent at a 90° angle so that it pointstoward the source of fluid flow, parallel to the pipe wall (Figure 3.14). The velocityof the moving fluid creates a high-impact pressure inside the probe. Using adifferential pressure transducer, this impact pressure is measured and compared



with the static pressure measured through a port on a surface parallel to the pipewall (usually on the probe). The differential pressure measured is proportional tothe square of the velocity of the fluid. In some pitot tube designs, both impact andstatic pressure are measured by the same device installed in one pipeline tap.

Because of its one-point velocity measurement, the accuracy of the pitot tube iseasily affected by changes in velocity profile. In order to attain an averagemeasurement, the tube must be moved back and forth in the flowstream. For thisreason, pitot tubes are most often used as a simple means for obtaining a roughmeasurement (e.g., for low- to medium-flow gas applications where high accuracyis not required).

AVERAGING PITOT TUBE

Averaging pitot tubes are also available, with designs that include several

measurement ports over the entire diameter of the pipeline (Figure 3.15). The Annubar port design yields a much more accurate flow measurement than theregular pitot tube.




Accuracy Averaging pitot tubes have good long-term accuracy (1 –3%) partially because theyhave no leading edge to wear. However, dirty fluids can clog the measurement

ports and reduce accuracy. Compared to other DP flow primary elements, pitottubes create a relatively low differential pressure, which can make measurement ofthe pressure drop difficult and may limit rangeability or turndown. In addition, pitottubes have a very low permanent pressure loss.

Compatibility Averaging pitot tubes are an insertion-type DP flow primary element that can beused in pipe sizes from 2 –72 inches. In larger lines especially, pitot tube installationis convenient and inexpensive. Some averaging pitot tubes can be used for themeasurement of fluids flowing in either direction (bidirectional capability), and canbe installed in the process pipe without shutting the process down (hot tap).

Wedge Flow Element

Wedge flow elements are inserted in the process pipe to create a wedgedobstruction on the inner wall of the pipe. A differential pressure is created as thefluid flows past the obstruction. Wedge flowmeters are usually used with remoteseals in applications where plugging of inpulse lines is a concern. When impulselines are used, heat tracing may be required on the impulse lines to preventsolidification of process fluids such as slurries and other viscous fluids (Figure3.16).


Because the wedge flow element presents no sudden changes in contour and nosharp corners, it can be used for measuring dirty fluids, slurries, and fluids at highviscosities (low Reynolds numbers) that tend to build up on or clog orifice platesand impulse lines.



V-Cone

The V-cone is a differential pressure type flowmeter with a unique design thatconditions the flow prior to measurement. Differential pressure is created by a coneplaced in the center of the pipe. The cone is shaped so that it “flattens” the fluid

velocity profile in the pipe, creating a more stable signal across wide flowdownturns. Flow rate is calculated by measuring the difference between thepressure upstream of the cone at the meter wall and the pressure downstream ofthe cone through its center.

A V-cone is normally lab-calibrated flowmeter (Figure 3.17). For users who havelimited room for straight piping requirements, the v-cone is useful because it worksequally well both with short and with long straight pipe requirements. In addition,the V-cone can be used with some dirty processes.

Venturi Tube

A venturi tube is composed of three main sections (Figure 3.18):

Converging inlet cone: The converging inlet cone gradually decreases thepipe diameter and creates a pressure drop. A high pressure tap is located atthe start of the inlet cone.

Throat: The inlet cone ends at the throat, where the low pressure tap isfound. Fluid velocity is neither increasing nor decreasing in the throat.

Diverging outlet cone: The outlet cone increases in cross-sectional area,which enables the fluid to return to very near its original pressure. The outletcone also eliminates air pockets and minimizes frictional losses.




Venturi tubes are usually used in applications that require a low pressure drop andhigh accuracy. Venturi tubes provide very low permanent pressure loss whencompared to other DP flowmeters, although they are also larger and moreexpensive. Venturi tubes work well with short straight piping requirements and,therefore, are useful for users who have limited space for straight piping. Becausethey present no sudden changes in contour, they can be used for measuring dirtyfluids and slurries that tend to build up on or clog orifice plates.

Flow Nozzle

Flow nozzles consist of two main sections (Figure 3.19):

Elliptical inlet: The flow nozzle is mounted in the pipeline so that the ellipticalentrance of the nozzle is facing the source of the fluid flow. Fluid velocityincreases as it enters the inlet and pressure decreases.

Throat: The inlet tapers to a cylindrical throat section, where the lowpressure tap is located.




AccuracyFlow nozzles retain long-term precise calibration even under severe conditions

because the exact contour of the flow nozzle is not particularly critical for accuratemeasurement. For this reason, flow nozzles are often used for measurement ofsteam flow and other high-temperature or high-velocity fluid flows where erosionmay be a problem.

Rotameter

Rotameters, also known as variable-area flowmeters, are tapered glass, plastic, ormetal tubes that must be mounted vertically (Figure 3.20). A float inside the tuberises in response to the fluid flow rate. Because the tube is tapered, pressure is

higher at the bottom, or narrow end, of the tube than at the top. The float restswhere the differential pressure between the upper and lower surfaces of the floatbalances the weight of the float. Depending on the meter design, the flowrate maybe read directly from a scale inscribed on the transparent tube or sensedelectronically. Rotameters are commonly used for indication only—that is, theyprovide only a local indication of flow and do not transmit the measurementreadings to another location.


AccuracyRotameters are not as accurate as other flowmeters, although they are highlyrepeatable. Rotameters must be removed and disassembled in order to changetheir flow range, by resetting the balance. Unlike with most flowmeters, pressureloss through a rotameter is constant throughout the flow range.



Compatibility

Rotameters are available in process pipe sizes from 1/4 –6 inches. They can betailored to specific applications by selection of various flowmeter components. Forexample, stainless steel rotameters are better for measurement of high-pressure

flows than are the glass tube rotameters. Rotameters have a Reynolds numberconstraint for liquid measurement and cannot be used with abrasive fluids. Theyhave no upstream or downstream straight piping requirements.

Maintenance and Cost

Rotameters are inexpensive and have a simple design, although they do havemoving parts that require some maintenance.

Velocity Flowmeters

Magnetic Flowmeter

Magnetic flowmeters, also called magmeters, provide obstructionless flowmeasurement that is ideal for metering any conductive process fluid. Magmetersconsist of two main components:

Sensor: The sensor generates an electronic signal.

Flow transmitter: The flow transmitter conditions the signal and sends it to aprocess control system or computer.

The operating principle of magmeters is based on Faraday’s law of induction,which states that a voltage will be induced in a conductor moving through amagnetic field (Figure 3.21):

E=kBDV

The magnitude of the induced voltage (E) is directly proportional to the conductorvelocity (V). Magnetic field coils placed on opposite sides of the pipe wall generatea magnetic field (B). As the conductive process fluid moves through the magneticfield, electrodes sense the induced voltage. The distance between electrodesrepresents the conductor width (D). An insulating liner prevents the signal from

shorting to the pipe wall. The output voltage from the magnetic flowmeter sensor isamplified and sent to a magnetic flowmeter transmitter where the signal can beconditioned and sent to a control system.




Accuracy

Magnetic flowmeters are not constrained by Reynolds number or flow profiles.They provide high accuracy and rangeability and do not contribute to pressure

loss. Voltages measured at the electrodes represent the average fluid velocity inlaminar and in turbulent flows.

Compatibility

Magnetic flowmeters provide flow measurement with a signal inherently linear tothe average volumetric flow rate regardless of fluid temperature, pressure, density,viscosity, or direction of flow. The only limitation is that the fluid must be electricallyconductive and non-magnetic. They are commonly used in applications thatcontain large particles, including highly corrosive chemicals or fibrous slurries. A

variety of construction materials provides compatibility with virtually all processfluids. Magnetic flowmeters do not measure gases or non-conductive fluids, suchas hydrocarbons, oils, or gases. Conductivity of a process fluid is expressed inmicroseimens. Typical magmeters require that process fluid conductivity measuregreater than five microseimens/cm.




Magnetic flowmeters have no moving parts, and thus require little, if any,maintenance. Occasionally, residues may deposit in the flowtube and coat theelectrode, but maintaining a higher fluid velocity would solve this problem. Older,

AC-powered magnetic flowmeters require power to be supplied at the flowtube,which consumes more energy than today’s pulsed DC-powered flowtubes. The

initial price of a magnetic flowmeter can be higher than other flow devices.Typically, an additional set of wires is required for the device to work properly—oneset to transmit the signal and one set to power the flowtube coils. The additionalwires add to normal installation costs.

Vortex Flowmeter

A vortex flowmeter is a bluff body, or shedder, placed in the fluid flow stream thatcauses vortices to form (Figure 3.22). The shedder acts as the primary device. Asthe fluid flows around the shedder, velocity increases and pressure decreases on

one side, while velocity decreases and pressure increases on the other side. Thealternating forces cause vortices to form that are picked up by the sensingmechanism. The fluid flow rate is obtained from the frequency (detected by thesensor), which is directly proportional to the velocity of the fluid.


Accuracy

In general, vortex flowmeters are highly accurate, and rangeability is commonly20:1 to 30:1. If properly sized, you may need to add a reducer to increase velocityat the part where the vortex meter is operational. Vortex meters produce only asmall pressure loss in the pipeline.

Compatibility



Vortex flowmeters are often thought of as good all-purpose flowmeters becausethey can be used with liquid, gas, or steam without recalibration. Their versatilitycan help simplify spare parts inventory and maintenance training.Vortex flowmeters have minimum requirements for velocity that vary with theviscosity and density of the measured fluid. In general, they are recommended for

measurement of fluids with Reynolds numbers over 10,000 (well-developedturbulent flow). They are not useful at very low flow rates or with fluids with verylow Reynolds numbers because of the absence of vortex formation. In addition,vortex meters are not recommended for the measurement of abrasive fluids orfibrous slurries because of the lack of vortex formation and the need to keep theshedder bar free of erosion.


Vortex flowmeters are fairly simple and have no moving parts and few connectionswhere leaks may occur. Their installation cost is low, and there is no need for themeter body to be winterized.

Turbine Flowmeter

Turbine flowmeters consist of a section of pipe that contains a multi-blade rotor anda magnetic pickup coil (Figure 3.23). The entire fluid to be measured enters theflowmeter and passes through the rotor, which then turns at a velocity that isproportional to the fluid velocity. The magnetic pickup probe converts the rotorvelocity to an output signal that has a frequency proportional to volumetric flowrate. The turbine flowmeter is based on the principle that the speed of a turbine

that is driven by a flowing fluid is proportional to the velocity of the fluid.




Accuracy

Turbine meters are high-accuracy (0.15 –0.5% of rate), highrangeability (up to 20:1)meters, although sudden flow surges could cause large calibration shifts ordamage the flowmeter.

Compatibility

Turbine meters have several applications: clean liquid and gas, custody transfer,and lubricating fluids operating at Reynolds numbers in excess of 4,000 –20,000.They are compatible with pipe sizes >1/4 inch with flow ranges of 0.06 –50,000gpm on liquids. The fluid momentum must be sufficient to operate the rotor.


Turbine meters have moving parts and thus require high maintenance and have ahigh ownership cost. One meter cannot be used for both liquid and gasapplications. Turbine meters create a high pressure loss.

Ultrasonic Flowmeter

Ultrasonic flowmeters determine flow by measuring the velocity of sound as itpasses through a fluid flowing through a pipe. Pulses from a piezoelectrictransducer travel through a moving fluid at the speed of sound and provide anindication of fluid velocity. Two different methods are currently used to make thisvelocity measurement:

Time-of-flight Doppler effect

TIME-OF-FLIGHT ULTRASONIC FLOWMETER

Time-of-flight ultrasonic flowmeters operate on the principle that the speed of anultrasonic sound wave (sound at a frequency too high to be heard by the humanear) will increase when directed with flow and decrease when directed against flow.

A simple analogy is that an airplane can travel faster when moving in the directionof the prevailing current than it can when moving against the current.

Two or more transducers, acting as primary elements, are used in transit timeflowmeters. The transducers are positioned so that a signal sent between them willtravel at an angle to the flowstream (Figure 3.24). An ultrasonic signal is sent fromthe upstream transducer to the downstream transducer and then back again. Asthe signal crosses the flowstream to the downstream transducer, its velocityincreases. As the signal travels back, its velocity decreases. The difference in timetaken for signals to move upstream and downstream is a direct measure of fluidvelocity and the basis for a volumetric flow rate measurement.



DOPPLER EFFECT ULTRASONIC FLOWMETER

The Doppler effect refers to the change in the frequency of sound waves. Thefrequency increases or decreases based on the velocity of the fluid. A commonexample of the Doppler effect is the change in the pitch of a train whistle as thetrain passes at high speed.

Doppler effect flowmeters direct an ultrasonic beam of known frequency into thepipeline, usually at an angle (Figure 3.25). Moving solids, bubbles, or particles in

the flow stream reflect the ultrasonic beam back to a receiver. Because theseparticles are moving, the frequency of the reflected beam is shifted away from theoriginal frequency of the transmitted beam. Flowmeter electronics detect the shift infrequency, calculate fluid velocity, and use the velocity measurement as the basisfor a volumetric flow rate calculation.




Design Options

Ultrasonic flowmeters are available in a variety of styles and configurations. Inwetted designs, the transducers are exposed to the process fluid. Wetted designsmay be more sensitive than noninvasive meters because the ultrasonic signal doesnot have to pass through a pipe wall. Noninvasive flowmeters use strap-on or bolt-on transducers that mount on existing piping.

Accuracy

Newer ultrasonic flowmeters with a multipath, microprocessor-based, spool design

are achieving good results in gas measurements and are gaining wideracceptance. The clamp-on design meters have had mixed success.Proper installation of ultrasonic flowmeters is essential for optimal performance.

Accuracy depends on the design of the flowmeter, and is typically as follows:

Multipath—0.5%

Wetted—1 to 2%

Clamp on—3 to 10%

Ultrasonic flowmeters have a rangeability of 20:1 –50:1, and because they presentno obstruction to flow, there is no pressure loss in the pipeline.

Compatibility

Ultrasonic flowmeters can measure liquids or gases, depending on the flowmeterdesign. Fluids measured must be above a certain Reynolds number as well. Thenoninvasive designs can be used for the measurement of sterile, corrosive,



erosive, or otherwise difficult or hostile fluids. Ultrasonic flowmeters arebidirectional and can be used in applications where flow direction is reversed.


The noninvasive flowmeter design provides low maintenance, easy replacement,and cost economy for large pipelines, although it may be more expensive thanother flowmeters in smaller pipes. Because it is mounted on the outside of the pipe,the noninvasive design requires no piping modifications (e.g., holes cut into thepipe). However, there are long upstream and downstream straight pipingrequirements. The ultrasonic flowmeter has a four-wire operation, which can alsoaffect cost and maintenance.

Mass Flowmeters

Coriolis Mass Flowmeter

Coriolis mass flowmeters use a curved tube as a sensor and apply Newton’sSecond Law of Motion to determine flow rate. An electromagnetic drive coil islocated in the center of the bend of the tube that causes the tube to vibrate like atuning fork (Figure 3.26).

When fluid moves through the sensor’s tubes, it is forced to take on the vertical

momentum of the vibrating tube. When the tube moves upward during the first halfof its vibration cycle, the fluid flowing into the sensor tube resists moving upwardand pushes down on the tube. The fluid has the tube’s upward momentum as ittravels around the bend and out of the tube— the fluid resists having its verticalmotion decreased by pushing up on the tube. The opposing forces of the fluid andthe vibrating tube causes the tube to twist. The twisting is referred to as the Corioliseffect (Figure 3.27). According to Newton’s Second Law of Motion, the angle of the



twist is directly proportional to the mass flow rate of the fluid flowing through thetube.


Accuracy

Coriolis mass flowmeters provide extremely accurate mass measurements that areindependent of such fluid properties as temperature, pressure, viscosity, and solidcontent, which eliminates the need for pressure and temperature compensation.

Their high accuracy makes Coriolis meters popular in many custody transferapplications and other applications that require tight control, such as chemicalprocesses and management of precious or expensive fluids. Once Coriolis metersare factory calibrated, they can be used in a variety of services withoutrecalibration.

One of the chief limitations of Coriolis meters is an inherent susceptibility to systemnoise—both hydraulic and mechanical. Because the sensors measure vibration ofthe tubes, any other influences that cause the tubes to vibrate may introduce error.Installation according to manufacturer’s guidelines, tranquilizers in the processpipe, and electronic filtering can help minimize these problems. However,conditions such as water hammer and other large disturbances must be avoided.

Compatibility

Coriolis meters are available in pipe sizes up to six inches. Coriolis meters arenoninvasive and can be used with sterile or difficult fluids and virtually any liquid or

gas flowing with sufficient mass flow rate to operate the meter. The density of low-pressure gases is usually too low to accurately operate the flowmeter. Coriolismeters have no Reynolds number constraints. One device provides multipleprocess variables, such as density, temperature, mass, and volumetric flow rate.




Coriolis meters require four-wire operation and have a very high initial cost. Theyare a low-maintenance meter and have no straight piping requirements. Coriolismeters introduce a high pressure drop.

Thermal Mass FlowmeterIn thermal mass flowmeters, part of the fluid flows through a bypass, or shunt,sensor tube. The process fluid is heated at the midpoint of the sensor tube (Figure3.28). The flowmeter measures the temperature of the fluid at resistancetemperature detectors (RTDs) located upstream and downstream of the meter. Thetemperature variation (change in temperature between the two points upstreamand downstream of the meter) is inversely proportional to mass flow rate.


Accuracy

In general, thermal mass flowmeters provide good measurement accuracy: ±0.5%of full scale for liquids and ±1.0% of full scale for gases. However, accuracy varieswith changes in fluid specific heat. With a constant specific heat, thermal mass

meters provide mass flow measurement without pressure or temperaturecorrection. They also have a widerangeability (50:1 –100:1) and high repeatability(±0.2% of rate). Thermal meters cause a significant pressure drop.

Compatibility



Thermal mass flowmeters are widely available as pressure and flow controllers.They can measure fluids with pressures up to 5,800 psi (liquids) and 1,500 psi(gases). However, thermal meters are generally limited to fluids with viscositiesunder 200 cp. In addition, thermal meters have a temperature maximum of 150 °F(66 °C).

Positive Displacement Flowmeters

An oval gear meter is an example of a positive displacement meter. Oval gearmeters consist of two touching oval gears that rotate as fluid flows through them.The gears trap a known quantity of fluid as they rotate (Figure 3.29). Eachcomplete revolution of both gears represents the passage of four times (4×) theamount of fluid that fills the space between the gear and the meter body.Therefore, the volumetric flow rate is directly proportional to the rotational velocityof the gears.


Accuracy

Positive displacement flowmeters can provide high accuracy (0.25 –0.5% of rate)and repeatability in many applications, although errors can be introduced by slip(leakage) around the gears.

Compatibility

Positive displacement flowmeters are mechanical devices with many moving parts

that are prone to wear and cannot be used with dirty or gritty fluids. To eliminatewear from excessive friction, the process fluid should have good lubricatingproperties.

Positive displacement flowmeters are recommended for use with high-viscosityfluids, which tend to seal small clearances and reduce slip. However, if a fluidresidue coats the inner chambers of the meter, the fluid volume is reduced, thusproducing an error.




Positive displacement flowmeters have a moderate amount of maintenancebecause of their moving parts, but have no upstream or downstream straight piping

requirements. Because positive displacement meters are self-powered, theyextract some energy from the fluid stream, which may result in a high pressureloss.

flow fundamentals

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