pressure calibration

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TRIGON Management & Industrial Corp.

Training Module 5

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ContentsContents

Topics: Slide No:• Why measure pressure? 3• What is pressure? 4 - 5• Pressure terminology 6 - 11• Inferring non-pressure variables 12 - 29• Pressure measurement technology 30 - 44• Pressure calibrators 45• Exercises 46 - 48

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Why measure pressure?Why measure pressure?4 Common Reasons4 Common Reasons

Safety• prevent pressurized pipes & vessels from burstingProcess Efficiency• variation of pressure below or above a set-point will result in

scrap rather than useable product in some manufacturing process

Cost Saving• preventing unnecessary expense of creating more pressure or

vacuum than is required saves moneyInferred Measurement of Other Variables• rate of flow through a pipe• level of fluid in a tank• density of fluid • how two or more liquids in a tank interface

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Pressure terminologyPressure terminologyEngineering UnitsEngineering Units

Pressure is defined as FORCE applied over a unit AREA.

P = F/AExamples of pressure units:Units of force per unit areaPascals Pa N / m2 (Newtons / square metre)psi lbs/in2 (Pounds / square inch)Bar Bar = 100,000 Pa

Units referenced to columns of liquidsins. water gauge in H2Omm water gauge mm H2O

ins. mercury in Hg mm mercury mm Hg

Atmosphere atm

Pressure applied by a 1 inch column of mercury with a density of 13.5951 g/cm³.

Pressure exerted by the earth’s atmosphere at sea level (approximately 14.6959psi)

Pressure applied by a 1 inch column of water at 20°C.

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What is pressure?What is pressure?The Same Weight, Different PressureThe Same Weight, Different Pressure

Weight = 100lb

100 sq ins1 sq ins

100 sq ins 1 sq ins

Pressure = 1lb/in² Pressure = 100 lb/in²

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What is pressure?What is pressure?Liquid & Gas PressuresLiquid & Gas Pressures

LIQUIDS The pressure exerted by a liquid is influenced by 3 main factors.

1. The height of the liquid.2. The density of the liquid.3. The pressure on the surface of the liquid.

GASESThe pressure exerted by a gas is influenced by 2 main factors.

1. Volume of the gas container.2. Temperature of the gas

Note. Gases are compressible whereas liquids are not

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Pressure terminologyPressure terminologyPressure Control LoopPressure Control Loop

I/P

PT

PIC • Pressure Loop Issues:– May be a Fast Process

» Liquid» Small Volume

– May Require Fast Equipment

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Pressure terminologyPressure terminologyReference PressureReference Pressure

Atmospheric PressureApprox. 14.7 psia

AbsoluteGage Compound

RangeBarometric

Range

Total Vacuum(Zero Absolute)

Pressure

Gage(psig) - Level of pressure relative to atmospheric– Positive or negative in magnitude

Absolute(psia) - based from zero absolute pressure - no massTypical atm reference: 14.73 psia

Compound Range (psig) - Gage reading vacuum as negative value

Differential(psid) - difference in pressure between two points

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Pressure terminologyPressure terminologyQuizQuiz

?Psia 19.7 5 psig

Atm. Pressure 14.7 psia5 psi vacuum

?Psia

?Psig -5 9.7

Absolute Zero

Total Vacuum

Assume: Patm = 14.7psia; 28 inches H2O per psi

1000 in H2O = ___________ psi35.71

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Pressure terminologyPressure terminologyMeasurable PressuresMeasurable Pressures

The four most common types of measurable pressures used in the process control industries are:

1. Head Pressure or Hydrostatic Pressure.Head Pressure or Hydrostatic Pressure.Pressure exerted by a column of liquid in a tank open to atmosphere, HEAD PRESSURE = HEIGHT x DENSITY

2. Static Pressure, Line Pressure, or Working pressureStatic Pressure, Line Pressure, or Working pressurePressure exerted in a closed system

3. Vapor PressureVapor PressureThe temperature at which a liquid boils, or turns into a vapor varies depending on the pressure. The higher the pressure, the higher the boiling point.

4. VacuumVacuumAbsolute pressure below atmospheric pressure ( a compound range gage transmitter will read a negative pressure)

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Pressure terminologyPressure terminologyMeasurable PressureMeasurable Pressure

Typical Vapor Pressure Curve

Pres

sure

(log) liquid

gasHigher Altitute

Lower Altitute(Sea Level)

T1 T2

Vapor pressure increases with temperature. • Liquid boils when its vapor pressure equals

atmospheric pressure.

Temperature

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Inferring nonInferring non--pressure variablespressure variablesFlowFlow

Flow Restriction in Line cause a differential Pressure

Line Pressure

Orifice Plate

QV= K DP

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Theoritical equations come from 3 sources:

Continuity Equation• Flow into pipe equals flow out of pipe and is the same at all pipe

cross sections (Conservation of Mass)

Bernoulli’s Equation• (Conservation of Energy for fluid in a pipe)

Experimentally Determined Correction Factors• Discharge Coefficient• Gas Expansion Factor

Qm= K DP

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Continuity EquationThe volume flowing into a pipe equals the volume flowing out of pipe, assuming constant density

FlowA1V1 Flow

A1v1 = A2v2A = area of pipe cross sectionv = velocity

A2V2

v1 = A2/A1 x v2 ⌫ πd2/4 x πD2/4 v1 = d2/D2 x v2 ⌫ d/D = βv1 = β2 x v2

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Bernoulli’s EquationThe total energy before the restriction in the pipe

⌫ cancel - off for level pipe

Three energies:Kinetic (1/2ρv2)Potential (ρgh)Static Pressure (P)

v1 v2

P1

must equal the total energy after the restriction.P2

Flow D d

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P 1 P 2..1

2ρ v 2

2 ..12

ρ v 12

P1 ..12ρv1

2 ..ρg h1 P2 ..12ρv2

2 ..ρg h2Before restriction After restriction

common

2 / ρ x dP = v22 - v1

2 V12 = (β2 x V2)2

2 / ρ x dP = v22 - β4 x v2

2

2 / ρ x dP = (1- β4)v22

common

dP = ½ ρ (v22 - v1

2)

subject

Re-arrangedv22 = (2 / ρ x dP) / (1- β4)

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v2 = [(2 / ρ x dP) / (1- β4)] ½

v2 = (2)½ x (1/ρ)½ x 1/ (1- β4)½ x (dP)½

Qv2 = A2 x v2

Qv2 = (πd2/4) x (2)½ x (1/ρ)½ x 1/ (1- β4)½ x (dP)½

constant constant assumed constant

velocity of approachconstant - “E”

Volumetric Flow Qv2 = k (dP/ρ)½

Mass Flow k (dP/ρ)½ x ρ Qm2 = k (dP x ρ)½

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(i) What would be the differential at 10m³/s?

Quiz:If an orifice plate creates a differential of 50 kPa at 30m³/s

(ii) What would be the flow rate at 30kPa differential?

Qv = K √DP

Qv1 √DP1--- = ----Qv2 √DP2

30/10 = √50/ √DP2

Qv = K √DP

Qv1 √DP1--- = ----Qv2 √DP2


30/Qv2 = √50/ √30

Qv2 = 23.26m³/sDP2 = 5.6kPa

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Inferring nonInferring non--pressure variablespressure variablesLevelLevel

H

P P P P

D

Liquid

Hydrostatic Pressure - The liquid will rise to the same level in each vessel regardless of its diameter & shape.

Unit Area (eg. per cm2)

Which shape gives higher pressure at the bottom of the vessel?

Similar height of column will have same mass acting on the same unit area

SAME PRESSURE

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The hydrostatic pressure exerted by the column of liquid depends on the S.G. (or density) of the liquid and its vertical height.Density of liquid = DAverage cross-section area of vessel = AVertical height of liquid = HVolume of liquid, V =Total weight of liquid, M =

=Pressure at the bottom of liquid = weight of liquid

cross-section area==

H x AD x V

A x H

D x HS.G x H

D x

(D x A x H) / A

With reference to inches or mm WATER

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P = r x g x height x area / area

mass x g

r x volume

P= force / area

g = gravitational acceleration

height x area

Phead = r x g x h Pascal

Density = mass/volume = r

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XMTR

HL

Ullage or Vapor

S.G

Phead

0%

100%

Hei

ght

Cancelled off since both L & H sides of transmitter experience it.

DP Transmitter at the bottom of the tank measures HEAD.HEAD = pressure at the bottom of a column of liquid with known relative density (S.G)Phead = S.G x Height

Height = Phead / S.G

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Quiz: Open TankWhat is the level if Pmax = 120 inH2O, s.g.= 1.2?

?Height = Phead / S.G

Height = 120 / 1.2XMTR

Height = 100 inchesL H

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Quiz: Closed TankDry leg: no fluid in low side impulse piping, or legPh = 105 psiPl = 100 psiWhat is level if s.g. = 1.0?

Phead

Ptop= Ullage

dP = 5 psi = 5 x 28 inH2O XMTRHeight = 140 / 1.0L H

Height = 140 inches

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Inferring nonInferring non--pressure variablespressure variablesDensityDensity

Phead(top)

Pbottom

Phead(bottom)

h1

h2

H

2 - h1)

diff. Pressure / dist. betw. taps

PtopPbottom =

Ptop =

Pbottom - Ptop =

Hence,

S.G =

S.G (h

S.G X h2

PtopS.G X h1

H

Liquid level must be above the Top transmitter tap.

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Inferring nonInferring non--pressure variablespressure variablesDensityDensity

Pbottom

Ptop

50”

H

H

Quiz:Determined the S.G of the process fluid if Ptop = 20 psiPbottom = 22 psiDistance between taps = 50 inchesAssuming 1 psi = 28”H2O

S.Gprocess = DP / dist. betw. Taps= 56 / 50= 1.12

DP = (22 -20) = 2 psi = 56”H2O

Ullage

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Inferring nonInferring non--pressure variablespressure variablesInterfaceInterface

Indirectly measures liquid Interface

Pbottom

Ptop

L H

Remote Seal

Vapor

0%

100%

SG1

SG2

Dist. Betw. Taps

(h1 - h2)

Total Liquid level must always be above the Top transmitter tap.

SGf

h1

h2

At 0% Liquid Interface (4mA)

DP = Hside - Lside

= (SG1*h1) - [(SGf*(h1-h2)) + (SG1*h2)]

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Indirectly measures liquid Interface

Total Liquid level must always be above the Top transmitter tap.

Pbottom

Ptop

L H

Vapor

0%

100%

h1

h2

Remote Seal SG1

SGf

Dist. Betw. Taps

(h1 - h2)

SG2

At 100% Liquid Interface (20mA)

DP = Hside - Lside

= [SG2*(h1-h2) + SG1*h2)] - [(SGf*(h1-h2)) + (SG1*h2)]

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Application Example:

• Transmitter calibrated from 120”H2Oto 132”H2O

• Determine % of interface of Liquid A with respect to Liquid B

Vapor

0%

100%

SG1= 1.0

SG2= 1.1

Pbottom

Ptop

L H

Remote Seal

10 ft

Liquid A

Liquid BIf transmitter reads 123 inH2O

% interface = (3/12) * 100%= 25%

123 inH2O

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Pressure measurement technologyPressure measurement technologyPressure IndicatorsPressure Indicators

BarometerUsed to measure Barometric Pressure

Reference is 0 psia, due to low vapor pressure of Hg.General operating principle:

PheadPatm

Barometric Pressure = Atmospheric Pressure

29.9 inHgWhat is the barometric Pressure?

• Tube completely filled with mercury & Invert into the container filled with mercury.

• The mercury level in the tube will drop until it reaches an equilibrium.

• This equilibrium height is a measure of atmospheric pressure. Phead = Patm

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Pressure measurement technologyPressure measurement technologyPressure IndicatorsPressure Indicators

ManometersU-tube with one side reference, one side measured pressure

H

dP = H (SGfill fluid - SGprocess fluid)How to check for dP ?– Reference side can be:

• Sealed (AP reference)• Open to atmosphere(GP reference)• Connected to reference pressure(DP reference)

– Typically used for low pressures, non process control

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Pressure measurement technologyPressure measurement technologyPressure GaugesPressure Gauges

Mechanical

The mechanical element techniques convert applied pressure into displacement.

The displacement may be converted into electrical signal with help of Linear Variable Displacement Transformer (LVDT).

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Pressure measurement technologyPressure measurement technologyPneumatic Pressure CellsPneumatic Pressure Cells

Output to Actuator (or Relay)Constant flowrate maintained

(Compressed air)

NozzleFlapper

Bourdon Tube

Process Pressure

Pneumatic ControllerRelay’s modulated output is the controller output which is usually a pneumatic signal that adjusts the final control element (Control valve)

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Pressure measurement technologyPressure measurement technologyPneumatic Pressure CellsPneumatic Pressure Cells

Pressure TransmitterProduce a linear output proportional to input pressure

Zero Scale: Full Scale:

3 psig15 psig

Disadvantages– Reconfiguration costly– Losses occur over long

piping runs– Performance levels are not

comparable to electronic instrumentation

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Pressure measurement technologyPressure measurement technologyElectronic Pressure TransmittersElectronic Pressure Transmitters

– Made up of 2 main elements:• Transducer - Electronic sensor module

that registers process variable and outputs a corresponding usable electrical signaleg. resistance, millivolts, capacitance, etc.

• Electronics - Convert transducer output to a standard output signaleg. 4 - 20 mA, 1 - 5 V dc, digital signal, etc.

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Pressure measurement technologyPressure measurement technologyElectronic Pressure TransmittersElectronic Pressure Transmitters

Example of Application

Transmitter configured to operate from:

0 to 50 psiElectronic Output:

4 to 20 mAThis mean 0% reading (0 psi) represents 4 mA and 100% reading (50 psi) represents 20 mA.

Transmitter

Signal To Controller(Standard signals)

Sensing Diaphragm

Signal fromsensor module(Transducer)

Process Variable (Line / Static Pressure)

What will be the output current at 25 psi reading?4 + (25/50)*16 = 12 mA

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Pressure measurement technologyPressure measurement technologyElectronic Pressure Sensor ModulesElectronic Pressure Sensor Modules

Characterized by the type of sensing element:

– Variable capacitance– Variable Resistance (Wheatstone bridge)

• Strain gauge» Thin -film strain gauge» Diffused, strain gauge

– Variable inductance– Variable reluctance– Vibrating wire– Piezoelectric

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Variable Capacitance

• Process pressure transmitted thru isolating diaphragm

• Distortion of sensing diaphragm proportional to the differential pressure

• Position of sensing diaphragm detected by capacitor plates

• Differential capacitance translated to 4-20mA or 10-50mA output dc signal.

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Variable Resistance / Piezo-Resistive

Thin Film Strain Gauge

Diffused Strain Gauge

• Process pressure transmitted thru isolating diaphragm• Very small distortion in sensing diaphragm• Applies strain to a wheatstone bridge circuit• Change in resistance translated to 4-20mA or 1-5V dc signal• GP XMTRs - ref. side of sensor exposed to atm. Pressure• AP XMTRs - sealed vacuum reference.

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• Piezoelectric crystal is a natural or a synthetic crystal that produces a voltage when pressure is applied to it.

• Voltage produce by crystal increases with increases in pressure and vice-versa.

• The produced small voltage is then amplified to a standard control signal.

Piezoelectric

Amplifier & electronics

Control Signal

Piezoelectric Crystal

Diaphragm

Process Pressure

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• Inductance is the opposition to a change in current flow

• Alternating current pass through the coil

• Elastic element connected to core

• Applied pressure deflects elastic element

• Position of core changes relative to coil resulting in change in inductance

• Resistor connected in series with inductor to measure change in voltage.

Variable Inductance

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Variable Reluctance• Reluctance is a property of

magnetic circuit• A moving magnetic element

located between two coils• Coil turn electromagnet when

excited by AC source• Position of element with respect to

the coils determines differential magnetic reluctance

• Thus differential inductance within the coils

• A bridge is used to measure changes in a circuit

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Vibrating Wire• Wire located in magnetic field

vibrate when current pass through it

• Wire movement within field induces current into it

• Induced voltage amplified as output signal

• Vibration frequency depends on wire tension

• Elastic element connected to wire.

• Frequency of wire vibration become a function of measured pressure

• Direct digital output signal

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– Sensor (transducer) module is part of the transmitter.– Sensor will become active only when the transmitter is

powered. (Attenuation)– Output Electronics in the transmitter translates the

userable electrical signal from the sensor into a standard output signal.

Output Electronics

Sensor Module

Output Electronics

Sensor Module

Diaphragm Seal

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Pressure calibratorsPressure calibratorsISO RequirementISO Requirement

ISO Require calibration device to be 4 times more accurate than the accuracy of the instrument being calibrated.If the reference accuracy of a 3051C transmitter is 0.075% of span,

– What should the accuracy of the C/V pressure source be?

– the equipment for calibrating the pressure source?

If the diameter of the ball on a dead weight tester is 0.75 inches. The weight of a plate is 723g.

– What is the pressure required to freely float that plate on the dead weight tester (g/cm2)?

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ExerciseExercise

1. If the atmospheric pressure drop by 0.1 % and the line pressure remains unchanged, what changes will occur in the

readings?(A) AP reading will change.(B) GP reading will change.(C) Both reading will change.(D) Both reading will not change.

[ ]

2. If a customer wants to measure vacuum, what type of transmitter should be used?(A) AP(B) DP(C) GP [ ]

Liquid flow

Line pressure = 80 psig

94.7psi 80.psi GP Transmitter

AP Transmitter

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ExerciseExercise

50 psig80 psig

c a b

Write down the readings in (psi) that are recorded by the transmitters in the above application (Atmosphere = 14.7 psi).

3. Differential Pressure Transmitter (a): [ ]

4. Gage Pressure Transmitter (b): [ ]

5. Absolute Pressure Transmitter (c): [ ]

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ExerciseExercise

S.G of Process Fluid @ Temp + Pressure = 1.0

P2P1

S.G. = 13.6200mm

(Note 1 mm H2O = 9.8 Pa)

6. What is the differential pressure (P1 - P2) in kPa being applied to the manometer in the the above application ?

pressure calibration

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