Training - Pressure1

Level 1 - Fundamental Training

Pressure 1

Level 1 Fundamental Training

1

Level 1 - Pressure 1

Contents Topics: • Why measure pressure? • What is pressure? • Pressure terminology • Inferring non-pressure variables • Pressure measurement technology • Pressure calibrators • Exercises

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Slide No: 3 4-5 6 - 11 12 - 29 30 - 44 45 46 - 48

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Why measure pressure? 4 Common Reasons

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Safety • prevent pressurized pipes & vessels from bursting

Process 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 money

Inferred 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 Level 1 - Pressure 1

What is pressure? The Same Weight, Different Pressure

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Weight = 100lb 1 sq ins

100 sq ins

100 sq ins

1 sq ins

Pressure = 1lb/in²

Pressure = 100 lb/in²

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What is pressure? Liquid & Gas Pressures

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LIQUIDS The pressure exerted by a liquid is influenced by 3 main factors. 1. 2. 3.

The height of the liquid. The density of the liquid. The pressure on the surface of the liquid.

GASES The pressure exerted by a gas is influenced by 2 main factors. 1. 2.

Volume of the gas container. Temperature of the gas

Note. Gases are compressible whereas liquids are not

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Pressure terminology Pressure Control Loop

I/P

PIC

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• Pressure Loop Issues: – May be a Fast Process » Liquid » Small Volume

– May Require Fast Equipment PT

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Pressure terminology Engineering Units

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Pressure is defined as FORCE applied over a unit AREA.

P = F/A Examples of pressure units: Units of force per unit area Pascals Pa N / m2 (Newtons / square metre) psi lbs/in2 (Pounds / square inch) Bar Bar = 100,000 Pa Units referenced to columns of liquids ins. water gauge in H2O Pressure applied by a 1 inch column of water at 20°C. mm water gauge mm H2O ins. mercury mm mercury

in Hg mm Hg

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

Atmosphere

atm

Pressure exerted by the earth’s atmosphere at sea level (approximately 14.6959psi) Level 1 - Pressure 1

Pressure terminology Reference Pressure Absolute

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Gage Compound Range Barometric Range Atmospheric Pressure Approx. 14.7 psia

Pressure

Total Vacuum (Zero Absolute)

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

Absolute(psia) - based from zero absolute pressure - no mass Typical atm reference: 14.73 psia Compound Range (psig) - Gage reading vacuum as negative value Differential(psid) - difference in pressure between two points Level 1 - Pressure 1

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Pressure terminology Quiz

9

? 19.7 Psia

5 psig

Atm. Pressure ? -5 Psig

5 psi vacuum

14.7 psia ? 9.7 Psia

Total Vacuum

Absolute Zero

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

35.71 1000 in H2O = ___________ psi Level 1 - Pressure 1

Pressure terminology Measurable Pressures

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The four most common types of measurable pressures used in the process control industries are: 1. 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 pressure Pressure exerted in a closed system 3. Vapor Pressure The 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. Vacuum Absolute pressure below atmospheric pressure ( a compound range gage transmitter will read a negative pressure) Level 1 - Pressure 1

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Pressure terminology Measurable Pressure

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Vapor pressure increases with temperature.

Higher Altitute

Pressure(log)

• Liquid boils when its vapor pressure equals atmospheric pressure. Lower Typical Vapor Pressure Curve Altitute (Sea Level) liquid gas

T1

T2

Temperature Level 1 - Pressure 1

Inferring non-pressure variables Flow

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Line Pressure Orifice Plate

Flow Restriction in Line cause a differential Pressure

QV= K

DP Level 1 - Pressure 1

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Inferring non-pressure variables Flow

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Theoritical equations come from 3 sources:

Qm= K

DP

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 Level 1 - Pressure 1

Inferring non-pressure variables Flow

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Continuity Equation The volume flowing into a pipe equals the volume flowing out of pipe, assuming constant density A1v1 = A2v2 A = area of pipe cross section v = velocity A1V1

Flow

A2V2

Flow

v1 = A2/A1 x v2

⌫

πd2/4 x πD2/4

v1 = d2/D2 x v2

⌫

d/D = β

v1 = β2 x v2 Level 1 - Pressure 1

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Inferring non-pressure variables Flow

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Bernoulli’s Equation The total energy before the restriction in the pipe must equal the total energy after the restriction. P1 P 2

Flow

v1

v2

D

Three energies: Kinetic Potential Static Pressure

d

(1/2ρv2) (ρgh) ⌫ cancel - off for level (P) pipe Level 1 - Pressure 1

Inferring non-pressure variables Flow

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P1

1. . 2 . . 1 . 2 . . ρv 1 ρg h 1 P 2 .ρv 2 ρg h 2 2 2

Before restriction P 1

P 2

1. . 2 ρ v2 2

After restriction

1. . 2 ρ v1 2

common

dP = ½ ρ (v22 - v12) 2 / ρ x dP = v22 - v12

V12 = (β2 x V2)2

2 / ρ x dP = v22 - β4 x v22

common

2 / ρ x dP = (1- β4) v22

subject

v22 = (2 / ρ x dP) / (1- β4)

Re-arranged Level 1 - Pressure 1

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Inferring non-pressure variables Flow

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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 approach constant - “E”

Volumetric Flow

Qv2 = k (dP/ρ)½

Mass Flow

Qm2 = k (dP x ρ)½

k (dP/ρ)½ x ρ

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Inferring non-pressure variables Flow

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Quiz: If an orifice plate creates a differential of 50 kPa at 30m³/s (i) What would be the differential at 10m³/s?

(ii)

What would be the flow rate at 30kPa differential?

Qv = K √DP

Qv = K √DP

Qv1 --Qv2

Qv1 --Qv2

√DP1 = ---√DP2

√DP1 = ---√DP2

30/10 =

√50/ √DP2

30/Qv2 = √50/ √30

DP2

5.6kPa

Qv2 = 23.26m³/s

=

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Inferring non-pressure variables Level

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

Unit Area (eg. per cm2)

Liquid

D

H P P

P

P

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

Level 1 - Pressure 1

Inferring non-pressure variables Level

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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 Average cross-section area of vessel Vertical height of liquid Volume of liquid, V Total weight of liquid, M Pressure at the bottom of liquid

With reference to inches or mm WATER

=D =A =H =H x A =D x V =D x A x H = weight of liquid cross-section area = (D x A x H) / A = D x H

S.G x H

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Inferring non-pressure variables Level

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P= force / area mass x g

g = gravitational acceleration Density = mass/volume = r

r x volume

height x area

P

=

Phead =

r x g x height x area / area r x g x h Pascal Level 1 - Pressure 1

Inferring non-pressure variables Level

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

Height =

Phead / S.G

Ullage or Vapor 100% S.G

Phead

Height

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

XMTR 0% L

H

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Inferring non-pressure variables Level

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

?

Height = Phead / S.G Height = 120 / 1.2 XMTR

Height = 100 inches L

H

Level 1 - Pressure 1

Inferring non-pressure variables Level

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Quiz: Closed Tank Dry leg: no fluid in low side impulse piping, or leg Ph = 105 psi Pl = 100 psi What is level if s.g. = 1.0?

Ptop= Ullage

Phead dP = 5 psi = 5 x 28 inH2O Height = 140 / 1.0

XMTR L

H

Height = 140 inches Level 1 - Pressure 1

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Inferring non-pressure variables Density

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Ptop

= S.G X h2

Pbottom Ptop

=

S.G X h1

Ptop

S.G (h2 - h1)

Phead(top) h1 H

h2

Pbottom - Ptop = Hence,

Phead(bottom)

H Pbottom diff. Pressure / dist. betw. taps

S.G = Liquid level must be above the Top transmitter tap. Level 1 - Pressure 1

Inferring non-pressure variables Density

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Quiz: Determined the S.G of the process fluid if Ptop Ptop = 20 psi Pbottom = 22 psi H Distance between taps = 50 inches Assuming 1 psi = 28”H2O

Ullage

50”

DP = (22 -20) = 2 psi = 56”H2O P H bottom S.Gprocess

= DP / dist. betw. Taps = 56 / 50 = 1.12 Level 1 - Pressure 1

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Inferring non-pressure variables Interface

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Indirectly measures liquid Interface

SGf

Remote Seal

Vapor

Ptop

h2

h1

Dist. Betw. Taps (h1 - h2)

L

H

SG1 100% Total Liquid level must always be above the Top transmitter tap. 0% SG2

Pbottom

At 0% Liquid Interface (4mA) DP

= Hside - Lside = (SG1*h1) - [(SGf*(h1-h2)) + (SG1*h2)] Level 1 - Pressure 1

Inferring non-pressure variables Interface

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Indirectly measures liquid Interface

SGf

Remote Seal

Vapor

Ptop

h2

SG1 100% Total Liquid level must always be above the Top transmitter tap.

h1

Dist. Betw. Taps (h1 - h2)

0% L

H

Pbottom

SG2

At 100% Liquid Interface (20mA) DP

= Hside - Lside = [SG2*(h1-h2) + SG1*h2)] - [(SGf*(h1-h2)) + (SG1*h2)] Level 1 - Pressure 1

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Inferring non-pressure variables Interface

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Application Example: • Transmitter calibrated from 120”H2Oto 132”H2O • Determine % of interface of Liquid A with respect to Liquid B If transmitter reads 123 inH2O % interface 123 inH2O = (3/12) * 100% = 25%

Remote Seal

Vapor

SG1= 1.0

Ptop 100%

Liquid B

10 ft L

H

Pbottom

SG2= 1.1 0%

Liquid A

Level 1 - Pressure 1

Pressure measurement technology Pressure Gauges

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Barometer Used to measure Barometric Pressure Reference is 0 psia, due to low vapor pressure of Hg. General operating principle: • 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. P =P head

atm

Patm

Phead

Barometric Pressure = Atmospheric Pressure

What is the barometric Pressure?

29.9 inHg Level 1 - Pressure 1

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Pressure measurement technology Pressure Gauges

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Manometers U-tube with one side reference, one side measured pressure H

How to check for dP ? –

–

dP = H (SGfill fluid - SGprocess

fluid)

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 Level 1 - Pressure 1

Pressure measurement technology Pressure Gauges

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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 technology Pneumatic Pressure Cells

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Pneumatic Controller Relay’s modulated output is the controller output which is usually a pneumatic signal that adjusts the final control Process Pressure element (Control valve) Flapper Nozzle

Bourdon Tube

Output to Actuator (or Relay) Constant flowrate maintained (Compressed air) Level 1 - Pressure 1

Pressure measurement technology Pneumatic Pressure Cells

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Pressure Transmitter Produce a linear output proportional to input pressure Zero Scale: Full Scale:

3 psig 15 psig

Disadvantages – Reconfiguration costly – Losses occur over long piping runs – Performance levels are not comparable to electronic instrumentation Level 1 - Pressure 1

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Pressure measurement technology Electronic Pressure Transmitters

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– Made up of 2 main elements: • Transducer Electronic sensor module that registers process variable and outputs a corresponding usable electrical signal eg. resistance, millivolts, capacitance, etc. • Electronics Convert transducer output to a standard output signal eg. 4 - 20 mA, 1 - 5 V dc, digital signal, etc. Level 1 - Pressure 1

Pressure measurement technology Electronic Pressure Transmitters (Standard signals)

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Example of Application

Signal To Controller

Transmitter Signal from sensor module (Transducer)

Sensing Diaphragm

Process Variable

Transmitter configured to operate from: 0 to 50 psi Electronic Output: 4 to 20 mA This mean 0% reading (0 psi) represents 4 mA and 100% reading (50 psi) represents 20 mA.

(Line / Static Pressure)

What will be the output current at 25 psi reading? 4 + (25/50)*16 = 12 mA Level 1 - Pressure 1

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Pressure measurement technology Electronic Pressure Sensor Modules

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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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Pressure measurement technology Electronic Pressure Sensor Modules

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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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Pressure measurement technology Electronic Pressure Sensor Modules

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Variable Resistance / Piezo-Resistive • • • • • •

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.

Thin Film Strain Gauge

Diffused Strain Gauge Level 1 - Pressure 1

Pressure measurement technology Electronic Pressure Sensor Modules

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Process Pressure

Piezoelectric • 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 Crystal Control Signal

Diaphragm

Amplifier & electronics Level 1 - Pressure 1

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Pressure measurement technology Electronic Pressure Sensor Modules

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Variable Inductance • 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. Level 1 - Pressure 1

Pressure measurement technology Electronic Pressure Sensor Modules

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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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Pressure measurement technology Electronic Pressure Sensor Modules

43

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 Level 1 - Pressure 1

Pressure measurement technology Electronic Pressure Sensor Modules Output Electronics

Sensor Module

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Output Electronics

Diaphragm Seal

Sensor Module

– 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. Level 1 - Pressure 1

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Pressure calibrators ISO Requirement

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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)? Level 1 - Pressure 1

Exercise

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1. If the atmospheric pressure drop by 0.1 % and the line pressure remains unchanged, what changes will occur in the readings? 80.psi GP AP 94.7psi (A) AP reading will change. Transmitter Transmitter (B) GP reading will change. Line pressure = 80 psig (C) Both reading will change. Liquid flow (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 [ ] Level 1 - Pressure 1

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Exercise

47

c

a

80 psig

b

50 psig

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):

[

]

Level 1 - Pressure 1

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

48

P1

P2

200mm

S.G. = 13.6

(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 ?

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