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1
DP Flow Introduction
TO PI C
PAGE
1.1
Introduction ............................................... 10
1.2
Objectives ................................................... 10
1.3
History of DP Flow ..................................... 10
1.4
Pressure ..................................................... 11
1.5
DP Flow 101 ............................................... 12
1.6
DP Flow Measurement Applications ......... 15
1.7
Flowmeter Installations ............................. 15
1.8
Alternate Flow Technologies ...................... 17
1.9
Summary .................................................... 17
1 – DP Flow Introduction
1.1 INTRODUCTION
This book focuses on practical engineering problems
and challenges. That said, the elements of theory
found here are crucial to the successful engineering of
most DP Flow solutions.
1.1.1 Differential Pressure
Flow Measurement
1.3 HISTORY OF DP FLOW
Differential pressure flow measurement (DP Flow) is
one of the most common technologies for measuring
flow in a closed pipe. Flow rate of the fluid in the pipe
is derived from the pressure differential between the
upstream (high) side and downstream (low) side of an
engineered restriction in the pipe.
Flow measurement in general began thousands of
years ago. Ancient Egyptians made approximate
predictions of harvests based on the relative level of
spring floods of the Nile. Centuries later, as Romans
engineered aqueducts to convey water into their
cities for sustenance, baths and sanitation, the need
to monitor steady flow became important. Operators
used flow through an orifice or the welling of water
over obstructions to roughly gauge flow rates. Marks
on the walls of the flow stream, strength of the stream
through the orifice or other methods gave a rough idea
of flow rates.
There are many reasons for the wide usage of DP Flow
technology:
• Its technology is based on well-known laws of
physics, particularly around fluid dynamics and
mass transport phenomena
• Its long history of use has also led to the
development of standards for manufacture
and use of DP flowmeters
• Manufacturers offer a large catalog of both
general and application-specific instrumentation
and installation choices
• Finally, DP Flow technologies can achieve high
accuracy and repeatability
Advancements toward measured, repeatable flow
metering increased after Newton’s discovery of the law
of gravitation in 1687. This concept enabled physicists
and mathematicians to begin to formulate a broad
range of theories and hypotheses around motion
and force. These in turn helped develop a range of
instruments that quantified flow volumes and rates.
1.3.1 Bernoulli
1.2 OBJECTIVES OF THIS BOOK
Swiss mathematician Daniel Bernoulli (1700-1782),
whose study of hydrodynamics centered on the
principle of conservation of energy, provided the first
key breakthrough in the development of technologies
for flow measurement.
This handbook is intended to help engineers and
process technicians bring all the elements of DP Flow
together in a comprehensive reference. The book will
present enough theory and technical background to
provide a solid context for engineering, procurement,
and configuration of DP Flow technologies. This
includes the following:
Bernoulli strove to discover as much as possible
about the flow of fluids and his work led to the
development of what is known as Bernoulli’s Principle.
This states that for a hypothetical fluid with no
viscosity, an increase in the speed of the fluid creates a
simultaneous decrease in the fluid’s potential energy.
• The necessary equations and calculations
commonly needed for developing DP Flow
systems
• A full discussion of components commonly
found in DP Flow systems in gas, liquid, and
steam applications
• Discussions of DP Flow instrumentation
technologies found in primary elements
and transmitters
• Common uses including the challenges and
points to consider with specific applications
• Installation guidelines
• Maintenance and calibration procedures
Conservation of energy is the basis for DP Flow
measurements. The Bernoulli principle says that the
sum of all energy in the fluid flow—remains constant
regardless of conditions. When the speed of the fluid
increases, its static pressure and potential energy
decrease, while its dynamic pressure and kinetic
energy increase.
10
1 – DP Flow Introduction
Bernoulli’s principle dictates that the total pressure
within a system is equivalent to the summation of its
dynamic and static pressures.
Most famously, he studied the flow of fluids in pipes,
and more specifically, the conditions under which the
flow transitions from laminar flow to turbulent flow.
Out of this was created the dimensionless Reynolds
number (Re).
Mathematically in the simplest terms, this is expressed
in Bernoulli’s equation:
The Reynolds number quantifies the relation of inertial
forces to viscous forces, thus:
(1.1)
Where:
q
p
p0
= Dynamic pressure
= Static pressure
= Total pressure
(1.2)
Reynolds number quantifies the relative importance
of these two types of flow forces in a given flow
condition.
Much more detail on Bernoulli’s equation can be found
in the next chapter. Bernoulli’s equation describes the
conservation of hydraulic energy across a constriction
in a pipe. It states that the sum of the static energy
(pressure), kinetic energy (velocity), and potential
energy (elevation) upstream and downstream of the
constriction are equal.
Because Reynolds number describes the flow regime
of a fluid, under certain conditions it is central to
designing and operating DP flowmeters. Specifically,
Reynolds number can be applied as a constraint on
the range of a flowmeter’s applicability. Operating
a flowmeter outside of its Reynolds number range
constraints can degrade accuracy.
In the years since Bernoulli, many follow-on
expressions of Bernoulli-based equations have been
developed. These capture the behaviors of a broad
range of compressible and incompressible liquids in
many types of applications.
1.4 PRESSURE
The most critical background concept in the domain of
DP Flow is pressure.
Much has been developed from Bernoulli’s work. For
example, flow over an airfoil, the mechanism of lift,
harnesses Bernoulli’s principle in aircraft. Flow through
a restriction, while named for another researcher,
Giovanni Battista Venturi (1746-1822), exhibits
Bernoulli’s principle in carbureted internal combustion
engines, where the pressure drop across a venturi
sucks gasoline into the air stream entering the engine.
Accurate measurement of liquid, gas, and steam
pressure is basic to many industrial processes. A
typical plant will use more pressure measurement
and pressure control devices than all other types of
measurement and control instruments combined.
1.4.1 What Is Pressure?
1.3.2 Reynolds
Pressure is the amount of force applied over a defined
area.
Osborne Reynolds (1842-1912) is a second key
researcher who contributed significantly to the
theoretical development of DP Flow technologies.
The Pressure Equation
The relationship between pressure, force, and area is
represented in the following formula:
Reynolds was not a physicist but a student of
mechanics. His work began with the practical
steamfitting of ships, though he progressed to an
astonishing array of studies. Among them are the
mechanism of the drag of ships in water, condensation
of steam, propeller design, turbine propulsion design,
and hydraulic brakes.
(1.3)
11
Where:
P
F
A
= Pressure
= Force
= Area
1 – DP Flow Introduction
1.5 DP FLOW 101–THE ROOTS
(SQUARED)
If a force is applied over an area, pressure is being
applied. Pressure increases if the force increases, or the
size of the area over which the force is being applied
decreases.
1.5.1 What Is Flow?
Why Measure Pressure?
Four of the most common reasons that process
industries measure pressure are:
Flow theory is the study of fluids in motion. A fluid is
anysubstance that can flow, and thus the term applies
to both liquids and gases. Precise measurement and
control of fluid flow through pipes requires in-depth
technical understanding, and is extremely important
in almost all process industries.
• Safety
• Process efficiency
• Cost savings
• Measurement of other process variables
1.5.2 Key Factors of Flow Through
Pipes
Safety: Pressure measurement helps prevent
overpressurization of pipes, tanks, valves, flanges,
and other equipment; minimizes equipment damage;
controls levels and flows; and helps prevent unplanned
pressure or process release or personal injury.
There are 5 factors that are key to flow:
1. Physical piping configuration
2. Fluid velocity
3. Friction of the fluid along the walls of the pipe
4. Fluid density
5. Fluid viscosity
6. Reynolds Number
Process Efficiency: In most cases, process efficiency is
highest when pressures (and other process variables)
are maintained at specific values or within a narrow
range of values.
Piping Configuration: The diameter and crosssectional area of the pipe enables both the
determination of fluid volume for any given length
of pipe and is included in the determination of the
Reynolds number for a given application.
Cost Savings: Pressure or vacuum equipment (e.g.,
pumps and compressors) uses considerable energy.
Pressure optimization can save money by reducing
energy costs.
Velocity: Depends on the pressure or vacuum that
forces fluid through the pipe.
Measurement of Other Process Variables: Pressure
is used to measure numerous processes. Pressure
transmitters are frequently used in a number of
applications, including:
Friction: Because no pipe is perfectly smooth, fluid in
contact with a pipe encounters friction, resulting in a
slower flow rate near the walls of the pipe compared to
at the center. The larger, smoother, or cleaner a pipe,
the less effect on the flow rate.
• Flow rates through a pipe
• Level of fluid in a tank
• Density of a substance
• Liquid interface measurement
Density: Density affects flow rates because the more
dense a fluid, the higher the pressure required to
obtain a given flow rate. Because liquids are (for all
practical purposes) incompressible and gases are
compressible, different methodologies are required to
measure their respective flow rates.
The square root of the differential pressure across
a restriction in a pipe is proportional to flow. This is
expressed mathematically as:
(1.4)
Where:
Q
∝
ΔP
Viscosity: Defined as the molecular friction of a fluid,
viscosity affects flow rates because in general, the
higher the viscosity more work is needed to achieve
the desired flow rates. Temperature affects viscosity,
but not always intuitively. For example, while higher
temperatures reduce most fluid viscosities, some
fluids actually increase in viscosity above a certain
temperature.
= Flow rate
= (signifies proportionality)
= Differential pressure
12
1 – DP Flow Introduction
Reynolds Number: By factoring in the relationships
between the various factors in a given system,
Reynolds number can be calculated to describe the
type of flow profile. This becomes important when
choosing how to measure the flow within the system.
Volume can be broken down to area multiplied by
length:
(1.6)
Where:
There are three different flow profiles that are defined
by different Reynolds number regimes. Laminar
flow, Reynolds number below 2000, is a smooth flow
in which a fluid flows in parallel layers. It is usually
characterized with low velocities, very little mixing,
and sometimes high fluid viscosity. When a fluid’s
flow profile has a Reynolds number between 2000
and 4000, it is in a transitional zone. A Reynolds
number above 4000 is called turbulent flow. This is
characterized by high velocity, low viscosity, and rapid
and complete fluid mixing.
A
s
= Area
= length
Flow can thus be expressed as:
(1.7)
This can be further simplified, since length divided by
time yields velocity:
Best accuracy in DP Flow metering occurs with
turbulent flow, where Reynolds number is greater
than 4000 (varies primary element to element). This is
because in turbulent flow, the point at which the fluid
separates from the edge of the flow restriction is more
predictable and consistent. This separation of the fluid
creates the low pressure zone on the downstream
side of the restriction, thus allowing that restriction
to function as the primary element of a DP meter.
Depending on the type of restriction and design of
the flowmeter, the minimum pipe Reynolds number
at which a specific meter should be operated can be
considerably higher than 4000.
(1.8)
Substituting velocity for s/t:
(1.9)
This yields the simplest representation of equation.
(1.10)
1.5.3 Flow Continuity
Hence,
When liquid flows through a pipe of varying diameter,
the same volume flows at all cross sectional slices. This
means that the velocity of flow must increase as the
diameter decreases and, conversely, velocity decreases
when the diameter increases.
(1.12)
(1.13)
Volumetric flow equates to the volume of fluid divided
by time:
(1.5)
Where:
Q
V
t
(1.11)
= Volumetric flow rate
= Volume
= Time
Figure 1.5.3.a - Graphical representation of the simplest
representation of the flow law where Q1 = Q2.
13
1 – DP Flow Introduction
1.5.5 Primary Element Types
The derivation of flow continuity above describes the
basic principle of energy conservation. The Bernoulli
equation, which will be covered in more detail in
Chapter 3, builds on this principle to define the energy
conservation appropriate for flowing fluid.
There are many kinds of primary elements:
• Single hole and conditioning orifice plates
• Single and multiple-port pitot tubes
• Venturi tubes
• Flow nozzles
• Cones
• Segmental wedges
1.5.4 The DP Flowmeter
Differential pressure is the most common flow
measurement methodology today. There are three
important elements that are combined to create a
differential pressure flowmeter.
The primary element creates a pressure drop across
the flowmeter by introducing a restriction in the pipe.
This pressure drop is measured by the secondary
element, a differential pressure transmitter. The
tertiary element consists of everything else within the
system needed to make it work, including impulse
piping and connectors that route the upstream and
downstream pressures to the transmitter.
PHigh
PLow
Flow
By creating an engineered restriction in a pipe,
Bernoulli’s equation can be used to calculate flow rate
because the square root of the pressure drop across
the restriction is proportional to the flow rate.
Figure 1.5.5.a - Pressure flow diagram showing how DP Flow
works. As fluids pass the restriction from the high side, the
restriction induces a pressure drop. Flow is then calculated from
the pressure drop (DP) across the restriction.
There are some important cautions around DP flow
metering, including (1) ensuring that impulse lines do
not clog with particles or sludge; (2) orienting impulse
lines correctly—they have to be sloped to prevent
gas accumulation in liquid applications and liquid
accumulations in gas applications; and (3) ensuring
that periodic calibration does not degrade accuracy—
avoided by the use of highly accurate calibration
equipment.
1.5.6 Transmitter Options
There are two main types of pressure transmitters
used to calculate flow using differential pressure.
The first is the traditional differential pressure type,
which only measures differential pressure, with no
ancillary functionality. The second is the multivariable
transmitter.
A multivariable transmitter is a differential pressure
transmitter that is capable of measuring a number of
independent process variables, including differential
pressure, static pressure, and temperature. When used
as a mass flow transmitter, these independent values
can be used to compensate for changes in density,
viscosity, and other flow parameters.
Although multivariable transmitters can be more
expensive than traditional differential pressure
transmitters, they eliminate the need for multiple
devices at a single measurement point. This means
fewer transmitters, less wiring, fewer process
penetrations, and lower overall installed cost.
Figure 1.5.4.a - An integrated DP flowmeter.
14
1 – DP Flow Introduction
Multivariable transmitters, unlike traditional
differential pressure transmitters, are capable of
calculating mass flow, energy flow, volumetric flow,
and totalized flow.
Internal Billing & Resource Allocation: Tighter
control over inventories and process rates contributes
directly to profitability. For many sophisticated
producers, internal billing around process costs
directly impacts the bottom line.
1.6 DP FLOW MEASUREMENT–
APPLICATIONS
Custody Transfer: Flow metering is the cash register
for products sold by volume or weight. An accurate
measurement on the dispensing side accounts for
every drop and on the receiving side minimizes overcharging.
DP Flow measurement allows the optimization of
many different aspects of a process including the
following:
1.7 FLOWMETER
INSTALLATIONS: TRADITIONAL
VERSUS INTEGRATED
• Product consistency
• Production efficiency
• Process variable control
• Safety
• Internal billing/allocation
• Custody transfer
Sensor and process instrumentation in general has
seen a great deal of integration of both form and
function over the last two decades with DP Flow being
no exception.
Product Consistency: Batch-based products depend
on accurate proportions of ingredients—DP Flow helps
ensure the accurate of delivery of liquids and gases.
At this point in time, there are two broad types of DP
flowmeters installations: traditional and integrated.
Production Efficiency: Metering and measurement
of flow are part of a broad range of process control
variables related to efficiency, from batch control, to
by-product scavenging, to emissions monitoring.
1.7.1 Traditional
The Traditional Installation Method calls for three
separate component categories.
1. Primary element (differential pressure producer)
2. Secondary element (transmitter)
3. Tertiary elements (impulse lines, connecting
hardware, tubing, fittings, valves, etc.)
1
3
Figure 1.6.a - Utility monitoring is a major component of
production efficiency.
2
Process Variable Control: Processes often include
multiple variable inputs. Control over these variables,
including flow rates, is key to quality production.
Figure 1.7.1.a - The traditional DP Flow installation has separate
primary element, top left, tertiary elements (impulse lines,
valves, connectors, and manifold), and secondary element, the
transmitter, center right).
Safety: DP Flow helps prevent a broad range of threats
to safety including overfilling, reactor control, and
others.
15
1 – DP Flow Introduction
The traditional form enables component-bycomponent engineering to meet a wide variety of
applications and can be engineered to meet custody
transfer standards.
The integrated flowmeter works much the same
way as that of the traditional flowmeter. It uses the
same equations, works largely with the same primary
elements, and is available with the same transmitters
(both differential pressure and multivariable).
Owing to its long history, many traditions around
DP-based flow measurement have emerged. Some
of these traditions, however, have led to inherent
limitations or problems. These include multiple
potential leak points at connectors, separate/incorrect
piping and manifolding; accuracy problems traceable
to long impulse lines. In addition, installation is
complex, requiring long straight runs (dependent on
the primary element used) and careful configuration of
components.
1.7.3 Benefits of the Integrated
Flowmeter
An integrated flowmeter design eliminates the need
for fittings, tubing, valves, adapters, manifolds, and
mounting brackets.
Compared to traditional installation, the benefits of
integrated flowmeters include:
• Fewer potential leak points (factory leakchecked)
• Fewer flow measurement error sources
• Simplified ordering and installation
• Decreased susceptibility to freezing and
plugging
• More compact footprint
Much work has been done over the years to correct for
some of these issues, and thus extend the usefulness
and value of DP Flow installations.
1.7.2 Integrated
The integrated flowmeter integrates the primary
element and the transmitter into a single flowmeter
assembly. It was in large part developed to minimize
the issues around installations of the older-style
traditional flowmeter. As a result, its installation
calls for components and less labor than traditional
flowmeters installations.
Rosemount integrated flowmeters combine industry
leading transmitters with innovative primary element
technologies and connection systems. There are
in effect 10 devices in one flowmeter, simplifying
engineering, procurement, and installation.
2
3
4
5
6
1
10
8
7
9
Figure 1.7.3.a - Traditional DP Flow structure. See page 17 for
callouts.
Figure 1.7.2.a - This integrated DP flowmeter combines both the
primary element and the transmitter into a single flowmeter
assembly, reducing potential leak points during installation and
use..
16
1 – DP Flow Introduction
Optical flow meters use photodetectors to gauge the
movement of particles in an illuminated fluid stream.
1 5
7 8
3
Vortex flow meters use electrical pulse generators—
commonly a piezoelectric crystal—to measure flow
disturbances (vortices) around a calibrated
obstruction.
6
4
Each of the various flow measurement technologies
in existence today has its ideal range of applications.
However, thanks to its long history, its ease of use, and
its immense range of applicability, DP Flow remains
the most commonly used form of flow measurement
in industry.
9
10
1.9 SUMMARY
2
Differential pressure flow metering is the most
common technology for measuring flow in a closed
pipe.
Figure 1.7.3.b - Integrated multivariable instrumentation.
In Figures 1.7.3.a and 1.7.3.b:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
• The technology is based on well-known laws
of physics, fluid dynamics and mass transport
• Its long history of use has led to the creation of
basic and practical engineering solutions for a
broad range of applications
• Manufacturers offer a large catalog of general
and application-specific DP Flow instrumentation
Flow Computer
Primary Element
Thermowell
Temperature Sensor
Temperature Transmitter
Sensor Wiring
Pressure Transmitter
DP Transmitter
Manifold
Connection Hardware
1.9.1 History
Over the past centuries great strides have been made
in the advancement of flow measurement. Two major
of the major players in these advancements were
Daniel Bernoulli and Osborne Reynolds.
1.8 ALTERNATE FLOW
TECHNOLOGIES
• Decreased susceptibility to freezing and
plugging
• More compact footprint
Flow measurement can be performed with a broad
range of technologies other than pressure-based.
These include open channel, mechanical, ultrasonic,
electromagnetic, Coriolis, optical, thermal mass, and
vortex types.
Rosemount integrated flowmeters combine industry
leading transmitters with innovative primary element
technologies and connection systems. There are
in effect 10 devices in one flowmeter, simplifying
engineering, procurement, and installation.
Electromagnetic flowmeters, which require an
electrically-conductive fluid and a means for inducing
magnetic energy to the flow, use electrodes to sense
current induction from the magnetic flux.
Coriolis flow meters, as the name implies, use the
Coriolis effect, which induces distortion in a vibrating
tube.
17
1 – DP Flow Introduction
1.9.2 The Phenomenon of Pressure
1.9.4 Applications of DP Flow
Measurement
The most crucial background concept in the domain
of DP flow is pressure, the physical phenomenon
that is harnessed to derive measurements. Accurate
measurement of liquid, gas, and steam pressure is
basic to many industrial processes—and, of course,
specific to DP flow measurement.
Process engineering and cost engineering are the two
primary disciplines that exploit DP flow. The primary
objectives include engineering for:
• Product consistency
• Production efficiency
• Process variable control
• Safety
• Internal billing/allocation
• Custody transfer
1.9.3 DP Flow 101—The Basics
A DP flowmeter consists of two major elements, a
primary element, a restrictor in a pipe; and a secondary
element, the differential pressure transmitter.
1.9.5 Instrument Form Factors:
Traditional Versus Integrated
There are many kinds of primary elements:
• Orifice plates
• Venturi tubes
• Elbows
• Flow nozzles
• Single - and multiple-port pitot tubes
• Cones
• Segmental wedges
There are two broad types of DP flow meters available,
traditional and integrated.
The traditional form consists of three component
categories.
1. Primary element (Differential pressure producer)
2. Secondary element (transmitter)
3. Tertiary elements (impulse lines, connecting
hardware, tubing, fittings, valves, etc.)
The integrated form integrates the primary element
and the transmitter into a single entity. See figure
1.9.3.a.
1.9.6 Alternate Flow Technologies
Flow measurement can be performed with a broad
range of technologies other than pressure-based.
These include:
• Open channel
• Mechanical
• Ultrasonic
• Electromagnetic
• Coriolis
• Optical
• Thermal mass
• Vortex
Figure 1.9.3.a - The modern DP flowmeter which integrates the
primary and secondary elements.
Thanks to its range of usability and its critical mass of
knowledge, DP flow remains the most-used form of
flow measurement in industry.
18
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Literature reference number: 00805-0100-1041 Rev AA March 2015