DP Flow Engineering Guide | · PDF fileDP Flow Engineering Guide Figure 1.1.a - The modern DP flowmeter. ... Measuring pressure helps prevent unplanned pressure or process release

DP Flow Engineering Guide

Figure 1.1.a - The modern DP flowmeter.

Chapter 1 - DP Flow

1.1 Introduction to DP Flow

Differential pressure flow measurement (DP Flow) is one of the most common

technologies for measuring flow in a closed pipe.

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

DP Flow technologies achieve high accuracy and repeatability

Video 1.1.a - How DP Flow Works

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1.2 History of DP Flow

Flow measurement began thousands of years ago as the Egyptians began to make approximate predictions of harvests based on the

relative level of spring floods of the Nile River. Romans later engineered aqueducts to provide water in cities for sustenance and 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 an orifice, etc. gave a rough measurement of the flow

rates. Newton's discovery of the law of gravitation in 1687 enabled physicists and mathematicians to formulate theories around motion and

force, which ultimately lead to the development of the ability to quantify flow rates.

The Bernoulli PrincipleDaniel Bernoulli was a Swiss mathematician who studied hydrodynamics. His work centered on the conservation of energy and provided

the first key breakthrough in the development of flow measurement technology. He developed the Bernoulli principle which states that the

sum of all energy in the flow must remain constant regardless of conditions. Specifically for DP Flow, this means that the sum of the static

energy (pressure), kinetic energy (velocity), and potential energy (elevation) upstream equals the static, kinetic, and potential energy

downstream.

Reynolds Number Osbourne Reynolds was not a student of physics but rather one of mechanics, and is most famous for his study of fluid flow through a

pipe, specifically the conditions under which the flow transitions from laminar flow to turbulent flow. The Reynolds number is a numeric

quantification of the internal forces over the viscous forces. In short it describes the flowing characteristics of a fluid. Reynolds number is a

key concept for designing flowmeters and is used as a constraint on the range of a flowmeter's applicability.

1.3 Pressure

What is pressure? Pressure is the amount of force applied over a defined area (Equation 1.1).

Pressure increases with increasing force or decreasing area

Pressure decreases with decreasing force or increasing area

Measuring pressure helps prevents over pressuring of equipment that may result in damage

Measuring pressure helps prevent unplanned pressure or process release that may cause injury

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Why Measure Pressure?The most common reasons that the process industry measures pressure are:

Figure 1.3.a - A multivariable flowmeterfor more acurate processmeasurements.

Safety

Process efficiency

Cost savings

Measurement of other process variables

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.

Process Efficiency: In most cases, process efficiency is highest when pressures (and otherprocess variables) are maintained at specific values or within a narrow range of values.

Cost Savings: Pressure or vacuum equipment (e.g., pumps and compressors) usesconsiderable energy. Pressure optimization can save money by reducing energy costs.

Measurement of Other Process Variables: Pressure is used to measure numerous processes. Pressure transmitters arefrequently used in a number of applications, including:

Flow rates through a pipe

Level of fluid in a tank

Density of a substance

Liquid interface measurement

1.4 DP Flow 101

Flow theory is the study of fluids in motion. A fluid is defined as any substance 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.

Key Factors of Flow Through PipesThere are 6 factors that are key to understanding pipe 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

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Piping Configuration: The diameter and cross-sectional area of the pipe enables both the determination of fluid volume for any givenlength of pipe and is included in the determination of the Reynolds number for a given application. Velocity: Depends on the pressure or

vacuum that forces fluid through the pipe.

Friction: Because no pipe is perfectly smooth, fluid in contact with a pipe encounters friction, resulting in a slower flow rate near the wallsof the pipe compared to at the center. The larger, smoother, or cleaner a pipe, the less effect on the flow rate.

Density: Density affects flow rates because the more dense a fluid, the higher the pressure required to obtain a given flow rate. Becauseliquids are (for all practical purposes) incompressible and gases are compressible, different methodologies are required to measure their

respective flow rates.

Viscosity: Defined as the molecular friction of a fluid, viscosity affects flow rates because in general, the higher the viscosity more work isneeded 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.

Reynolds Number: By factoring in the relationships between the various factors in a given system, Reynolds number can be calculated todescribe the type of flow profile. This becomes important when choosing how to measure the flow within the system.

Video 1.4.a - A visualization of flow through a pipe.

There are three different flow profiles that are defined by different Reynolds number regimes. Laminar flow, characterized by having a

Reynolds number below 2000, is a smooth flow in which a fluid flows in parallel layers. It usually has low fluid 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 considered to be

transitional. A Reynolds number above 4000 is called turbulent flow. This is characterized by high fluid velocity, low fluid viscosity, and

rapid and complete fluid mixing.

The best accuracy in DP Flow metering occurs with turbulent flow. 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.

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Flow Continuity

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. Equation 1.2 highlights

this relationship.

Volumetric flow equates to the volume of fluid divided by time:

Volume can be broken down to area, A, multiplied by length, s. Volumetric flow can thus be expressed as:

Equation 1.3 can be further simp