DP Flow Engineering Guide | Emerson

1 DP Flow Engineering Guide Chapter 1 - DP Flow Introduction to DP Flow Differential pressure flow measurement (DP Flow) is one of the most common Figure - The modern DP flowmeter . 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 - How DP Flow Works 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.

2 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 Principle Daniel 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.

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

4 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 Why Measure Pressure? The most common reasons that the process industry measures pressure are: Figure - A multivariable flowmeter Safety for more acurate process measurements. 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 other process variables) are maintained at specific values or within a narrow range of values.

5 Cost Savings: Pressure or vacuum equipment ( , pumps and compressors) uses considerable energy. Pressure optimization can save money by reducing energy costs. Measurement of Other Process Variables: Pressure is used to measure numerous processes. Pressure transmitters are frequently 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 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 Pipes There are 6 factors that are key to understanding pipe flow: 1.

6 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 Piping Configuration: The diameter and cross-sectional 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. 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 walls of 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.

7 Because liquids 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 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. 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. Video - A visualization of flow through a pipe.

8 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.

9 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. 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 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 can be further simplified, since length, l, divided by time yields velocity, v. Velocity can now be substituted for the term s/t tielding: Since the volumetric flow rate is the same at all cross-sectional slices: Substituting Equation into Equatation : Figure - Graphical representation of the flow law where Q1 = Q2.

10 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. The DP 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. 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.