Richard Thorn. "Flow." Copyright 2000 CRC Press LLC. <http://www.engnetbase.com>. Richard Thorn University of Derby Adrian Melling Universitaet Erlangen-Nuember Herbert Köchner Flow Measurement Universitaet Erlangen-Nuember Reinhard Haak Universitaet Erlangen-Nuember 28.1 Differential Pressure Flowmeters Zaki D. Husain Important Principles of Fluid Flow in Pipes • Bernoulli’s Daniel Flow Products, Inc. Equation • Common Differential Pressure Flowmeters • Donald J. Wass Other Differential Pressure Flowmeters • Performance and Applications • Installation • Differential Pressure Daniel Flow Products, Inc. Measurement • Standards • Future Developments David Wadlow 28.2 Variable Area Flowmeters Sensors Research Consulting, Inc. General Description of Variable Area Flowmeters • Measuring Principles of Variable Area Flowmeters Harold M. Miller 28.3 Positive Displacement Flowmeters Data Industrial Corporation Design and Construction • Some Commercially Available Halit Eren PD Meter Designs • Advantages and Disadvantages of PD Meters • Applications • Accessories • Price and Performance Curtin University of Technology 28.4 Turbine and Vane Flowmeters Hans-Peter Vaterlaus Axial Turbine Flowmeters • Insertion Axial Turbine Rittmeyer Ltd. Flowmeters • Angular Momentum Flowmeters • Multijet Turbine Flowmeters • Cylindrical Rotor Flowmeter • Thomas Hossle Manufacturers • Conclusion Rittmeyer Ltd. 28.5 Impeller Flowmeters Paolo Giordano Sensing Principles • Flow Ranges • Installation • Manufacturers Rittmeyer Ltd. 28.6 Electromagnetic Flowmeters Christophe Bruttin Faraday’s Law of Induction • Construction and Operation Rittmeyer Ltd. of Electromagnetic Flowmeters • Types of Electromagnetic Flowmeters • Installation and Practical Applications of Wade M. Mattar Electromagnetic Flowmeters • Effects of Electric The Foxboro Company Conductivity of Fluid • Signal Pickup and Demodulation Techniques James H. Vignos 28.7 Ultrasonic Flowmeters The Foxboro Company Transit Time Flowmeter Nam-Trung Nguyen 28.8 Vortex Shedding Flowmeters University of California at Berkeley Principle of Operation • Calculation of Mass Flow and Standard Volume • Flowmeter Construction • Application Jesse Yoder Considerations • Recent Developments Automation Research Corporation 28.9 Thermal Mass Flow Sensors Rekha Philip-Chandy Principles of Conventional Thermal Mass Flowmeters • Mass and Heat Transfer • Analytical Models for Calorimetric Liverpool John Moores University Flowmeters • Principles of Microflow Sensors • Smart Roger Morgan Thermal Flow Sensors and Advanced Evaluation Circuits • Calibration Conditions Liverpool John Moores University 28.10 Coriolis Effect Mass Flowmeters Patricia J. Scully Theory of Operation • Construction • Advantages • Liverpool John Moores University Disadvantages • Applications • A Look Ahead © 1999 by CRC Press LLC 28.11 Drag Force Flowmeters Design of the Flow Sensor • Principle of the Fluid Flow Measurement • Implementation Using Resistive Strain Gages • Optical Fiber Strain Gage Drag Force Flowmeter • Conclusion 28.1Differential Pressure Flowmeters Richard Thorn Flow measurement is an everyday event. Whether you are filling up a car with petrol (gasoline) or wanting to know how much water the garden sprinkler is consuming, a flowmeter is required. Similarly, it is also difficult to think of a sector of industry in which a flowmeter of one type or another does not play a part. The world market in flowmeters was estimated to be worth $2500 million in 1995, and is expected to grow steadily for the foreseeable future. The value of product being measured by these meters is also very large. For example, in the U.K. alone, it was estimated that in 1994 the value of crude oil produced was worth $15 billion. Given the size of the flowmeter market, and the value of product being measured, it is somewhat surprising that both the accuracy and capability of many flowmeters are poor in comparison to those instruments used for measurement of other common process variables such as pressure and temperature. For example, the orifice plate flowmeter, which was first used commercially in the early 1900s and has a typical accuracy of ±2% of reading, is still the only flowmeter approved by most countries for the fiscal measurement of natural gas. Although newer techniques such as Coriolis flowmeters have become increas- ingly popular in recent years, the flow measurement industry is by nature conservative and still dominated by traditional measurement techniques. For a review of recent flowmeter developments, refer to [1]. Over 40% of all liquid, gas, and steam measurements made in industry are still accomplished using common types of differential pressure flowmeter; that is, the orifice plate, Venturi tube, and nozzle. The operation of these flowmeters is based on the observation made by Bernoulli that if an annular restriction is placed in a pipeline, then the velocity of the fluid through the restriction is increased. The increase in velocity at the restriction causes the static pressure to decrease at this section, and a pressure difference is created across the element. The difference between the pressure upstream and pressure downstream of this obstruction is related to the rate of fluid flowing through the restriction and therefore through the pipe. A differential pressure flowmeter consists of two basic elements: an obstruction to cause a pressure drop in the flow (a differential producer) and a method of measuring the pressure drop across this obstruction (a differential pressure transducer). One of the major advantages of the orifice plate, Venturi tube, or nozzle is that the measurement uncertainty can be predicted without the need for calibration, if it is manufactured and installed in accordance with one of the international standards covering these devices. In addition, this type of differential pressure flowmeter is simple, has no moving parts, and is therefore reliable. The main disad- vantages of these devices are their limited range (typically 3:1), the permanent pressure drop they produce in the pipeline (which can result in higher pumping costs), and their sensitivity to installation effects (which can be minimized using straight lengths of pipe before and after the flowmeter). The combined advantages of this type of flowmeter are still quite hard to beat, and although it has limitations, these have been well investigated and can be compensated for in most circumstances. Unless very high accuracy is required, or unless the application makes a nonintrusive device essential, the differential flowmeter should be considered. Despite the predictions of its demise, there is little doubt that the differential pressure flowmeter will remain a common method of flow measurement for many years to come. Important Principles of Fluid Flow in Pipes There are a number of important principles relating to the flow of fluid in a pipe that should be understood before a differential pressure flowmeter can be used with confidence. These are the difference © 1999 by CRC Press LLC between laminar and turbulent flow, the meaning of Reynolds number, and the importance of the flow’s velocity profile. Fluid motion in a pipe can be characterized as one of three types: laminar, transitional, or turbulent. In laminar flow, the fluid travels as parallel layers (known as streamlines) that do not mix as they move in the direction of the flow. If the flow is turbulent, the fluid does not travel in parallel layers, but moves in a haphazard manner with only the average motion of the fluid being parallel to the axis of the pipe. If the flow is transitional, then both types may be present at different points along the pipeline or the flow may switch between the two. In 1883, Osborne Reynolds performed a classic set of experiments at the University of Manchester that showed that the flow characteristic can be predicted using a dimensionless number, now known as the Reynolds number. The Reynolds number Re is the ratio of the inertia forces in the flow(ρvD– ) to the viscous forces in the flow (η) and can be calculated using: ρvD Re= (28.1) η where ρ = Density of the fluid v– = Mean velocity of the fluid D = Pipe diameter η = Dynamic viscosity of the fluid If Re is less than 2000, viscous forces in the flow dominate and the flow will be laminar. If Re is greater than 4000, inertia forces in the flow dominate and the flow will be turbulent. If Re is between 2000 and 4000, the flow is transitional and either mode can be present. The Reynolds number is calculated using mainly properties of the fluid and does not take into account factors such as pipe roughness, bends, and valves that also affect the flow characteristic. Nevertheless, the Reynolds number is a good guide to the type of flow that can be expected in most situations. The fluid velocity across a pipe cross-section is not constant, and depends on the type of flow present. In laminar flow, the velocity profile is parabolic since the large viscous forces present cause the fluid to move more slowly near the pipe walls. Under these conditions, the velocity at the center of the pipe is twice the average velocity across the pipe cross-section. The laminar flow profile is unaffected by the roughness of the pipe wall. In turbulent flow, inertia forces dominate, pipe wall effects are less, and the flow’s velocity profile is flatter, with the velocity at the center being about 1.2 times the mean velocity. The exact flow profile in a turbulent flow depends on pipe wall roughness and Reynolds number. Figure 28.1 shows the “fully developed” flow profiles for laminar and turbulent flow. These are the flow