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446 Chapter 8 ■ Viscous Flow in Pipes Magnetic sensor IN OUT Flow out Flow in FLOW Turbine F I G U R E 8.47 Turbine-type flow meter. (Courtesy of E G & G Flow Technology, Inc.) Another useful pipe flowrate meter is a turbine meter as is shown in Fig. 8.47. A small, freely rotating propeller or turbine within the turbine meter rotates with an angular velocity that is a function of 1nearly proportional to2 the average fluid velocity in the pipe. This angular velocity is picked up magnetically and calibrated to provide a very accurate measure of the flowrate through the meter. Volume flow meters measure volume rather than volume flowrate. 8.6.2 Volume Flow Meters In many instances it is necessary to know the amount 1volume or mass2 of fluid that has passed through a pipe during a given time period, rather than the instantaneous flowrate. For example, we are interested in how many gallons of gasoline are pumped into the tank in our car rather than the rate at which it flows into the tank. There are numerous quantity-measuring devices that provide such information. The nutating disk meter shown in Fig. 8.48 is widely used to measure the net amount of water used in domestic and commercial water systems as well as the amount of gasoline delivered to your gas tank. This meter contains only one essential moving part and is relatively inexpensive and accurate. Its operating principle is very simple, but it may be difficult to understand its operation without actually inspecting the device firsthand. The device consists of a metering chamber with spherical sides and conical top and bottom. A disk passes through a central sphere and divides the chamber into two portions. The disk is constrained to be at an angle not normal to the axis of symmetry of the chamber. A radial plate 1diaphragm2 divides the chamber so that the entering fluid causes the disk to wobble 1nutate2, with fluid flowing alternately above or below the disk. The fluid exits the chamber after the disk has completed one wobble, which corresponds to a specific volume of fluid passing through the chamber. During each wobble of the disk, the pin attached to the tip Calibration gears V8.14 Water meter Pin Metering chamber Flow in Flow out Casing Diaphragm Sphere Disk assembly F I G U R E 8.48 Nutating disk flow meter. (Courtesy of Badger Meter, Inc.)
8.7 Chapter Summary and Study Guide 447 Inlet Outlet Slider valves driven by diaphragm Back case Back diaphragm Front case Front diaphragm (a) (b) (c) (d) F I G U R E 8.49 Bellows-type flow meter. (Courtesy of BTR—Rockwell Gas Products). (a) Back case emptying, back diaphragm filling. (b) Front diaphragm filling, front case emptying. (c) Back case filling, back diaphragm emptying. (d) Front diaphragm emptying, front case filling. The nutating disk meter has only one moving part; the bellows meter has a complex set of moving parts. of the center sphere, normal to the disk, completes one circle. The volume of fluid that has passed through the meter can be obtained by counting the number of revolutions completed. Another quantity-measuring device that is used for gas flow measurements is the bellows meter as shown in Fig. 8.49. It contains a set of bellows that alternately fill and empty as a result of the pressure of the gas and the motion of a set of inlet and outlet valves. The common household natural gas meter is of this type. For each cycle [1a2 through 1d2] a known volume of gas passes through the meter. The nutating disk meter 1water meter2 is an example of extreme simplicity—one cleverly designed moving part. The bellows meter 1gas meter2, on the other hand, is relatively complex—it contains many moving, interconnected parts. This difference is dictated by the application involved. One measures a common, safe-to-handle, relatively high-pressure liquid, whereas the other measures a relatively dangerous, low-pressure gas. Each device does its intended job very well. There are numerous devices used to measure fluid flow, only a few of which have been discussed here. The reader is encouraged to review the literature to gain familiarity with other useful, clever devices 1Refs. 25, 262. 8.7 Chapter Summary and Study Guide This chapter discussed the flow of a viscous fluid in a pipe. General characteristics of laminar, turbulent, fully developed, and entrance flows are considered. Poiseuille’s equation is obtained to describe the relationship among the various parameters for fully developed laminar flow.
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Achieve Positive Learning Outcomes
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WileyPLUS combines robust course ma
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Sixth Edition F undamentals of Flui
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About the Authors vii Bruce R. Muns
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P reface This book is intended for
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Preface xi Life Long Learning Probl
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Preface xiii WileyPLUS offers today
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Featured in this Book xv LEARNING O
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C ontents 1 INTRODUCTION 1 Learning
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Contents xix 6.4.3 Irrotational Flo
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12.6 Axial-Flow and Mixed-Flow Pump
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10 8 Jupiter red spot diameter 2 Ch
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4 Chapter 1 ■ Introduction and do
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6 Chapter 1 ■ Introduction up the
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8 Chapter 1 ■ Introduction the SI
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10 Chapter 1 ■ Introduction E XAM
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12 Chapter 1 ■ Introduction TABLE
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18 Chapter 1 ■ Introduction Visco
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20 Chapter 1 ■ Introduction Kinem
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22 Chapter 1 ■ Introduction As th
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24 Chapter 1 ■ Introduction Boili
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26 Chapter 1 ■ Introduction E XAM
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28 Chapter 1 ■ Introduction The r
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30 Chapter 1 ■ Introduction fluid
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32 Chapter 1 ■ Introduction Secti
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2 Fluid Statics CHAPTER OPENING PHO
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40 Chapter 2 ■ Fluid Statics in a
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42 Chapter 2 ■ Fluid Statics p Fo
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66 Chapter 2 ■ Fluid Statics SOLU
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92 Chapter 2 ■ Fluid Statics 2.12
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94 Chapter 3 ■ Elementary Fluid D
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100 Chapter 3 ■ Elementary Fluid
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148 Chapter 4 ■ Fluid Kinematics
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264 Chapter 6 ■ Differential Anal
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7 Dimensional Analysis, Similitude,
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334 Chapter 7 ■ Dimensional Analy
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384 Chapter 8 ■ Viscous Flow in P
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496 Chapter 9 ■ Flow over Immerse
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∋ 530 Chapter 9 ■ Flow over Imm
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10 Open-Channel Flow CHAPTER OPENIN
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536 Chapter 10 ■ Open-Channel Flo
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580 Chapter 11 ■ Compressible Flo
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646 Chapter 12 ■ Turbomachines Ex
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722 Appendix D ■ Compressible Flo
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724 Appendix D ■ Compressible Flo
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Answers to Selected Even-Numbered H
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I ndex Absolute pressure, 13, 48 Ab
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V10.3 Water strider V10.13 Triangul
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■ TABLE 1.4 Conversion Factors fr
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■ TABLE 1.7 Approximate Physical
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