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Featured in this Book FLUIDS IN THE NEWS Throughout the book are many brief news stories involving current, sometimes novel, applications of fluid phenomena. Many of these stories have homework problems associated with them. F l u i d s i n t h e N e w s Weather, barometers, and bars One of the most important indicators of weather conditions is atmospheric pressure. In general, a falling or low pressure indicates bad weather; rising or high pressure, good weather. During the evening TV weather report in the United States, atmospheric pressure is given as so many inches (commonly around 30 in.). This value is actually the height of the mercury column in a mercury barometer adjusted to sea level. To determine the true atmospheric pressure at a particular location, the elevation relative to sea level must be known. Another unit used by meteorologists to indicate atmospheric pressure is the bar, first used in weather reporting in 1914, and defined as 10 5 Nm 2 . The definition of a bar is probably related to the fact that standard sealevel pressure is 1.0133 10 5 Nm 2 , that is, only slightly larger than one bar. For typical weather patterns, “sea-level equivalent” atmospheric pressure remains close to one bar. However, for extreme weather conditions associated with tornadoes, hurricanes, or typhoons, dramatic changes can occur. The lowest atmospheric sea-level pressure ever recorded was associated with a typhoon, Typhoon Tip, in the Pacific Ocean on October 12, 1979. The value was 0.870 bars (25.8 in. Hg). (See Problem 2.19.) SUMMARY SENTENCES A brief summary sentence is given on each page to prepare or remind the reader about an important concept discussed on that page. PHOTOGRAPHS AMD ILLUSTRATIONS More than 515 new photographs and illustrations have been added to help illustrate various concepts in the text. FLUID VIDEOS A set of 159 videos illustrating interesting and practical applications of fluid phenomena is provided on the book website. An icon in the margin identifies each video. Approximately 160 homework problems are tied to the videos. 2.6 Manometry Manometers use vertical or inclined liquid columns to measure pressure. (Photograph courtesy of Cameron Balloons.) V2.6 Atmospheric buoyancy A standard technique for measuring pressure involves the use of liquid columns in vertical or inclined tubes. Pressure measuring devices based on this technique are called manometers. The mercury barometer is an example of one type of manometer, but there are many other configurations possible, depending on the particular application. Three common types of manometers include the piezometer tube, the U-tube manometer, and the inclined-tube manometer. 2.11.1 Archimedes’ Principle When a stationary body is completely submerged in a fluid 1such as the hot air balloon shown in the figure in the margin2, or floating so that it is only partially submerged, the resultant fluid force acting on the body is called the buoyant force. A net upward vertical force results because pressure increases with depth and the pressure forces acting from below are larger than the pressure forces acting from above. This force can be determined through an approach similar to that used in the previous section for forces on curved surfaces. Consider a body of arbitrary shape, having a volume V, that is immersed in a fluid as illustrated in Fig. 2.24a. We enclose the body in a parallelepiped and draw a free-body diagram of the parallelepiped with the body removed as shown in Fig. 2.24b. Note that the forces F 1 , F 2 , F 3 , and F 4 are simply the forces exerted on the plane surfaces of the parallelepiped 1for simplicity the forces in the x direction are not shown2, w is the weight of the shaded fluid volume 1parallelepiped minus body2, and F B is the force the body is exerting on the fluid. The forces on the vertical surfaces, such as F 3 and F 4 , are all equal and cancel, so the equilibrium equation of interest is in the z direction and can be expressed as F B F 2 F 1 w (2.21) If the specific weight of the fluid is constant, then F 2 F 1 g1h 2 h 1 2A where A is the horizontal area of the upper 1or lower2 surface of the parallelepiped, and Eq. 2.21 can be written as F B g1h 2 h 1 2A g31h 2 h 1 2A V4 Simplifying, we arrive at the desired expression for the buoyant force F B gV (2.22) 2.13 Chapter Summary and Study Guide Pascal’s law surface force body force incompressible fluid hydrostatic pressure distribution pressure head compressible fluid U.S. standard atmosphere absolute pressure gage pressure vacuum pressure barometer manometer Bourdon pressure gage center of pressure buoyant force Archimedes’ principle center of buoyancy In this chapter the pressure variation in a fluid at rest is considered, along with some important consequences of this type of pressure variation. It is shown that for incompressible fluids at rest the pressure varies linearly with depth. This type of variation is commonly referred to as hydrostatic pressure distribution. For compressible fluids at rest the pressure distribution will not generally be hydrostatic, but Eq. 2.4 remains valid and can be used to determine the pressure distribution if additional information about the variation of the specific weight is specified. The distinction between absolute and gage pressure is discussed along with a consideration of barometers for the measurement of atmospheric pressure. Pressure measuring devices called manometers, which utilize static liquid columns, are analyzed in detail. A brief discussion of mechanical and electronic pressure gages is also included. Equations for determining the magnitude and location of the resultant fluid force acting on a plane surface in contact with a static fluid are developed. A general approach for determining the magnitude and location of the resultant fluid force acting on a curved surface in contact with a static fluid is described. For submerged or floating bodies the concept of the buoyant force and the use of Archimedes’ principle are reviewed. The following checklist provides a study guide for this chapter. When your study of the entire chapter and end-of-chapter exercises has been completed you should be able to write out meanings of the terms listed here in the margin and understand each of the related concepts. These terms are particularly important and are set in italic, bold, and color type in the text. calculate the pressure at various locations within an incompressible fluid at rest. calculate the pressure at various locations within a compressible fluid at rest using Eq. 2.4 if the variation in the specific weight is specified. use the concept of a hydrostatic pressure distribution to determine pressures from measurements using various types of manometers. determine the magnitude, direction, and location of the resultant hydrostatic force acting on a plane surface. BOXED EQUATIONS Important equations are boxed to help the user identify them. CHAPTER SUMMARY AND STUDY GUIDE At the end of each chapter is a brief summary of key concepts and principles introduced in the chapter along with key terms and a summary of key equations involved. xiv
Featured in this Book xv LEARNING OBJECTIVES At the beginning of each chapter is a set of learning objectives that provides the student a preview of topics covered in the chapter. 2 Fluid Statics EXAMPLE PROBLEMS A set of example problems provides the student detailed solutions and comments for interesting, real-world situations. CHAPTER OPENING PHOTO: Floating iceberg: An iceberg is a large piece of fresh water ice that originated as snow in a glacier or ice shelf and then broke off to float in the ocean. Although the fresh water ice is lighter than the salt water in the ocean, the difference in densities is relatively small. Hence, only about one ninth of the volume of an iceberg protrudes above the ocean’s surface, so that what we see floating is literally “just the tip of the iceberg.” (Photograph courtesy of Corbis Digital Stock/Corbis Images) E XAMPLE 2.4 Simple U-Tube Manometer GIVEN A closed tank contains compressed air and oil Pressure gage 1SG oil 0.902 as is shown in Fig. E2.4. A U-tube manometer using mercury 1SG Hg 13.62 is connected to the tank as shown. The column heights are h 1 36 in., h 2 6 in., and h 3 9 in. Air FIND Determine the pressure reading 1in psi2 of the gage. Open Learning Objectives After completing this chapter, you should be able to: ■ determine the pressure at various locations in a fluid at rest. ■ explain the concept of manometers and apply appropriate equations to determine pressures. ■ calculate the hydrostatic pressure force on a plane or curved submerged surface. ■ calculate the buoyant force and discuss the stability of floating or submerged objects. SOLUTION Following the general procedure of starting at one end of the manometer system and working around to the other, we will start at the air–oil interface in the tank and proceed to the open end where the pressure is zero. The pressure at level 112 is This pressure is equal to the pressure at level 122, since these two points are at the same elevation in a homogeneous fluid at rest. As we move from level 122 to the open end, the pressure must decrease by g Hgh 3, and at the open end the pressure is zero. Thus, the manometer equation can be expressed as or For the values given so that p 1 p air g oil1h 1 h 22 p air g oil1h 1 h 22 g Hgh 3 0 p air 1SG oil21g H2O21h 1 h 22 1SG Hg21g H2O2 h 3 0 p air 10.92162.4 lbft 3 2a 36 6 ftb 12 113.62162.4 lbft 3 2a 9 12 ftb p air 440 lbft 2 2.115 A closed cylindrical tank that is 8 ft in diameter and 24 ft long is completely filled with gasoline. The tank, with its long axis horizontal, is pulled by a truck along a horizontal surface. Determine the pressure difference between the ends (along the long axis of the tank) when the truck undergoes an acceleration of 5 fts 2 . Oil F I G U R E E2.4 h 1 h 2 h 3 (1) (2) Since the specific weight of the air above the oil is much smaller than the specific weight of the oil, the gage should read the pressure we have calculated; that is, Hg 440 lbft2 p gage 3.06 psi 144 in. 2 2 ft (Ans) COMMENTS Note that the air pressure is a function of the height of the mercury in the manometer and the depth of the oil (both in the tank and in the tube). It is not just the mercury in the manometer that is important. Assume that the gage pressure remains at 3.06 psi, but the manometer is altered so that it contains only oil. That is, the mercury is replaced by oil. A simple calculation shows that in this case the vertical oil-filled tube would need to be h 3 11.3 ft tall, rather than the original h 3 9 in. There is an obvious advantage of using a heavy fluid such as mercury in manometers. cumference and a point on the axis. 2.111 An open container of oil rests on the flatbed of a truck that is traveling along a horizontal road at 55 mihr. As the truck slows 2.121 (See Fluids in the News article titled “Rotating mercury uniformly to a complete stop in 5 s, what will be the slope of the oil mirror telescope,” Section 2.12.2.) The largest liquid mirror telescope uses a 6-ft-diameter tank of mercury rotating at 7 rpm to pro- surface during the period of constant deceleration? duce its parabolic-shaped mirror as shown in Fig. P2.121. Determine the difference in elevation of the mercury, ¢h, between the 2.112 A 5-gal, cylindrical open container with a bottom area of 120 in. 2 is filled with glycerin and rests on the floor of an elevator. edge and the center of the mirror. (a) Determine the fluid pressure at the bottom of the container when the elevator has an upward acceleration of 3 fts 2 . (b) What resultant force does the container exert on the floor of the elevator Receiver during this acceleration? The weight of the container is negligible. Light rays (Note: 1 gal 231 in. 3 ) 2.113 An open rectangular tank 1 m wide and 2 m long contains 6 ft gasoline to a depth of 1 m. If the height of the tank sides is 1.5 m, what is the maximum horizontal acceleration (along the long axis of Δh the tank) that can develop before the gasoline would begin to spill? Mercury ω = 7 rpm 2.114 If the tank of Problem 2.113 slides down a frictionless plane F I G U R E P2.121 that is inclined at 30° with the horizontal, determine the angle the free surface makes with the horizontal. ■ Lab Problems LAB PROBLEMS WileyPLUS and on the book website is a set of lab problems in Excel format involving actual data for experiments of the type found in many introductory fluid mechanics labs. 2.122 This problem involves the force needed to open a gate that covers an opening in the side of a water-filled tank. To proceed with this problem, go to Appendix H which is located on the book’s web site, www.wiley.com/college/munson. Review Problems Go to Appendix G for a set of review problems with answers. Detailed solutions can be found in Student Solution Manual and Study Problems In this chapter we will consider an important class of problems in which the fluid is either at rest or moving in such a manner that there is no relative motion between adjacent particles. In both instances there will be no shearing stresses in the fluid, and the only forces that develop on the surfaces of the particles will be due to the pressure. Thus, our principal concern is to investigate pressure and its variation throughout a fluid and the effect of pressure on submerged surfaces. The absence of shearing stresses greatly simplifies the analysis and, as we will see, allows us to obtain relatively simple solutions to many important practical problems. Note: Unless otherwise indicated, use the values of fluid properties found in the tables on the inside of the front cover. Problems designated with an 1*2 are intended to be solved with the aid of a programmable calculator or a computer. Problems designated with a 1†2 are “open-ended” problems and require critical thinking in that to work them one must make various assumptions and provide the necessary data. There is not a unique answer to these problems. Answers to the even-numbered problems are listed at the end of the book. Access to the videos that accompany problems can be obtained through the book’s web site, www.wiley.com/ college/munson. The lab-type problems can also be accessed on this web site. Section 3.2 F ma along a Streamline 3.1 Obtain a photograph/image of a situation which can be analyzed by use of the Bernoulli equation. Print this photo and write a brief paragraph that describes the situation involved. 3.2 Air flows steadily along a streamline from point (1) to point (2) with negligible viscous effects. The following conditions are measured: At point (1) z 1 2 m and p 1 0 kPa; at point (2) z 2 10 m, p 2 20 N/m 2 , and V 2 0. Determine the velocity at point (1). REVIEW PROBLEMS WileyPLUS on the book web site are nearly 200 Review Problems covering most of the main topics in the book. Complete, detailed solutions to these problems are found WileyPLUS or in the supplement Student Solution Manual and Study Guide for Fundamentals of Fluid Mechanics, by Munson, et al. (© 2009 John Wiley and Sons, Inc.). Guide for Fundamentals of Fluid Mechanics, by Munson et al. (© 2009 John Wiley and Sons, Inc.). front of the object and V 0 is the upstream velocity. (a) Determine the pressure gradient along this streamline. (b) If the upstream pressure is p 0, integrate the pressure gradient to obtain the pressure p1x2 for x a. (c) Show from the result of part (b) that the pressure at the stagnation point 1x a2 is p 0 rV 2 02, as expected from the Bernoulli equation. V 0 Dividing streamline x = 0 x p o Stagnation a point F I G U R E P3.5 36 What pressure gradient along the streamline dpds is required
Page 3 and 4: Achieve Positive Learning Outcomes
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Page 7 and 8: Sixth Edition F undamentals of Flui
Page 9 and 10: About the Authors vii Bruce R. Muns
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Page 19 and 20: C ontents 1 INTRODUCTION 1 Learning
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7 Dimensional Analysis, Similitude,
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WARNING Stand clear of Hazard areas
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462 Chapter 9 ■ Flow over Immerse
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A ppendix B Physical Properties of
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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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Index I-3 guidelines for selection,
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Index I-5 hydrostatic: on curved su
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Index I-7 piezometer tube, 50, 105,
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Index I-9 Pressure force, 40 Pressu
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Index I-11 Stress field, 277 Strouh
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Index I-13 Weber, M., 29, 350 Weber
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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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