Chapter3 - 03-R3868 7/20/06 10:10 AM Page 49 CHAPTER...

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PRESSURE AND FLUID STATICS T his chapter deals with forces applied by fluids at rest. The fluid prop- erty responsible for those forces is pressure , which is a normal force exerted by a fluid per unit area. We start this chapter with a detailed discussion of pressure, including absolute and gage pressures , the pressure at a point , the variation of pressure with depth in a gravitational field, the manometer , the barometer , and other pressure measurement devices. This is followed by a discussion of the hydrostatic forces applied on submerged bodies with plane or curved surfaces. We then consider the buoyant force applied by fluids on submerged or floating bodies, and discuss the stability of such bodies. This chapter makes extensive use of force balances for bod- ies in static equilibrium, and it will be helpful if the relevant topics from statics are first reviewed. 49 CHAPTER 3 OBJECTIVES When you finish reading this chapter, you should be able to n Determine the variation of pressure in a fluid at rest n Calculate the forces exerted by a fluid at rest on plane or curved submerged surfaces n Analyze the stability of floating and submerged bodies. John Ninomiya Fying a cluster of 72-balloon helium- ±lled balloons over Temecula, California in April of 2003. The helium balloons displace approximately 230 m 3 of air, providing the necessary buoyant force. Photograph by Susan Dawson. Used by permission.
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3–1 n PRESSURE Pressure is defined as a normal force exerted by a fluid per unit area . We speak of pressure only when we deal with a gas or a liquid. The counterpart of pressure in solids is normal stress . Since pressure is defined as force per unit area, it has the unit of newtons per square meter (N/m 2 ), which is called a pascal (Pa). That is, The pressure unit pascal is too small for pressures encountered in prac- tice. Therefore, its multiples kilopascal (1 kPa 5 10 3 Pa) and megapascal (1 MPa 5 10 6 Pa) are commonly used. Three other pressure units com- monly used in practice, especially in Europe, are bar , standard atmosphere , and kilogram-force per square centimeter : Note the pressure units bar, atm, and kgf/cm 2 are almost equivalent to each other. In the English system, the pressure unit is pound-force per square inch (lbf/in 2 , or psi), and 1 atm 5 14.696 psi. The pressure units kgf/cm 2 and lbf/in 2 are also denoted by kg/cm 2 and lb/in 2 , respectively, and they are commonly used in tire gages. It can be shown that 1 kgf/cm 2 5 14.223 psi. Pressure is also used for solids as synonymous to normal stress ,wh ich ±is force acting perpendicular to the surface per unit area. For example, a 150- pound person with a total foot imprint area of 50 in 2 exerts a pressure of 150 lbf/50 in 2 5 3.0 psi on the floor (Fig. 3–1). If the person stands on one foot, the pressure doubles. If the person gains excessive weight, he or she is likely to encounter foot discomfort because of the increased pressure on the foot (the size of the foot does not change with weight gain). This also explains how a person can walk on fresh snow without sinking by wearing
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This note was uploaded on 10/16/2010 for the course GEEN 3311 taught by Professor Dr.ra’fatal-waked during the Fall '10 term at Prince Mohammad Bin Fahd University, Dhahran.

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Chapter3 - 03-R3868 7/20/06 10:10 AM Page 49 CHAPTER...

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