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458 c h a p t e r Fluid Mechanics Have you ever wondered why a tennis ball is fuzzy and why a golf ball has dim- ples? A “spitball” is an illegal baseball pitch because it makes the ball act too much like the fuzzy tennis ball or the dim- pled golf ball. What principles of physics govern the behavior of these three pieces of sporting equipment (and also keep airplanes in the sky)? (George Semple) P U Z Z L E R P U Z Z L E R 15.1 Pressure 15.2 Variation of Pressure with Depth 15.3 Pressure Measurements 15.4 Buoyant Forces and Archimedes’s Principle 15.5 Fluid Dynamics 15.6 Streamlines and the Equation of Continuity 15.7 Bernoulli’s Equation 15.8 (Optional) Other Applications of Bernoulli’s Equation C h a p t e r O u t l i n e
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15.1 Pressure 459 atter is normally classified as being in one of three states: solid, liquid, or gas. From everyday experience, we know that a solid has a definite volume and shape. A brick maintains its familiar shape and size day in and day out. We also know that a liquid has a definite volume but no definite shape. Finally, we know that an unconfined gas has neither a definite volume nor a definite shape. These definitions help us picture the states of matter, but they are somewhat artifi- cial. For example, asphalt and plastics are normally considered solids, but over long periods of time they tend to flow like liquids. Likewise, most substances can be a solid, a liquid, or a gas (or a combination of any of these), depending on the temperature and pressure. In general, the time it takes a particular substance to change its shape in response to an external force determines whether we treat the substance as a solid, as a liquid, or as a gas. A fluid is a collection of molecules that are randomly arranged and held to- gether by weak cohesive forces and by forces exerted by the walls of a container. Both liquids and gases are fluids. In our treatment of the mechanics of fluids, we shall see that we do not need to learn any new physical principles to explain such effects as the buoyant force acting on a submerged object and the dynamic lift acting on an airplane wing. First, we consider the mechanics of a fluid at rest—that is, fluid statics —and derive an expression for the pressure exerted by a fluid as a function of its density and depth. We then treat the mechanics of fluids in motion—that is, fluid dynamics. We can describe a fluid in motion by using a model in which we make certain sim- plifying assumptions. We use this model to analyze some situations of practical im- portance. An analysis leading to Bernoulli’s equation enables us to determine rela- tionships between the pressure, density, and velocity at every point in a fluid. PRESSURE Fluids do not sustain shearing stresses or tensile stresses; thus, the only stress that can be exerted on an object submerged in a fluid is one that tends to compress the object. In other words, the force exerted by a fluid on an object is always per- pendicular to the surfaces of the object, as shown in Figure 15.1.
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