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14 - Fluid Mechanics

# 14 - Fluid Mechanics - Chapter 14 Fluid Mechanics CHAPTE R...

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Chapter 14 Fluid Mechanics CHAPTER OUTLINE 14.1 Pressure 14.2 Variation of Pressure with Depth 14.3 Pressure Measurements 14.4 Buoyant Forces and Archimedes’s Principle 14.5 Fluid Dynamics 14.6 Bernoulli’s Equation 14.7 Other Applications of Fluid Dynamics 420 ± These hot-air balloons ﬂoat because they are ﬁlled with air at high temperature and are surrounded by denser air at a lower temperature. In this chapter, we will explore the buoyant force that supports these balloons and other ﬂoating objects. (Richard Megna/Fundamental Photographs)

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421 M 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 descriptions help us picture the states of matter, but they are somewhat artiﬁcial. 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 par- ticular substance to change its shape in response to an external force determines whether we treat the substance as a solid, a liquid, or a gas. A ﬂuid is a collection of molecules that are randomly arranged and held together 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 do not need to learn any new physi- cal principles to explain such effects as the buoyant force acting on a submerged ob- ject and the dynamic lift acting on an airplane wing. First, we consider the mechanics of a ﬂuid at rest—that is, ﬂuid statics . We then treat the mechanics of ﬂuids in motion— that is, ﬂuid dynamics . We can describe a ﬂuid in motion by using a model that is based upon certain simplifying assumptions. 14.1 Pressure Fluids do not sustain shearing stresses or tensile stresses; thus, the only stress that can be exerted on an object submerged in a static ﬂuid is one that tends to compress the object from all sides. In other words, the force exerted by a static ﬂuid on an object is always perpendicular to the surfaces of the object, as shown in Figure 14.1. The pressure in a ﬂuid can be measured with the device pictured in Figure 14.2. The device consists of an evacuated cylinder that encloses a light piston connected to a spring. As the device is submerged in a ﬂuid, the ﬂuid presses on the top of the piston and compresses the spring until the inward force exerted by the ﬂuid is balanced by the outward force exerted by the spring. The ﬂuid pressure can be measured directly if the spring is calibrated in advance. If F is the magnitude of the force exerted on the piston and A
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14 - Fluid Mechanics - Chapter 14 Fluid Mechanics CHAPTE R...

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