Fluid Statics and Buoyancy

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Fluid statics concerns the behavior of fluids that possess no linear acceleration within a global (Earth) coordinate system. This includes fluids at rest as well as fluids possessing steady motion such that no net forces exist. Such motions may include steady linear motion within the global coordinate system as well as rotation with constant angular velocity about a fixed vertical axis. In this latter case, centrifugal forces must be balanced by centripetal forces (which arise, for example, from a pressure gradient acting toward the axis of rotation). Moreover, we assert that no relative motion between adjacent fluid elements exists. Fluid motion, if present, is therefore like that of a rigid body. In addition, we neglect molecular motions that lead to mass transport by diffusion. Thus, the idea of a static fluid is a macroscopic one. The developments in this chapter clarify how pressure varies with coordinate position in a static fluid. Both compressible and incompressible fluids are treated. In the simplest case in which the density of a fluid is constant, we will see that pressure varies linearly with vertical position in the fluid according to the hydrostatic equation. In addition, we will consider the possibility that fluid density is not constant. Then, variations in density must be taken into account when computing the pressure at a given position in a fluid column; the pressure arising from the weight of the overlying fluid no longer varies linearly with depth. In the case of an isothermal fluid, whose temperature is constant throughout, any variation in density must arise purely from the compressible behavior of the fluid in response to variations in pressure. In the case where temperature varies with position, fluid density may vary with both pressure and temperature. We will in this regard consider the case of a thermally stratified fluid whose temperature varies only with the vertical coordinate direction. Because fluid statics requires treating how fluid temperature, pressure, and density are related, the developments below make use of thermodynamical principles developed in Chapter 4.