The simplest state of a fluid is the state of rest: the macroscopically observed velocity vanishes, and the forces developing in the fluid are described in terms of the pressure field established in response to a body force. The subject of hydrostatics encompasses two main topics: the computation of forces exerted on immersed surfaces and submerged bodies, and the study of the shapes of interfaces separating two stationary, translating, or rotating fluids. The problem statement and mathematical formulation in both cases is straightforward, but deriving solutions for all but the simplest configurations requires the use of numerical methods for solving algebraic, ordinary, and partial differential equations.
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