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The hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids. A hydrostatic balance is a particular balance for weighing substances in water. Hydrostatic balance allows the discovery of their specific gravities. This equilibrium is strictly applicable when an ideal fluid is in steady horizontal laminar flow ...
This article summarizes equations in the theory of fluid mechanics. Definitions. Flux F through a surface, dS is the differential vector area element, ...
Balance for some integrated fluid quantity in a control volume enclosed by a control surface. The assumptions inherent to a fluid mechanical treatment of a physical system can be expressed in terms of mathematical equations. Fundamentally, every fluid mechanical system is assumed to obey: Conservation of mass; Conservation of energy
Fluid statics or hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium [1] and "the pressure in a fluid or exerted by a fluid on an immersed body". [ 2 ] It encompasses the study of the conditions under which fluids are at rest in stable equilibrium as opposed to fluid dynamics , the study of fluids in motion.
The equation to calculate the pressure inside a fluid in equilibrium is: + = where f is the force density exerted by some outer field on the fluid, and σ is the Cauchy stress tensor. In this case the stress tensor is proportional to the identity tensor:
The preceding equilibrium equations are typically applied for each phase (liquid or vapor) individually, but the result can be plotted in a single diagram. In a binary boiling-point diagram, temperature ( T ) (or sometimes pressure) is graphed vs. x 1 .
The compressible Euler equations consist of equations for conservation of mass, balance of momentum, and balance of energy, together with a suitable constitutive equation for the specific energy density of the fluid. Historically, only the equations of conservation of mass and balance of momentum were derived by Euler.
This equation is called the mass continuity equation, or simply the continuity equation. This equation generally accompanies the Navier–Stokes equation. In the case of an incompressible fluid, Dρ / Dt = 0 (the density following the path of a fluid element is constant) and the equation reduces to: