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Diagram of a newly formed planet in a state of hydrostatic equilibrium. In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. [1]
For a sunken object, the entire volume displaces water, and there will be an additional force of reaction from the solid floor. In order for Archimedes' principle to be used alone, the object in question must be in equilibrium (the sum of the forces on the object must be zero), therefore; =,
This vertical force is termed buoyancy or buoyant force and is equal in magnitude, but opposite in direction, to the weight of the displaced fluid. Mathematically, = where ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of fluid directly above the curved surface. [8]
In fluid mechanics, the pressure-gradient force is the force that results when there is a difference in pressure across a surface. In general, a pressure is a force per unit area across a surface. A difference in pressure across a surface then implies a difference in force, which can result in an acceleration according to Newton's second law of ...
Heath called it "a veritable tour de force which must be read in full to be appreciated." [5] The book contains a detailed investigation of the stable equilibrium positions of floating right paraboloids of various shapes and relative densities when floating in a fluid of greater specific gravity, according to geometric and hydrostatic ...
Buoyancy is a function of the force of gravity or other source of acceleration on objects of different densities, and for that reason is considered an apparent force, in the same way that centrifugal force is an apparent force as a function of inertia. Buoyancy can exist without gravity in the presence of an inertial reference frame, but ...
The energy entering through A 1 is the sum of the kinetic energy entering, the energy entering in the form of potential gravitational energy of the fluid, the fluid thermodynamic internal energy per unit of mass (ε 1) entering, and the energy entering in the form of mechanical p dV work: = (+ + +) where Ψ = gz is a force potential due to the ...
The normal force N is equal, opposite, and collinear to the gravitational force mg so the net force and moment is zero. Consequently, the object is in a state of static mechanical equilibrium. In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero.