- Fluid statics
Fluid statics (also called hydrostatics) is the
scienceof fluids at rest, and is a sub-field within fluid mechanics. The term usually refers to the mathematical treatment of the subject. It embraces the study of the conditions under which fluids are at rest in stable equilibrium. The use of fluid to do work is called hydraulics, and the scienceof fluids in motion is fluid dynamics.
Pressure in fluids at rest
Due to the inability to resist deformation,
fluids exert pressurenormal to any contacting surface. In addition, when the fluid is at rest that pressureis isotropic, i.e. it acts with equal magnitude in all directions. This characteristic allows fluids to transmit force through the length of pipes or tubes, i.e., a force applied to a fluid in a pipe is transmitted, via the fluid, to the other end of the pipe. If the forces are not balanced, the fluid will move in the direction of the resulting force.
This concept was first formulated, in a slightly extended form, by the French
mathematicianand philosopher Blaise Pascalin 1647and would later be known as Pascal's law. This law has many important applications in hydraulics.
Considering a small cube of liquid at rest below a
free surface, pressure caused by the height of the liquid above must be balanced by a resisting pressure in this small cube. For an infinitely small cube the stress is the same in all directions and liquid weight or equivalent pressurecan be expressed as :where,
* "P" is the hydrostatic pressure (Pa);
* "ρ" is the liquid
* "g" is gravitational acceleration (m/s2);
* "h" is the height of liquid above (m);
* "Pa" is the atmospheric pressure (Pa).
ideal gas lawpredicts that, for a gas of constant temperature, "T", its density, ρ, will vary with height, "h", as:
where::"g" = the acceleration due to gravity:"T" = Absolute
temperature(e.g. kelvins):"R" = Ideal gas constant:"M" = Molar mass:"ρ" = Density:"h" = height
solidbody immersed in a fluid will have an upward buoyant force acting on it equal to the weight of displaced fluid. This is due to the hydrostatic pressure in the fluid.
In the case of a
container ship, for instance, its weight force is balanced by a buoyant force from the displaced water, allowing it to float. If more cargo is loaded onto the ship, it would sit lower in the water - displacing more water and thus receive a higher buoyant force to balance the increased weight force.
Discovery of the principle of
buoyancyis attributed to Archimedes.
A floating object is stable if it tends to restore itself to an equilibrium position after a small displacement. For example, floating objects will generally have vertical stability, as if the object is pushed down slightly, this will create a greater buoyant force, which, unbalanced against the weight force will push the object back up.
Rotational stability is of great importance to floating vessels. Given a small angular displacement, the vessel may return to its original position (stable), move away from its original position (unstable), or remain where it is (neutral).
Rotational stability depends on the relative lines of action of forces on an object. The upward buoyant force on an object acts through the centre of buoyancy, being the centroid of the displaced volume of fluid. The weight force on the object acts through its
center of gravity. An object will be stable if an angular displacement moves the line of action of these forces to set up a 'righting moment'. See also Angle of loll.
Liquids-fluids with free surfaces
Liquids can have free surfaces at which they interface with gases, or with a
vacuum. In general, the lack of the ability to sustain a shear stressentails that free surfaces rapidly adjust towards an equilibrium. However, on small length scales, there is an important balancing force from surface tension.
urface tension effects
When liquids are constrained in vessels whose dimensions are small, compared to the relevant length scales,
surface tensioneffects become important leading to the formation of a meniscusthrough capillary action. This capillary action has profound consequences for biological systems as it is part of one of the two driving mechanisms of the flow of water in plant xylem, the transpirational pull.
Without surface tension,
drops would not be able to form. The dimensions and stability of drops are determined by surface tension.
Angle of loll
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