The Fluid Static In Oil & Gas Indutry - Wikipedia

Fluid statics - Wikipedia, the free encyclopedia

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Fluid statics From Wikipedia, the free encyclopedia Continuum mechanics

Fluid statics (also called hydrostatics) is the science of 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 science of fluids in motion is fluid dynamics. Laws

Contents ■ 1 Pressure in fluids at rest ■ 1.1 Hydrostatic pressure ■ 1.2 Atmospheric pressure ■ 1.3 Buoyancy ■ 2 Liquids-fluids with free surfaces ■ 2.1 Capillary action ■ 2.2 Drops

Pressure in fluids at rest

Conservation of mass Conservation of momentum Conservation of energy Entropy Inequality Solid mechanics Solids · Stress · Deformation · Finite strain theory · Infinitesimal strain theory · Elasticity · Linear elasticity · Plasticity · Viscoelasticity · Hooke's law · Rheology Fluid mechanics Fluids · Fluid statics Fluid dynamics · Viscosity · Newtonian fluids Non-Newtonian fluids Surface tension

Due to the fundamental nature of fluids, a fluid cannot remain at rest under the presence of a shear stress. Scientists However, fluids can exert pressure normal to any Newton · Stokes · Navier · Cauchy· Hooke · contacting surface. If a point in the fluid is thought of Bernoulli as an infinitesimally small cube, then it follows from the principles of equilibrium that the pressure on every side of this unit of fluid must be equal. If this were not the case, the fluid would move in the direction of the resulting force. Thus, the pressure on a fluid at rest is 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. This concept was first formulated, in a slightly extended form, by the French mathematician and philosopher Blaise Pascal in 1647 and would later be known as Pascal's law. This law has many important applications in hydraulics.

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Hydrostatic pressure In equilibrium, the properties of a fluid can be determined from a control volume analysis of an infinitesimally small cube of water. From the knowledge that the stress on all sides of this cube must be normal and equal in magnitude, the pressure gradient can be found to be linearly increasing in a potential gradient. This potential gradient is most often recognized as gravity but can also be realized from the presence of an electric field or other potential fields. Within a potential gradient imposed by gravity, the pressure within a fluid will increase linearly as the product of the fluids density and gravity. Since many liquids can be considered incompressible, a reasonably good estimation can be made from assuming a constant density throughout a liquid. The same assumption cannot be made within a gaseous environment. After integration is performed to determine the pressure within the fluid, the constant of integration is dependent on the atmospheric pressure if the fluid is exposed to the open air. If the water is in a closed system, the pressure's constant of integration is equal to some reference pressure within the system. Table of Hydraulics and Hydrostatics, from the 1728 Cyclopaedia

where, ■ ■ ■ ■

P is the hydrostatic pressure (Pa); ρ is the liquid density (kg/m3); f is the body force per unit volume acting on the fluid (N/m3) for gravity this is g, for EM fields it is dependent on the charge of the fluid

For water that is only exposed to a gravitational force, the water can typically be considered incompressible and as such varies only in the gravitational direction (up and down).

where, ■ ■ ■ ■ ■

P is the hydrostatic pressure (Pa); ρ is the liquid density (kg/m3); g is gravitational acceleration (m/s2); h is the height of liquid above (m). P0 is the reference pressure(Pa)

This argument can be generalized to non-uniform fluids in a gravitational field, giving

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where the integral over the dummy variable s is from the depth in question to the location where pressure is defined to be zero (often, the liquid surface).

Atmospheric pressure Statistical mechanics shows that, for a gas of constant temperature, T, its pressure, p will vary with height, h, as:

where: g = the acceleration due to gravity T = Absolute temperature (i.e. kelvins) k = Boltzmann constant M = mass of a single molecule of gas p = pressure h = height If there are multiple types of molecules in the gas, the partial pressure of each type will be given by this equation. Under most conditions, the distribution of each species of gas is independent of the other species.

Buoyancy Any body of arbitrary shape which is immersed, partly or fully, in a fluid will experience the action of a net force in the opposite direction of the local pressure gradient. If this pressure gradient arises from gravity, the net force is in the vertical direction opposite that of the gravitational force. 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. In the case of a ship, for instance, its weight is balanced by a buoyant force from the displaced water, allowing it to float. If more cargo is loaded onto the ship, it would sink more into the water - displacing more water and thus receive a higher buoyant force to balance the increased weight. Discovery of the principle of buoyancy is attributed to Archimedes.

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 stress entails that free surfaces rapidly adjust towards an equilibrium. However, on small length scales, there is an important balancing force from surface tension. Capillary action When liquids are constrained in vessels whose dimensions are small, compared to the relevant length scales, surface tension effects become important leading to the formation of a meniscus through 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.

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Drops Without surface tension, drops would not be able to form. The dimensions and stability of drops are determined by surface tension.The drop's surface tension is directly proportional to the cohesion property of the fluid. Retrieved from "http://en.wikipedia.org/wiki/Fluid_statics" Categories: Continuum mechanics | Pressure | Hydrostatics Hidden categories: Articles lacking sources (Erik9bot) ■ This page was last modified on 31 July 2009 at 18:42. ■ Text is available under the Creative Commons Attribution/Share-Alike License; additional terms may apply. See Terms of Use for details. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.

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