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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 mot

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Fluid statics
Continuum mechanics
Laws
Conservation of massConservation of momentumConservation of energyEntropy Inequality
Solid mechanics
Solids · Stress · Deformation · Finite straintheory · Infinitesimal strain theory · Elasticity ·Linear elasticity · Plasticity · Viscoelasticity ·Hooke's law · Rheology
Fluid mechanics
Fluids ·
Fluid statics
Fluid dynamics · Viscosity · Newtonian fluidsNon-Newtonian fluidsSurface tension
Scientists
Newton · Stokes · Navier · Cauchy· Hooke ·Bernoulli
From Wikipedia, the free encyclopedia
Fluid statics
(also called
hydrostatics
) is the scienceof fluids at rest, and is a sub-field within fluidmechanics. The term usually refers to the mathematicaltreatment of the subject. It embraces the study of theconditions under which fluids are at rest in stableequilibrium. The use of fluid to do work is calledhydraulics, and the science of fluids in motion is fluiddynamics.
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
Due to the fundamental nature of fluids, a fluid cannotremain at rest under the presence of a shear stress.However, fluids can exert pressure normal to anycontacting surface. If a point in the fluid is thought of as an infinitesimally small cube, then it follows fromthe principles of equilibrium that the pressure on everyside of this unit of fluid must be equal. If this were notthe case, the fluid would move in the direction of the resulting force. Thus, the pressure on a fluid at restis isotropic, i.e. it acts with equal magnitude in all directions. This characteristic allows fluids to transmitforce through the length of pipes or tubes, i.e., a force applied to a fluid in a pipe is transmitted, via thefluid, to the other end of the pipe.This concept was first formulated, in a slightly extended form, by the French mathematician andphilosopher Blaise Pascal in 1647 and would later be known as Pascal's law. This law has manyimportant applications in hydraulics.Page 1 of 4Fluid statics - Wikipedia, the free encyclopedia8/3/2009http://en.wikipedia.org/w/index.php?title=Fluid_statics&printable=yes
Table of Hydraulics and Hydrostatics,from the 1728
Cyclopaedia
Hydrostatic pressure
In equilibrium, the properties of a fluid can be determinedfrom a control volume analysis of an infinitesimally smallcube of water. From the knowledge that the stress on allsides of this cube must be normal and equal in magnitude,the pressure gradient can be found to be linearly increasingin a potential gradient. This potential gradient is most oftenrecognized as gravity but can also be realized from thepresence of an electric field or other potential fields. Withina potential gradient imposed by gravity, the pressure withina fluid will increase linearly as the product of the fluidsdensity and gravity. Since many liquids can be consideredincompressible, a reasonably good estimation can be madefrom assuming a constant density throughout a liquid. Thesame assumption cannot be made within a gaseousenvironment. After integration is performed to determine thepressure within the fluid, the constant of integration isdependent on the atmospheric pressure if the fluid isexposed to the open air. If the water is in a closed system,the pressure's constant of integration is equal to somereference pressure within the system.where,
P
is the hydrostatic pressure (Pa);
■
ρ
is the liquid density (kg/m
3
);
■
f
is the body force per unit volume acting on the fluid (N/m
3
)
■
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 consideredincompressible 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/m
3
);
■
g
is gravitational acceleration (m/s
2
);
■
h
is the height of liquid above (m).
■
P
0
is the reference pressure(Pa)
■
This argument can be generalized to non-uniform fluids in a gravitational field, givingPage 2 of 4Fluid statics - Wikipedia, the free encyclopedia8/3/2009http://en.wikipedia.org/w/index.php?title=Fluid_statics&printable=yes
where the integral over the dummy variable
s
is from the depth in question to the location wherepressure 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 withheight,
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
= heightIf there are multiple types of molecules in the gas, the partial pressure of each type will be given by thisequation. Under most conditions, the distribution of each species of gas is independent of the otherspecies.
Buoyancy
Any body of arbitrary shape which is immersed, partly or fully, in a fluid will experience the action of anet force in the opposite direction of the local pressure gradient. If this pressure gradient arises fromgravity, the net force is in the vertical direction opposite that of the gravitational force. This verticalforce is termed buoyancy or buoyant force and is equal in magnitude, but opposite in direction, to theweight 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 - displacingmore 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 lengthscales, surface tension effects become important leading to the formation of a meniscus throughcapillary 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.Page 3 of 4Fluid statics - Wikipedia, the free encyclopedia8/3/2009http://en.wikipedia.org/w/index.php?title=Fluid_statics&printable=yes
This page was last modified on 31 July 2009 at 18:42.
■
Text is available under the Creative Commons Attribution/Share-Alike License; additional termsmay apply. See Terms of Use for details.Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profitorganization.
■
Drops
Without surface tension, drops would not be able to form. The dimensions and stability of drops aredetermined by surface tension.The drop's surface tension is directly proportional to the cohesionproperty of the fluid.Retrieved from http://en.wikipedia.org/wiki/Fluid_statics Categories: Continuum mechanics | Pressure | HydrostaticsHidden categories: sources (Erik9bot)Articles lackingPage 4 of 4Fluid statics - Wikipedia, the free encyclopedia8/3/2009http://en.wikipedia.org/w/index.php?title=Fluid_statics&printable=yes

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