reynold's no

8/7/2019 Reynold's No

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In fluid mechanics, the Reynolds numberRe is a dimensionless numberthat gives a measure of

the ratio ofinertial forces toviscousforces and consequently quantifies the

relative importance of these two types of forces for given flow conditions. The concept was

introduced by George Gabriel Stokesin 1851,[1]but the Reynolds number is named afterOsborne

Reynolds (18421912), who popularized its use in 1883.[2][3]

Reynolds numbers frequently arise when performingdimensional analysis of fluid dynamics

problems, and as such can be used to determinedynamic similitude between different

experimental cases. They are also used to characterize different flow regimes, such

aslaminarorturbulent flow: laminar flow occurs at low Reynolds numbers, where viscous forces

are dominant, and is characterized by smooth, constant fluid motion, while turbulent flow occurs

at high Reynolds numbers and is dominated by inertial forces, which tend to produce

random eddies,vorticesand other flow instabilities.

Contents

[hide]

1 Definition

o 1.1 Flow in Pipe

o 1.2 Flow in a non-circular duct

o 1.3 Flow in a Wide Duct

o 1.4 Flow in an Open Channel

o 1.5 Object in a fluid

1.5.1 Sphere in a fluid

1.5.2 Oblong object in a fluid

1.5.3 Fall velocity

o 1.6 Packed Bed

o 1.7 Stirred Vessel

2 Transition Reynolds number

3 Reynolds number in pipe friction

4 The similarity of flows

5 Reynolds number sets the smallest scales of turbulent motion

6 Example of the importance of the Reynolds number

7 Reynolds number in physiology

8 Reynolds number in viscous fluids
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_numberhttp://en.wikipedia.org/wiki/Reynolds_number#Reynolds_number_in_pipe_friction%23Reynolds_number_in_pipe_frictionhttp://en.wikipedia.org/wiki/Reynolds_number#The_similarity_of_flows%23The_similarity_of_flowshttp://en.wikipedia.org/wiki/Reynolds_number#Reynolds_number_sets_the_smallest_scales_of_turbulent_motion%23Reynolds_number_sets_the_smallest_scales_of_turbulent_motionhttp://en.wikipedia.org/wiki/Reynolds_number#Example_of_the_importance_of_the_Reynolds_number%23Example_of_the_importance_of_the_Reynolds_numberhttp://en.wikipedia.org/wiki/Reynolds_number#Reynolds_number_in_physiology%23Reynolds_number_in_physiologyhttp://en.wikipedia.org/wiki/Reynolds_number#Reynolds_number_in_viscous_fluids%23Reynolds_number_in_viscous_fluids


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9 Where does it come from?

10 See also

11 References and notes

o 11.1 Further reading

12 External links

[edit]Definition

Reynolds number can be defined for a number of different situations where a fluid is in relative

motion to a surface (the definition of the Reynolds number is not to be confused with

the Reynolds Equation or lubrication equation). These definitions generally include the fluid

properties of density and viscosity, plus a velocity and a characteristic length orcharacteristic

dimension. This dimension is a matter of convention - for example a radius or diameter areequally valid for spheres or circles, but one is chosen by convention. For aircraft or ships, the

length or width can be used. For flow in a pipe or a sphere moving in a fluid the internal diameter

is generally used today. Other shapes (such as rectangular pipes or non-spherical objects) have

an equivalent diameterdefined. For fluids of variable density (e.g. compressible gases) or

variable viscosity (non-Newtonian fluids) special rules apply. The velocity may also be a matter of

convention in some circumstances, notably stirred vessels.

[4]

where:

is the mean fluid velocity (SI units: m/s)

L is a characteristic linear dimension, (traveled length of fluid, or hydraulic radius

when dealing with river systems) (m)

is the dynamic viscosity of thefluid (Pas or Ns/m or kg/ms)

is the kinematic viscosity ( = /) (m/s)

is the density of the fluid (kg/m)

Q is the volumetricflow rate(m/s)

A is the pipe cross-sectionalarea (m).
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Note that this is equal to the ratio between , which is the drag (up to a numerical

factor, half the drag coefficient), and , which is the force due to viscosity(up to a

numerical factor depending on the form of the flow).

[edit]Flow in Pipe

For flow in a pipe or tube, the Reynolds number is generally defined as:[5]

where:

D is the hydraulic diameter of the pipe (m).

[edit]Flow in a non-circular duct

For shapes such as squares, rectangular or annular ducts (where the height and width

are comparable) the characteristic dimension for internal flow situations is taken to be

the hydraulic diameter,DH, defined as 4 times the cross-sectional area, divided by

the wetted perimeter. The wetted perimeter for a channel is the total perimeter of all

channel walls that are in contact with the flow.[6]

For a circular pipe, the hydraulic diameter is exactly equal to the inside pipe

diameter, as can be shown mathematically.

For an annular duct, such as the outer channel in a tube-in-tubeheat exchanger,

the hydraulic diameter can be shown algebraically to reduce to

DH,annulus = Do Di

where

Di is the inside diameter of the outside pipe, and

Do is the outside diameter of the inside pipe.

For calculations involving flow in non-circular ducts, the hydraulic

diameter can be substituted for the diameter of a circular duct,

with reasonable accuracy.

[edit]Flow in a Wide Duct
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For a fluid moving between two plane parallel surfaces (where the width is much greater than the

space between the plates) then the characteristic dimension is twice the distance between the

plates.[7]

[edit]Flow in an Open Channel

For flow of liquid with a free surface, the hydraulic radius must be determined. This is the cross-

sectional area of the channel divided by the wetted perimeter. For a semi-circular channel, it is

half the radius. For a rectangular channel, the hydraulic radius is the cross-sectional area divided

by the wetted perimeter. Some texts then use a characteristic dimension that is 4 times the

hydraulic radius (chosen because it gives the same value of Re for the onset of turbulence as in

pipe flow),[8]while others the hydraulic radius as the characteristic length-scale with consequently

different values of Re for transition and turbulent flow.

[edit]Object in a fluid

The Reynolds number for an object in a fluid, called the particle Reynolds number and often

denotedRep, is important when considering the nature of flow around that grain, whether or

notvortex sheddingwill occur, and its fall velocity.

[edit]Sphere in a fluid

For a sphere in a fluid, the characteristic length-scale is the diameter of the sphere and the

characteristic velocity is that of the sphere relative to the fluid some distance away from the

sphere (such that the motion of the sphere does not disturb that reference parcel of fluid). The

density and viscosity are those belonging to the fluid.[9]Note that purely laminar flow only exists

up to Re = 0.1 under this definition.

Under the condition of low Re, the relationship between force and speed of motion is given

by Stokes' law.[10]

[edit]Oblong object in a fluid

The equation for an oblong object is identical to that of a sphere, with the object being

approximated as anellipsoidand the axis of intermediate length being chosen as the

characteristic length scale. Such considerations are important in natural streams, for example,

where there are few perfectly spherical grains. For grains in which measurement of each axis isimpractical (e.g., because they are too small), sieve diameters are used instead as the

characteristic particle length-scale. Both approximations alter the values of the critical Reynolds

number.

[edit]Fall velocity
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The particle Reynolds number is important in determining the fall velocity of a particle. When the

particle Reynolds number indicates laminar flow,Stokes' lawcan be used to calculate its fall

velocity. When the particle Reynolds number indicates turbulent flow, a turbulent drag law must

be constructed to model the appropriate settling velocity.

[edit]Packed Bed

For flow of fluid through a bed of approximately spherical particles of diameterDin contact, if the

voidage (fraction of the bed not filled with particles) is and the superficial velocityV(i.e. the

velocity through the bed as if the particles were not there - the actual velocity will be higher) then

a Reynolds number can be defined as:

Laminar conditions apply up to Re = 10, fully turbulent from 2000.[9][edit]Stirred Vessel

In a cylindrical vessel stirred by a central rotating paddle, turbine or propellor, the characteristic

dimension is the diameter of the agitatorD. The velocity isNDwhereNis the

rotational speed (revolutions per second). Then the Reynolds number is:

The system is fully turbulent for values of Re above 10 000.[11]

[edit]Transition Reynolds number

[citation needed]Inboundary layerflow over a flat plate, experiments can confirm

that, after a certain length of flow, a laminar boundary layer will become unstable and become

turbulent. This instability occurs across different scales and with different fluids, usually

when , wherexis the distance from the leading edge of the flat plate, and the

flow velocity is the freestream velocity of the fluid outside the boundary layer.

For flow in a pipe of diameterD, experimental observations show that for 'fully developed' flow

(Note:[12]), laminar flow occurs whenReD < 2300and turbulent flow occurs whenReD >

4000[13]. In the interval between 2300 and 4000, laminar and turbulent flows are possible

('transition' flows), depending on other factors, such as pipe roughness and flow uniformity). This

result is generalised to non-circular channels using thehydraulic diameter, allowing a transition

Reynolds number to be calculated for other shapes of channel.
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ThesetransitionReynolds numbers are also calledcritical Reynolds numbers, and

were studied by Osborne Reynolds around 1895 [see

Rott].

[edit]Reynolds number in pipe friction

Pressure drops seen for fully-developed flow of fluids through pipes can be predicted using

theMoody diagramwhich plots the DarcyWeisbachfriction factorfagainst Reynolds

numberReand relative roughness / D. The diagram clearly shows the laminar, transition, and

turbulent flow regimes as Reynolds number increases. The nature of pipe flow is strongly

dependent on whether the flow is laminar or turbulant

[edit]The similarity of flows

In order for two flows to be similar they must have the same geometry, and have equal Reynolds

numbers andEuler numbers. When comparing fluid behaviour at corresponding points in a

model and a full-scale flow, the following holds:

marked with 'm' concern the flow around the model and the others the actual flow. This allows

engineers to perform experiments with reduced models in water channelsorwind tunnels, and

correlate the data to the actual flows, saving on costs during experimentation and on lab time.

Note that true dynamic similitude may require matching otherdimensionless numbersas well,

such as theMach numberused incompressible flows, or the Froude numberthat governs

open-channel flows. Some flows involve more dimensionless parameters than can be practically

satisfied with the available apparatus and fluids (for example air or water), so one is forced to

decide which parameters are most important. For experimental flow modeling to be useful, it

requires a fair amount of experience and judgement of the engineer.

Reynolds number[14][15]

Bacteria ~105

Spermatozoa ~104[16]

Ciliate ~101
http://en.wikipedia.org/wiki/Laminar-turbulent_transitionhttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=13http://en.wikipedia.org/wiki/Moody_diagramhttp://en.wikipedia.org/wiki/Friction_factorhttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=14http://en.wikipedia.org/wiki/Euler_number_(physics)http://en.wikipedia.org/wiki/Euler_number_(physics)http://en.wikipedia.org/wiki/Water_channelhttp://en.wikipedia.org/wiki/Wind_tunnelhttp://en.wikipedia.org/wiki/Wind_tunnelhttp://en.wikipedia.org/wiki/Dimensionless_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Compressible_flowhttp://en.wikipedia.org/wiki/Froude_numberhttp://en.wikipedia.org/wiki/Reynolds_number#cite_note-13%23cite_note-13http://en.wikipedia.org/wiki/Reynolds_number#cite_note-13%23cite_note-13http://en.wikipedia.org/wiki/Reynolds_number#cite_note-14%23cite_note-14http://en.wikipedia.org/wiki/Bacteriahttp://en.wikipedia.org/wiki/Spermatozoahttp://en.wikipedia.org/wiki/Reynolds_number#cite_note-15%23cite_note-15http://en.wikipedia.org/wiki/Ciliatehttp://en.wikipedia.org/wiki/File:Moody_diagram.jpghttp://en.wikipedia.org/wiki/Laminar-turbulent_transitionhttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=13http://en.wikipedia.org/wiki/Moody_diagramhttp://en.wikipedia.org/wiki/Friction_factorhttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=14http://en.wikipedia.org/wiki/Euler_number_(physics)http://en.wikipedia.org/wiki/Water_channelhttp://en.wikipedia.org/wiki/Wind_tunnelhttp://en.wikipedia.org/wiki/Dimensionless_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Compressible_flowhttp://en.wikipedia.org/wiki/Froude_numberhttp://en.wikipedia.org/wiki/Reynolds_number#cite_note-13%23cite_note-13http://en.wikipedia.org/wiki/Reynolds_number#cite_note-14%23cite_note-14http://en.wikipedia.org/wiki/Bacteriahttp://en.wikipedia.org/wiki/Spermatozoahttp://en.wikipedia.org/wiki/Reynolds_number#cite_note-15%23cite_note-15http://en.wikipedia.org/wiki/Ciliate


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Smallest Fish~1

Blood flow inbrain~ 1 102

Blood flow inaorta~ 1 103

t flow~ 2.3 103to 5.0 104for pipe flow to 106for boundary layers

Typical pitch inMajor League

Baseball ~ 2 105

Personswimming~ 4 106

FastestFish~106

Blue Whale ~ 3 108

A large ship (RMS Queen Elizabeth

2) ~ 5 109

[edit]Reynolds number sets the smallest scales of turbulent motion

In a turbulent flow, there is a range of

scales of the time-varying fluid motion. The size of the largest scales of fluid motion (sometimes

called eddies) are set by the overall geometry of the flow. For instance, in an industrial smoke

stack, the largest scales of fluid motion are as big as the diameter of the stack itself. The size of

the smallest scales is set by the Reynolds number. As the Reynolds number increases, smaller

and smaller scales of the flow are visible. In a smoke stack, the smoke may appear to have many

very small velocity perturbations or eddies, in addition to large bulky eddies. In this sense, the

Reynolds number is an indicator of the range of scales in the flow. The higher the Reynolds

number, the greater the range of scales. The largest eddies will always be the same size; the

smallest eddies are determined by the Reynolds number.

What is the explanation for this

phenomenon? A large Reynolds number indicates that viscous forces are not important at large

scales of the flow. With a strong predominance of inertial forces over viscous forces, the largest

scales of fluid motion are undampedthere is not enough viscosity to dissipate their motions.

The kinetic energy must "cascade" from these large scales to progressively smaller scales until a

level is reached for which the scale is small enough for viscosity to become important (that is,

viscous forces become of the order of inertial ones). It is at these small scales where the

dissipation of energy by viscous action finally takes place. The Reynolds number indicates at

what scale this viscous dissipation occurs. Therefore, since the largest eddies are dictated by the
http://en.wikipedia.org/wiki/Fishhttp://en.wikipedia.org/wiki/Blood_flowhttp://en.wikipedia.org/wiki/Brainhttp://en.wikipedia.org/wiki/Aortahttp://en.wikipedia.org/wiki/Major_League_Baseballhttp://en.wikipedia.org/wiki/Major_League_Baseballhttp://en.wikipedia.org/wiki/Human_swimminghttp://en.wikipedia.org/wiki/Fishhttp://en.wikipedia.org/wiki/Blue_Whalehttp://en.wikipedia.org/wiki/RMS_Queen_Elizabeth_2http://en.wikipedia.org/wiki/RMS_Queen_Elizabeth_2http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=15http://en.wikipedia.org/wiki/Fishhttp://en.wikipedia.org/wiki/Blood_flowhttp://en.wikipedia.org/wiki/Brainhttp://en.wikipedia.org/wiki/Aortahttp://en.wikipedia.org/wiki/Major_League_Baseballhttp://en.wikipedia.org/wiki/Major_League_Baseballhttp://en.wikipedia.org/wiki/Human_swimminghttp://en.wikipedia.org/wiki/Fishhttp://en.wikipedia.org/wiki/Blue_Whalehttp://en.wikipedia.org/wiki/RMS_Queen_Elizabeth_2http://en.wikipedia.org/wiki/RMS_Queen_Elizabeth_2http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=15


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flow geometry and the smallest scales are dictated by the viscosity, the Reynolds number can be

understood as the ratio of the largest scales of the turbulent motion to the smallest scales.

[edit]Example of theimportance of the Reynolds number

If an airplane wing needs testing, one can

make a scaled down model of the wing and test it in a wind tunnel using the same Reynolds

number that the actual airplane is subjected to. If for example the scale model has linear

dimensions one quarter of full size, the flow velocity of the model would have to be multiplied by a

factor of 4 to obtain similar flow behavior.

Alternatively, tests could be conducted in a

water tank instead of in air (provided the compressibility effects of air are not significant). As the

kinematic viscosity of water is around 13 times less than that of air at 15 C, in this case the scalemodel would need to be about one thirteenth the size in all dimensions to maintain the same

Reynolds number, assuming the full-scale flow velocity was used.

The results of the laboratory model will be

similar to those of the actual plane wing results. Thus there is no need to bring a full scale plane

into the lab and actually test it. This is an example of "dynamic similarity".

Reynolds number is important in the

calculation of a body's dragcharacteristics. A notable example is that of the flow around a

cylinder[1]. Above roughly 3106

Re thedrag coefficientdrops considerably. This is important

when calculating the optimal cruise speeds for low drag (and therefore long range) profiles for

airplanes.

[edit]Reynolds number inphysiology

Poiseuille's law on blood circulation in the

body is dependent onlaminar flow. In turbulent flow the flow rate is proportional to the square root

of the pressure gradient, as opposed to its direct proportionality to pressure gradient in laminar

flow.

Using the definition of the Reynolds

number we can see that a large diameter with rapid flow, where the density of the blood is high,

tends towards turbulence. Rapid changes in vessel diameter may lead to turbulent flow, for

instance when a narrower vessel widens to a larger one. Furthermore, an atheroma may be the
http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=16http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=16http://en.wikipedia.org/wiki/Drag_(physics)http://en.wikipedia.org/wiki/Drag_(physics)http://scienceworld.wolfram.com/physics/CylinderDrag.htmlhttp://en.wikipedia.org/wiki/Drag_coefficienthttp://en.wikipedia.org/wiki/Drag_coefficienthttp://en.wikipedia.org/wiki/Drag_coefficienthttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=17http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=17http://en.wikipedia.org/wiki/Poiseuille's_lawhttp://en.wikipedia.org/wiki/Laminar_flowhttp://en.wikipedia.org/wiki/Laminar_flowhttp://en.wikipedia.org/wiki/Atheromahttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=16http://en.wikipedia.org/wiki/Drag_(physics)http://scienceworld.wolfram.com/physics/CylinderDrag.htmlhttp://en.wikipedia.org/wiki/Drag_coefficienthttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=17http://en.wikipedia.org/wiki/Poiseuille's_lawhttp://en.wikipedia.org/wiki/Laminar_flowhttp://en.wikipedia.org/wiki/Atheroma


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cause of turbulent flow, and as such detecting turbulence with a stethoscope may be a sign of

such a condition.

[edit]Reynolds number inviscous fluids

Creeping flow past a sphere:streamlines, drag

force Fd and force by gravity Fg.

Where the viscosity is naturally high, such

as polymer solutions and polymer melts, flow is normally laminar. The Reynolds number is very

small and Stokes' Lawcan be used to measure theviscosityof the fluid. Spheres are allowed to

fall through the fluid and they reach the terminal velocityquickly, from which the viscosity can be

determined.

The laminar flow of polymer solutions is

exploited by animals such as fish and dolphins, who exude viscous solutions from their skin to aid

flow over their bodies while swimming. It has been used in yacht racing by owners who want to

gain a speed advantage by pumping a polymer solution such as low molecular

weight polyoxyethylenein water, over the wetted surface of the hull. It is however, a problem formixing of polymers, because turbulence is needed to distribute fine filler (for example) through the

material. Inventions such as the "cavity transfer mixer" have been developed to produce multiple

folds into a moving melt so as to improve mixing efficiency. The device can be fitted

ontoextrudersto aid mixing.

[edit]Where does it come from?
http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=18http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=18http://en.wikipedia.org/wiki/Streamlinehttp://en.wikipedia.org/wiki/Streamlinehttp://en.wikipedia.org/wiki/Stokes'_Lawhttp://en.wikipedia.org/wiki/Stokes'_Lawhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Terminal_velocityhttp://en.wikipedia.org/wiki/Terminal_velocityhttp://en.wikipedia.org/wiki/Polyoxyethylenehttp://en.wikipedia.org/wiki/Polyoxyethylenehttp://en.wikipedia.org/wiki/Mixturehttp://en.wikipedia.org/wiki/Extruderhttp://en.wikipedia.org/wiki/Extruderhttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=19http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=19http://en.wikipedia.org/wiki/File:Stokes_sphere.svghttp://en.wikipedia.org/wiki/File:Stokes_sphere.svghttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=18http://en.wikipedia.org/wiki/Streamlinehttp://en.wikipedia.org/wiki/Stokes'_Lawhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Terminal_velocityhttp://en.wikipedia.org/wiki/Polyoxyethylenehttp://en.wikipedia.org/wiki/Mixturehttp://en.wikipedia.org/wiki/Extruderhttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=19


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The Reynolds number can be obtained

when one uses the nondimensional form of the incompressibleNavier-Stokes equations:

Each term in the above equation has the

units of a volume force or, equivalently, an acceleration times a density. Each term is thus

dependent on the exact measurements of a flow. When one renders the equation

nondimensional, that is that we multiply it by a factor with inverse units of the base

equation, we obtain a form which does not depend directly on the physical sizes. One

possible way to obtain a nondimensional equation is to multiply the whole equation by

the following factor:

where the symbols are the same as those used in the definition of the Reynolds number. If we

now set:

we can rewrite the Navier-Stokes equation without dimensions:

where the term :

Finally, dropping the primes for ease of reading:

This is why mathematically all flows with the same Reynolds number are comparable.

[edit]See also

DarcyWeisbach equation

HagenPoiseuille law

NavierStokes equations

Reynolds transport theorem
http://en.wikipedia.org/wiki/Nondimensional_numberhttp://en.wikipedia.org/wiki/Navier-Stokes_equationshttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=20http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=20http://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equationhttp://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_lawhttp://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equationshttp://en.wikipedia.org/wiki/Reynolds_transport_theoremhttp://en.wikipedia.org/wiki/Nondimensional_numberhttp://en.wikipedia.org/wiki/Navier-Stokes_equationshttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=20http://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equationhttp://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_lawhttp://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equationshttp://en.wikipedia.org/wiki/Reynolds_transport_theorem


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Stokes Law

[edit]References and notes

1. ^Stokes, George(1851). "On the Effect of the Internal Friction of Fluids on the Motion ofPendulums". Transactions of the Cambridge Philosophical Society9: 8106.

2. ^Reynolds, Osborne(1883). "An experimental investigation of the circumstances which

determine whether the motion of water shall be direct or sinuous, and of the law of

resistance in parallel channels".Philosophical Transactions of the Royal Society174:

935982.doi:10.1098/rstl.1883.0029. JSTOR.

3. ^ Rott, N., Note on the history of the Reynolds number, Annual Review of Fluid

Mechanics, Vol. 22, 1990, pp. 111.

4. ^www.grc.nasa.gov

5. ^Reynolds Number(engineeringtoolbox.com)

6. ^ J.P. Holman, Heat Transfer, McGraw Hill.

7. ^ R. W. Fox, A. T. McDonald, Phillip J. Pritchard Introduction to Fluid Mechanics,6th ed

(John Wiley and Sons)ISBN 0 471 20231 2page 348

8. ^ V. L. Streeter (1962)Fluid Mechanics, 3rd edn (McGraw-Hill)

9. ^ ab M. Rhodes (1989) Introduction to Particle TechnologyWiley ISBN 0-471-98482-5at

Google Books

10. ^ Dusenbery, David B. (2009). Living at Micro Scale, p.49. Harvard University Press,

Cambridge, Mass. ISBN 978-0-674-03116-6.

11. ^ R. K. Sinnott Coulson & Richardson's Chemical Engineering, Volume 6: Chemical

Engineering Design,4th ed (Butterworth-Heinemann)ISBN 0 7506 6538 6page 473

12. ^ Full development of the flow occurs as the flow enters the pipe, the boundary layer

thickens and then stabilises after several diameters distance into the pipe.

13. ^ J.P Holman Heat transfer, McGraw-Hill, 2002, p.207

14. ^ Patel, V. C., W. Rodi, and G. Scheuerer. "Turbulence Models for Near-Wall and Low

Reynolds Number Flows- A Review." AIAA Journal 23.9 (1985): 1308-19.

15. ^ Dusenbery, David B. (2009). Living at Micro Scale, p.136. Harvard University Press,

Cambridge, Mass. ISBN 978-0-674-03116-6.

16. ^ Wiggins, C. H., and R. E. Goldstein. "Flexive and Propulsive Dynamics of Elastica at

Low Reynolds Number." Physical Review Letters 80.17 (1998): 3879-82.

[edit]Further reading
http://en.wikipedia.org/wiki/Stokes_Lawhttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=21http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=21http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Stokes_0-0%23cite_ref-Stokes_0-0http://en.wikipedia.org/wiki/George_Gabriel_Stokeshttp://en.wikipedia.org/wiki/George_Gabriel_Stokeshttp://en.wikipedia.org/wiki/Transactions_of_the_Cambridge_Philosophical_Societyhttp://en.wikipedia.org/wiki/Reynolds_number#cite_ref-PTRS174_1-0%23cite_ref-PTRS174_1-0http://en.wikipedia.org/wiki/Osborne_Reynoldshttp://en.wikipedia.org/wiki/Osborne_Reynoldshttp://en.wikipedia.org/wiki/Philosophical_Transactions_of_the_Royal_Societyhttp://en.wikipedia.org/wiki/Philosophical_Transactions_of_the_Royal_Societyhttp://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.1098%2Frstl.1883.0029http://www.jstor.org/stable/109431http://www.jstor.org/stable/109431http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Rott_2-0%23cite_ref-Rott_2-0http://dx.doi.org/10.1146/annurev.fl.22.010190.000245http://dx.doi.org/10.1146/annurev.fl.22.010190.000245http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-NASA_3-0%23cite_ref-NASA_3-0http://www.grc.nasa.gov/WWW/BGH/reynolds.htmlhttp://en.wikipedia.org/wiki/Reynolds_number#cite_ref-4%23cite_ref-4http://www.engineeringtoolbox.com/reynolds-number-d_237.htmlhttp://en.wikipedia.org/wiki/Reynolds_number#cite_ref-5%23cite_ref-5http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Fox_6-0%23cite_ref-Fox_6-0http://en.wikipedia.org/wiki/Special:BookSources/0471202312http://en.wikipedia.org/wiki/Special:BookSources/0471202312http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Streeter_7-0%23cite_ref-Streeter_7-0http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Rhodes_8-0%23cite_ref-Rhodes_8-0http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Rhodes_8-1%23cite_ref-Rhodes_8-1http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Rhodes_8-1%23cite_ref-Rhodes_8-1http://en.wikipedia.org/wiki/Special:BookSources/0471984825http://en.wikipedia.org/wiki/Special:BookSources/0471984825http://books.google.com/books?id=P9Qgvh7kMP8C&pg=PA29http://books.google.com/books?id=P9Qgvh7kMP8C&pg=PA29http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-9%23cite_ref-9http://en.wikipedia.org/wiki/Special:BookSources/9780674031166http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Sinnott_10-0%23cite_ref-Sinnott_10-0http://en.wikipedia.org/wiki/Special:BookSources/0750665386http://en.wikipedia.org/wiki/Special:BookSources/0750665386http://en.wikipedia.org/wiki/Special:BookSources/0750665386http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-11%23cite_ref-11http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-12%23cite_ref-12http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-13%23cite_ref-13http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-14%23cite_ref-14http://en.wikipedia.org/wiki/Special:BookSources/9780674031166http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-15%23cite_ref-15http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=22http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=22http://en.wikipedia.org/wiki/Stokes_Lawhttp://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=21http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Stokes_0-0%23cite_ref-Stokes_0-0http://en.wikipedia.org/wiki/George_Gabriel_Stokeshttp://en.wikipedia.org/wiki/Transactions_of_the_Cambridge_Philosophical_Societyhttp://en.wikipedia.org/wiki/Reynolds_number#cite_ref-PTRS174_1-0%23cite_ref-PTRS174_1-0http://en.wikipedia.org/wiki/Osborne_Reynoldshttp://en.wikipedia.org/wiki/Philosophical_Transactions_of_the_Royal_Societyhttp://en.wikipedia.org/wiki/Digital_object_identifierhttp://dx.doi.org/10.1098%2Frstl.1883.0029http://www.jstor.org/stable/109431http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Rott_2-0%23cite_ref-Rott_2-0http://dx.doi.org/10.1146/annurev.fl.22.010190.000245http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-NASA_3-0%23cite_ref-NASA_3-0http://www.grc.nasa.gov/WWW/BGH/reynolds.htmlhttp://en.wikipedia.org/wiki/Reynolds_number#cite_ref-4%23cite_ref-4http://www.engineeringtoolbox.com/reynolds-number-d_237.htmlhttp://en.wikipedia.org/wiki/Reynolds_number#cite_ref-5%23cite_ref-5http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Fox_6-0%23cite_ref-Fox_6-0http://en.wikipedia.org/wiki/Special:BookSources/0471202312http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Streeter_7-0%23cite_ref-Streeter_7-0http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Rhodes_8-0%23cite_ref-Rhodes_8-0http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Rhodes_8-1%23cite_ref-Rhodes_8-1http://en.wikipedia.org/wiki/Special:BookSources/0471984825http://books.google.com/books?id=P9Qgvh7kMP8C&pg=PA29http://books.google.com/books?id=P9Qgvh7kMP8C&pg=PA29http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-9%23cite_ref-9http://en.wikipedia.org/wiki/Special:BookSources/9780674031166http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-Sinnott_10-0%23cite_ref-Sinnott_10-0http://en.wikipedia.org/wiki/Special:BookSources/0750665386http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-11%23cite_ref-11http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-12%23cite_ref-12http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-13%23cite_ref-13http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-14%23cite_ref-14http://en.wikipedia.org/wiki/Special:BookSources/9780674031166http://en.wikipedia.org/wiki/Reynolds_number#cite_ref-15%23cite_ref-15http://en.wikipedia.org/w/index.php?title=Reynolds_number&action=edit&section=22


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Zagarola, M.V. and Smits, A.J., Experiments in High Reynolds Number Turbulent Pipe

Flow. AIAApaper #96-0654, 34th AIAA Aerospace Sciences Meeting, Reno, Nevada,

January 1518, 1996.

Jermy M., Fluid Mechanics A Course Reader, Mechanical Engineering Dept., University

of Canterbury, 2005, pp. d5.10.

Hughes, Roger "Civil Engineering Hydraulics," Civil and Environmental Dept., University

of Melbourne 1997, pp. 107152

Fouz, Infaz "Fluid Mechanics," Mechanical Engineering Dept., University of Oxford, 2001,

pp96

E.M. Purcell. "Life at Low Reynolds Number", American Journal of Physics vol 45, p. 3-11

(1977)[2]

Truskey, G.A., Yuan, F, Katz, D.F. (2004). Transport Phenomena in Biological

Systems Prentice Hall, pp. 7. ISBN 0-13-042204-5.ISBN 978-0-13-042204-0.

Fluid dynamicsFrom Wikipedia, the free encyclopedia

Continuum mechanics

[show]Laws

[show]Solid mechanics

[show]Fluid mechanics

[show]Scientists

vde
http://jilawww.colorado.edu/perkinsgroup/Purcell_life_at_low_reynolds_number.pdfhttp://en.wikipedia.org/wiki/Special:BookSources/0130422045http://en.wikipedia.org/wiki/Special:BookSources/9780130422040http://en.wikipedia.org/wiki/Special:BookSources/9780130422040http://en.wikipedia.org/wiki/Special:BookSources/9780130422040http://en.wikipedia.org/wiki/Continuum_mechanicshttp://en.wikipedia.org/wiki/Solid_mechanicshttp://en.wikipedia.org/wiki/Fluid_mechanicshttp://en.wikipedia.org/wiki/Template:Continuum_mechanicshttp://en.wikipedia.org/wiki/Template:Continuum_mechanicshttp://en.wikipedia.org/wiki/Template_talk:Continuum_mechanicshttp://en.wikipedia.org/wiki/Template_talk:Continuum_mechanicshttp://en.wikipedia.org/w/index.php?title=Template:Continuum_mechanics&action=edithttp://en.wikipedia.org/wiki/File:Teardrop_shape.svghttp://en.wikipedia.org/wiki/File:BernoullisLawDerivationDiagram.svghttp://jilawww.colorado.edu/perkinsgroup/Purcell_life_at_low_reynolds_number.pdfhttp://en.wikipedia.org/wiki/Special:BookSources/0130422045http://en.wikipedia.org/wiki/Special:BookSources/9780130422040http://en.wikipedia.org/wiki/Continuum_mechanicshttp://en.wikipedia.org/wiki/Solid_mechanicshttp://en.wikipedia.org/wiki/Fluid_mechanicshttp://en.wikipedia.org/wiki/Template:Continuum_mechanicshttp://en.wikipedia.org/wiki/Template_talk:Continuum_mechanicshttp://en.wikipedia.org/w/index.php?title=Template:Continuum_mechanics&action=edit


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Typical aerodynamic teardrop shape, showing the pressure distribution as the thickness of the black line and

showing the velocity in the boundary layeras the violet triangles. The green vortex generators prompt the transition

toturbulent flowand prevent back-flow also calledflow separation from the high pressure region in the back. The

surface in front is as smooth as possible or even employsshark like skin, as any turbulence here will reduce the

energy of the airflow. TheKammback also prevents back flow from the high pressure region in the back across

thespoilersto the convergent part. Putting stuff inside out results intubes; they also face the problem of flow

separation in their divergent parts, so calleddiffusers. Cutting the shape into halves results in an aerofoil with the

low pressure region on top leading to lift (force).

Inphysics,fluid dynamics is a sub-discipline offluid mechanics that deals with fluid flow

the natural scienceoffluids(liquids and gases) in motion. It has several subdisciplines itself,

including aerodynamics(the study of air and other gases in motion) and hydrodynamics (the study of

liquids in motion). Fluid dynamics has a wide range of applications, including

calculatingforcesandmoments onaircraft, determining themass flow rate ofpetroleum through

pipelines, predictingweatherpatterns, understandingnebulaein interstellarspace and reportedly

modeling fission weapon detonation. Some of its principles are even used in traffic engineering, where

traffic is treated as a continuous fluid.

Fluid dynamics offers a systematic structure that underlies these practical disciplines, that embraces

empirical and semi-empirical laws derived from flow measurementand used to solve practical

problems. The solution to a fluid dynamics problem typically involves calculating various properties of

the fluid, such as velocity, pressure,density, and temperature, as functions of space and time.

Historically, hydrodynamics meant something different than it does today. Before the twentieth century,

hydrodynamics was synonymous with fluid dynamics. This is still reflected in names of some fluid

dynamics topics, like magnetohydrodynamics andhydrodynamic stabilityboth also applicable in, as

well as being applied to, gases. [1]

Contents

[hide]

1 Equations of fluid dynamics

o 1.1 Compressible vs incompressible flow

o 1.2 Viscous vs inviscid flow

o 1.3 Steady vs unsteady flow

o 1.4 Laminar vs turbulent flow

o 1.5 Newtonian vs non-Newtonian fluids

o 1.6 Subsonic vs transonic, supersonic and hypersonic flows
http://en.wikipedia.org/wiki/Boundary_layerhttp://en.wikipedia.org/wiki/Vortex_generatorhttp://en.wikipedia.org/wiki/Turbulent_flowhttp://en.wikipedia.org/wiki/Turbulent_flowhttp://en.wikipedia.org/wiki/Turbulent_flowhttp://en.wikipedia.org/wiki/Flow_separationhttp://en.wikipedia.org/wiki/Flow_separationhttp://en.wikipedia.org/wiki/Dermal_denticlehttp://en.wikipedia.org/wiki/Dermal_denticlehttp://en.wikipedia.org/wiki/Kammbackhttp://en.wikipedia.org/wiki/Kammbackhttp://en.wikipedia.org/wiki/Spoiler_(aeronautics)http://en.wikipedia.org/wiki/Spoiler_(aeronautics)http://en.wikipedia.org/wiki/Spoiler_(aeronautics)http://en.wikipedia.org/wiki/Pipinghttp://en.wikipedia.org/wiki/Pipinghttp://en.wikipedia.org/wiki/Diffuser_(automotive)http://en.wikipedia.org/wiki/Diffuser_(automotive)http://en.wikipedia.org/wiki/Diffuser_(automotive)http://en.wikipedia.org/wiki/Airfoilhttp://en.wikipedia.org/wiki/Lift_(force)http://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Fluid_mechanicshttp://en.wikipedia.org/wiki/Natural_sciencehttp://en.wikipedia.org/wiki/Natural_sciencehttp://en.wikipedia.org/wiki/Fluidhttp://en.wikipedia.org/wiki/Fluidhttp://en.wikipedia.org/wiki/Liquidhttp://en.wikipedia.org/wiki/Liquidhttp://en.wikipedia.org/wiki/Gashttp://en.wikipedia.org/wiki/Aerodynamicshttp://en.wikipedia.org/wiki/Aerodynamicshttp://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Moment_(physics)http://en.wikipedia.org/wiki/Moment_(physics)http://en.wikipedia.org/wiki/Aircrafthttp://en.wikipedia.org/wiki/Aircrafthttp://en.wikipedia.org/wiki/Mass_flow_ratehttp://en.wikipedia.org/wiki/Mass_flow_ratehttp://en.wikipedia.org/wiki/Petroleumhttp://en.wikipedia.org/wiki/Weatherhttp://en.wikipedia.org/wiki/Weatherhttp://en.wikipedia.org/wiki/Nebulahttp://en.wikipedia.org/wiki/Nebulahttp://en.wikipedia.org/wiki/Nebulahttp://en.wikipedia.org/wiki/Interstellarhttp://en.wikipedia.org/wiki/Traffic_engineering_(transportation)http://en.wikipedia.org/wiki/Flow_measurementhttp://en.wikipedia.org/wiki/Flow_measurementhttp://en.wikipedia.org/wiki/Velocityhttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Temperaturehttp://en.wikipedia.org/wiki/Temperaturehttp://en.wikipedia.org/wiki/Magnetohydrodynamicshttp://en.wikipedia.org/wiki/Hydrodynamic_stabilityhttp://en.wikipedia.org/wiki/Fluid_dynamics#cite_note-0%23cite_note-0http://toggletoc%28%29/http://en.wikipedia.org/wiki/Fluid_dynamics#Equations_of_fluid_dynamics%23Equations_of_fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamics#Compressible_vs_incompressible_flow%23Compressible_vs_incompressible_flowhttp://en.wikipedia.org/wiki/Fluid_dynamics#Viscous_vs_inviscid_flow%23Viscous_vs_inviscid_flowhttp://en.wikipedia.org/wiki/Fluid_dynamics#Steady_vs_unsteady_flow%23Steady_vs_unsteady_flowhttp://en.wikipedia.org/wiki/Fluid_dynamics#Laminar_vs_turbulent_flow%23Laminar_vs_turbulent_flowhttp://en.wikipedia.org/wiki/Fluid_dynamics#Newtonian_vs_non-Newtonian_fluids%23Newtonian_vs_non-Newtonian_fluidshttp://en.wikipedia.org/wiki/Fluid_dynamics#Subsonic_vs_transonic.2C_supersonic_and_hypersonic_flows%23Subsonic_vs_transonic.2C_supersonic_and_hypersonic_flowshttp://en.wikipedia.org/wiki/File:Teardrop_shape.svghttp://en.wikipedia.org/wiki/Boundary_layerhttp://en.wikipedia.org/wiki/Vortex_generatorhttp://en.wikipedia.org/wiki/Turbulent_flowhttp://en.wikipedia.org/wiki/Flow_separationhttp://en.wikipedia.org/wiki/Dermal_denticlehttp://en.wikipedia.org/wiki/Kammbackhttp://en.wikipedia.org/wiki/Spoiler_(aeronautics)http://en.wikipedia.org/wiki/Pipinghttp://en.wikipedia.org/wiki/Diffuser_(automotive)http://en.wikipedia.org/wiki/Airfoilhttp://en.wikipedia.org/wiki/Lift_(force)http://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Fluid_mechanicshttp://en.wikipedia.org/wiki/Natural_sciencehttp://en.wikipedia.org/wiki/Fluidhttp://en.wikipedia.org/wiki/Liquidhttp://en.wikipedia.org/wiki/Gashttp://en.wikipedia.org/wiki/Aerodynamicshttp://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Moment_(physics)http://en.wikipedia.org/wiki/Aircrafthttp://en.wikipedia.org/wiki/Mass_flow_ratehttp://en.wikipedia.org/wiki/Petroleumhttp://en.wikipedia.org/wiki/Weatherhttp://en.wikipedia.org/wiki/Nebulahttp://en.wikipedia.org/wiki/Interstellarhttp://en.wikipedia.org/wiki/Traffic_engineering_(transportation)http://en.wikipedia.org/wiki/Flow_measurementhttp://en.wikipedia.org/wiki/Velocityhttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Temperaturehttp://en.wikipedia.org/wiki/Magnetohydrodynamicshttp://en.wikipedia.org/wiki/Hydrodynamic_stabilityhttp://en.wikipedia.org/wiki/Fluid_dynamics#cite_note-0%23cite_note-0http://toggletoc%28%29/http://en.wikipedia.org/wiki/Fluid_dynamics#Equations_of_fluid_dynamics%23Equations_of_fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamics#Compressible_vs_incompressible_flow%23Compressible_vs_incompressible_flowhttp://en.wikipedia.org/wiki/Fluid_dynamics#Viscous_vs_inviscid_flow%23Viscous_vs_inviscid_flowhttp://en.wikipedia.org/wiki/Fluid_dynamics#Steady_vs_unsteady_flow%23Steady_vs_unsteady_flowhttp://en.wikipedia.org/wiki/Fluid_dynamics#Laminar_vs_turbulent_flow%23Laminar_vs_turbulent_flowhttp://en.wikipedia.org/wiki/Fluid_dynamics#Newtonian_vs_non-Newtonian_fluids%23Newtonian_vs_non-Newtonian_fluidshttp://en.wikipedia.org/wiki/Fluid_dynamics#Subsonic_vs_transonic.2C_supersonic_and_hypersonic_flows%23Subsonic_vs_transonic.2C_supersonic_and_hypersonic_flows


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o 1.7 Non-relativistic vs relativistic flows

o 1.8 Magnetohydrodynamics

o 1.9 Other approximations

2 Terminology in fluid dynamics

o 2.1 Terminology in incompressible fluid dynamics

o 2.2 Terminology in compressible fluid dynamics

3 See also

o 3.1 Fields of study

o 3.2 Mathematical equations and concepts

o 3.3 Types of fluid flow

o 3.4 Fluid properties

o 3.5 Fluid phenomena

o 3.6 Applications

o 3.7 Miscellaneous

4 References

5 Notes

6 External links

[edit]Equations of fluid dynamics

The foundational axioms of fluid dynamics are theconservation laws, specifically, conservation of

mass, conservation of linear momentum(also known as Newton's Second Law of Motion),

andconservation of energy(also known as First Law of Thermodynamics). These are based

onclassical mechanics and are modified inquantum mechanicsandgeneral relativity. They are

expressed using the Reynolds Transport Theorem.

In addition to the above, fluids are assumed to obey the continuum assumption. Fluids are composed

of molecules that collide with one another and solid objects. However, the continuum assumption

considers fluids to be continuous, rather than discrete. Consequently, properties such as density,

pressure, temperature, and velocity are taken to be well-defined at infinitesimally small points, and are

assumed to vary continuously from one point to another. The fact that the fluid is made up of discrete

molecules is ignored.

For fluids which are sufficiently dense to be a continuum, do not contain ionized species, and have

velocities small in relation to the speed of light, the momentum equations forNewtonian fluids are

the Navier-Stokes equations, which is anon-linearset ofdifferential equationsthat describes the flow
http://en.wikipedia.org/wiki/Fluid_dynamics#Non-relativistic_vs_relativistic_flows%23Non-relativistic_vs_relativistic_flowshttp://en.wikipedia.org/wiki/Fluid_dynamics#Magnetohydrodynamics%23Magnetohydrodynamicshttp://en.wikipedia.org/wiki/Fluid_dynamics#Other_approximations%23Other_approximationshttp://en.wikipedia.org/wiki/Fluid_dynamics#Terminology_in_fluid_dynamics%23Terminology_in_fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamics#Terminology_in_incompressible_fluid_dynamics%23Terminology_in_incompressible_fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamics#Terminology_in_compressible_fluid_dynamics%23Terminology_in_compressible_fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamics#See_also%23See_alsohttp://en.wikipedia.org/wiki/Fluid_dynamics#Fields_of_study%23Fields_of_studyhttp://en.wikipedia.org/wiki/Fluid_dynamics#Mathematical_equations_and_concepts%23Mathematical_equations_and_conceptshttp://en.wikipedia.org/wiki/Fluid_dynamics#Types_of_fluid_flow%23Types_of_fluid_flowhttp://en.wikipedia.org/wiki/Fluid_dynamics#Fluid_properties%23Fluid_propertieshttp://en.wikipedia.org/wiki/Fluid_dynamics#Fluid_phenomena%23Fluid_phenomenahttp://en.wikipedia.org/wiki/Fluid_dynamics#Applications%23Applicationshttp://en.wikipedia.org/wiki/Fluid_dynamics#Miscellaneous%23Miscellaneoushttp://en.wikipedia.org/wiki/Fluid_dynamics#References%23Referenceshttp://en.wikipedia.org/wiki/Fluid_dynamics#Notes%23Noteshttp://en.wikipedia.org/wiki/Fluid_dynamics#External_links%23External_linkshttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=1http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=1http://en.wikipedia.org/wiki/Conservation_lawhttp://en.wikipedia.org/wiki/Conservation_lawhttp://en.wikipedia.org/wiki/Conservation_lawhttp://en.wikipedia.org/wiki/Conservation_of_masshttp://en.wikipedia.org/wiki/Conservation_of_masshttp://en.wikipedia.org/wiki/Conservation_of_momentumhttp://en.wikipedia.org/wiki/Conservation_of_momentumhttp://en.wikipedia.org/wiki/Newton's_laws_of_motionhttp://en.wikipedia.org/wiki/Newton's_laws_of_motionhttp://en.wikipedia.org/wiki/Conservation_of_energyhttp://en.wikipedia.org/wiki/Conservation_of_energyhttp://en.wikipedia.org/wiki/Conservation_of_energyhttp://en.wikipedia.org/wiki/First_Law_of_Thermodynamicshttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Quantum_mechanicshttp://en.wikipedia.org/wiki/Quantum_mechanicshttp://en.wikipedia.org/wiki/Quantum_mechanicshttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/Reynolds_transport_theoremhttp://en.wikipedia.org/wiki/Reynolds_transport_theoremhttp://en.wikipedia.org/wiki/Newtonian_fluidhttp://en.wikipedia.org/wiki/Navier-Stokes_equationshttp://en.wikipedia.org/wiki/Navier-Stokes_equationshttp://en.wikipedia.org/wiki/Non-linearhttp://en.wikipedia.org/wiki/Non-linearhttp://en.wikipedia.org/wiki/Non-linearhttp://en.wikipedia.org/wiki/Differential_equationshttp://en.wikipedia.org/wiki/Differential_equationshttp://en.wikipedia.org/wiki/Fluid_dynamics#Non-relativistic_vs_relativistic_flows%23Non-relativistic_vs_relativistic_flowshttp://en.wikipedia.org/wiki/Fluid_dynamics#Magnetohydrodynamics%23Magnetohydrodynamicshttp://en.wikipedia.org/wiki/Fluid_dynamics#Other_approximations%23Other_approximationshttp://en.wikipedia.org/wiki/Fluid_dynamics#Terminology_in_fluid_dynamics%23Terminology_in_fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamics#Terminology_in_incompressible_fluid_dynamics%23Terminology_in_incompressible_fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamics#Terminology_in_compressible_fluid_dynamics%23Terminology_in_compressible_fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamics#See_also%23See_alsohttp://en.wikipedia.org/wiki/Fluid_dynamics#Fields_of_study%23Fields_of_studyhttp://en.wikipedia.org/wiki/Fluid_dynamics#Mathematical_equations_and_concepts%23Mathematical_equations_and_conceptshttp://en.wikipedia.org/wiki/Fluid_dynamics#Types_of_fluid_flow%23Types_of_fluid_flowhttp://en.wikipedia.org/wiki/Fluid_dynamics#Fluid_properties%23Fluid_propertieshttp://en.wikipedia.org/wiki/Fluid_dynamics#Fluid_phenomena%23Fluid_phenomenahttp://en.wikipedia.org/wiki/Fluid_dynamics#Applications%23Applicationshttp://en.wikipedia.org/wiki/Fluid_dynamics#Miscellaneous%23Miscellaneoushttp://en.wikipedia.org/wiki/Fluid_dynamics#References%23Referenceshttp://en.wikipedia.org/wiki/Fluid_dynamics#Notes%23Noteshttp://en.wikipedia.org/wiki/Fluid_dynamics#External_links%23External_linkshttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=1http://en.wikipedia.org/wiki/Conservation_lawhttp://en.wikipedia.org/wiki/Conservation_of_masshttp://en.wikipedia.org/wiki/Conservation_of_masshttp://en.wikipedia.org/wiki/Conservation_of_momentumhttp://en.wikipedia.org/wiki/Newton's_laws_of_motionhttp://en.wikipedia.org/wiki/Conservation_of_energyhttp://en.wikipedia.org/wiki/First_Law_of_Thermodynamicshttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Quantum_mechanicshttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/Reynolds_transport_theoremhttp://en.wikipedia.org/wiki/Newtonian_fluidhttp://en.wikipedia.org/wiki/Navier-Stokes_equationshttp://en.wikipedia.org/wiki/Non-linearhttp://en.wikipedia.org/wiki/Differential_equations


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of a fluid whose stress depends linearly on velocity gradients and pressure. The unsimplified equations

do not have a generalclosed-form solution, so they are primarily of use in Computational Fluid

Dynamics. The equations can be simplified in a number of ways, all of which make them easier to

solve. Some of them allow appropriate fluid dynamics problems to be solved in closed form.

In addition to the mass, momentum, and energy conservation equations, athermodynamical equation

of state giving the pressure as a function of other thermodynamic variables for the fluid is required to

completely specify the problem. An example of this would be the perfect gas equation of state:

wherep is pressure, is density,Ru is thegas constant,Mis themolar

mass and Tis temperature.

[edit]Compressible vs incompressible flow

All fluids arecompressibleto some extent, that is changes in pressure or temperature will result

in changes in density. However, in many situations the changes in pressure and temperature are

sufficiently small that the changes in density are negligible. In this case the flow can be modeled

as an incompressible flow. Otherwise the more general compressible flow equations must be

used.

Mathematically, incompressibility is expressed by saying that the density of a fluid parcel does

not change as it moves in the flow field, i.e.,

where D / Dtis the substantial derivative, which is the sum of local and convective

derivatives. This additional constraint simplifies the governing equations, especially in the

case when the fluid has a uniform density.

For flow of gases, to determine whether to use compressible or incompressible fluid

dynamics, theMach numberof the flow is to be evaluated. As a rough guide, compressible

effects can be ignored at Mach numbers below approximately 0.3. For liquids, whether the

incompressible assumption is valid depends on the fluid properties (specifically the critical

pressure and temperature of the fluid) and the flow conditions (how close to the critical

pressure the actual flow pressure becomes).Acousticproblems always require allowing

compressibility, since sound wavesare compression waves involving changes in pressure

and density of the medium through which they propagate.

[edit]Viscous vs inviscid flow
http://en.wikipedia.org/wiki/Solution_in_closed_formhttp://en.wikipedia.org/wiki/Solution_in_closed_formhttp://en.wikipedia.org/wiki/Solution_in_closed_formhttp://en.wikipedia.org/wiki/Computational_Fluid_Dynamicshttp://en.wikipedia.org/wiki/Computational_Fluid_Dynamicshttp://en.wikipedia.org/wiki/Thermodynamicshttp://en.wikipedia.org/wiki/Thermodynamicshttp://en.wikipedia.org/wiki/Ideal_gas_lawhttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Gas_constanthttp://en.wikipedia.org/wiki/Gas_constanthttp://en.wikipedia.org/wiki/Gas_constanthttp://en.wikipedia.org/wiki/Molar_masshttp://en.wikipedia.org/wiki/Molar_masshttp://en.wikipedia.org/wiki/Molar_masshttp://en.wikipedia.org/wiki/Temperaturehttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=2http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=2http://en.wikipedia.org/wiki/Compressibilityhttp://en.wikipedia.org/wiki/Compressibilityhttp://en.wikipedia.org/wiki/Compressibilityhttp://en.wikipedia.org/wiki/Incompressible_flowhttp://en.wikipedia.org/wiki/Compressible_flowhttp://en.wikipedia.org/wiki/Substantial_derivativehttp://en.wikipedia.org/wiki/Convective_derivativehttp://en.wikipedia.org/wiki/Convective_derivativehttp://en.wikipedia.org/wiki/Convective_derivativehttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Acousticshttp://en.wikipedia.org/wiki/Acousticshttp://en.wikipedia.org/wiki/Acousticshttp://en.wikipedia.org/wiki/Sound_waveshttp://en.wikipedia.org/wiki/Sound_waveshttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=3http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=3http://en.wikipedia.org/wiki/Solution_in_closed_formhttp://en.wikipedia.org/wiki/Computational_Fluid_Dynamicshttp://en.wikipedia.org/wiki/Computational_Fluid_Dynamicshttp://en.wikipedia.org/wiki/Thermodynamicshttp://en.wikipedia.org/wiki/Ideal_gas_lawhttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Gas_constanthttp://en.wikipedia.org/wiki/Molar_masshttp://en.wikipedia.org/wiki/Molar_masshttp://en.wikipedia.org/wiki/Temperaturehttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=2http://en.wikipedia.org/wiki/Compressibilityhttp://en.wikipedia.org/wiki/Incompressible_flowhttp://en.wikipedia.org/wiki/Compressible_flowhttp://en.wikipedia.org/wiki/Substantial_derivativehttp://en.wikipedia.org/wiki/Convective_derivativehttp://en.wikipedia.org/wiki/Convective_derivativehttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Acousticshttp://en.wikipedia.org/wiki/Sound_waveshttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=3


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Viscousproblems are those in which fluid friction has significant effects on the fluid motion.

The Reynolds number, which is a ratio between inertial and viscous forces, can be used to

evaluate whether viscous or inviscid equations are appropriate to the problem.

Stokes flow is flow at very low Reynolds numbers, Re


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Hydrodynamics simulation of theRayleighTaylor instability[2]

When all the time derivatives of a flow field vanish, the flow is considered to be a steady flow. Steady-

state flow refers to the condition where the fluid properties at a point in the system do not change over

time. Otherwise, flow is called unsteady. Whether a particular flow is steady or unsteady, can depend

on the chosenframe of reference. For instance, laminar flow over asphereis steady in the frame of

reference that is stationary with respect to the sphere. In a frame of reference that is stationary with

respect to a background flow, the flow is unsteady.

Turbulent flows are unsteady by definition. A turbulent flow can, however, be statistically stationary.

According to Pope:[3]

The random field U(x,t) is statistically stationary if all statistics are invariant under a shift in time.

This roughly means that all statistical properties are constant in time. Often, the mean field is the

object of interest, and this is constant too in a statistically stationary flow.

Steady flows are often more tractable than otherwise similar unsteady flows. The governing

equations of a steady problem have one dimension less (time) than the governing

equations of the same problem without taking advantage of the steadiness of the flow field.

[edit]Laminar vs turbulent flow

Turbulence is flow characterized by recirculation, eddies, and apparent randomness. Flow in which

turbulence is not exhibited is called laminar. It should be noted, however, that the presence of eddies

or recirculation alone does not necessarily indicate turbulent flowthese phenomena may be present

in laminar flow as well. Mathematically, turbulent flow is often represented via a Reynolds
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decomposition, in which the flow is broken down into the sum of anaverage component and a

perturbation component.

It is believed that turbulent flows can be described well through the use of the Navier

Stokes equations.Direct numerical simulation (DNS), based on the NavierStokes equations, makes it

possible to simulate turbulent flows at moderate Reynolds numbers. Restrictions depend on the power

of the computer used and the efficiency of the solution algorithm. The results of DNS agree with the

experimental data.

Most flows of interest have Reynolds numbers much too high for DNS to be a viable

option[4], given the state of computational power for the next few decades. Any flight vehicle large

enough to carry a human (L > 3 m), moving faster than 72 km/h (20 m/s) is well beyond the limit of

DNS simulation (Re = 4 million). Transport aircraft wings (such as on an Airbus A300orBoeing 747)

have Reynolds numbers of 40 million (based on the wing chord). In order to solve these real-life flow

problems, turbulence models will be a necessity for the foreseeable future.Reynolds-averaged Navier

Stokes equations (RANS) combined with turbulence modeling provides a model of the effects of the

turbulent flow. Such a modeling mainly provides the additional momentum transfer by theReynolds

stresses, although the turbulence also enhances theheat and mass transfer. Another promising

methodology is large eddy simulation(LES), especially in the guise ofdetached eddy simulation(DES)

which is a combination of RANS turbulence modeling and large eddy simulation.

[edit]Newtonian vs non-Newtonian fluids

SirIsaac Newton showed howstress and the rate ofstrainare very close to linearly related for many

familiar fluids, such aswaterand air. These Newtonian fluids are modeled by a coefficient

calledviscosity, which depends on the specific fluid.

However, some of the other materials, such as emulsions and slurries and some visco-elastic

materials (e.g.blood, some polymers), have more complicated non-Newtonian stress-strain

behaviours. These materials include sticky liquids such as latex,honey, and lubricants which are

studied in the sub-discipline ofrheology.

[edit]Subsonic vs transonic, supersonic and hypersonic flows

While many terrestrial flows (e.g. flow of water through a pipe) occur at low mach numbers, many flows

of practical interest (e.g. in aerodynamics) occur at high fractions of the Mach Number M=1 or in

excess of it (supersonic flows). New phenomena occur at these Mach number regimes (e.g. shock

waves for supersonic flow, transonic instability in a regime of flows with M nearly equal to 1, non-

equilibrium chemical behavior due to ionization in hypersonic flows) and it is necessary to treat each of

these flow regimes separately.
http://en.wikipedia.org/wiki/Reynolds_decompositionhttp://en.wikipedia.org/wiki/Reynolds_decompositionhttp://en.wikipedia.org/wiki/Averagehttp://en.wikipedia.org/wiki/Averagehttp://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equationshttp://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equationshttp://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equationshttp://en.wikipedia.org/wiki/Direct_numerical_simulationhttp://en.wikipedia.org/wiki/Direct_numerical_simulationhttp://en.wikipedia.org/wiki/Fluid_dynamics#cite_note-3%23cite_note-3http://en.wikipedia.org/wiki/Airbus_A300http://en.wikipedia.org/wiki/Airbus_A300http://en.wikipedia.org/wiki/Boeing_747http://en.wikipedia.org/wiki/Reynolds-averaged_Navier%E2%80%93Stokes_equationshttp://en.wikipedia.org/wiki/Reynolds-averaged_Navier%E2%80%93Stokes_equationshttp://en.wikipedia.org/wiki/Turbulence_modelinghttp://en.wikipedia.org/wiki/Reynolds_stresseshttp://en.wikipedia.org/wiki/Reynolds_stresseshttp://en.wikipedia.org/wiki/Reynolds_stresseshttp://en.wikipedia.org/wiki/Reynolds_stresseshttp://en.wikipedia.org/wiki/Heat_transferhttp://en.wikipedia.org/wiki/Mass_transferhttp://en.wikipedia.org/wiki/Mass_transferhttp://en.wikipedia.org/wiki/Large_eddy_simulationhttp://en.wikipedia.org/wiki/Large_eddy_simulationhttp://en.wikipedia.org/wiki/Detached_eddy_simulationhttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=6http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=6http://en.wikipedia.org/wiki/Isaac_Newtonhttp://en.wikipedia.org/wiki/Isaac_Newtonhttp://en.wikipedia.org/wiki/Stress_(physics)http://en.wikipedia.org/wiki/Stress_(physics)http://en.wikipedia.org/wiki/Strain_(materials_science)http://en.wikipedia.org/wiki/Strain_(materials_science)http://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Earth's_atmospherehttp://en.wikipedia.org/wiki/Earth's_atmospherehttp://en.wikipedia.org/wiki/Newtonian_fluidhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Bloodhttp://en.wikipedia.org/wiki/Bloodhttp://en.wikipedia.org/wiki/Polymerhttp://en.wikipedia.org/wiki/Polymerhttp://en.wikipedia.org/wiki/Non-Newtonian_fluidhttp://en.wikipedia.org/wiki/Latexhttp://en.wikipedia.org/wiki/Honeyhttp://en.wikipedia.org/wiki/Honeyhttp://en.wikipedia.org/wiki/Honeyhttp://en.wikipedia.org/wiki/Rheologyhttp://en.wikipedia.org/wiki/Rheologyhttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=7http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=7http://en.wikipedia.org/wiki/Reynolds_decompositionhttp://en.wikipedia.org/wiki/Averagehttp://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equationshttp://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equationshttp://en.wikipedia.org/wiki/Direct_numerical_simulationhttp://en.wikipedia.org/wiki/Fluid_dynamics#cite_note-3%23cite_note-3http://en.wikipedia.org/wiki/Airbus_A300http://en.wikipedia.org/wiki/Boeing_747http://en.wikipedia.org/wiki/Reynolds-averaged_Navier%E2%80%93Stokes_equationshttp://en.wikipedia.org/wiki/Reynolds-averaged_Navier%E2%80%93Stokes_equationshttp://en.wikipedia.org/wiki/Turbulence_modelinghttp://en.wikipedia.org/wiki/Reynolds_stresseshttp://en.wikipedia.org/wiki/Reynolds_stresseshttp://en.wikipedia.org/wiki/Heat_transferhttp://en.wikipedia.org/wiki/Mass_transferhttp://en.wikipedia.org/wiki/Large_eddy_simulationhttp://en.wikipedia.org/wiki/Detached_eddy_simulationhttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=6http://en.wikipedia.org/wiki/Isaac_Newtonhttp://en.wikipedia.org/wiki/Stress_(physics)http://en.wikipedia.org/wiki/Strain_(materials_science)http://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Earth's_atmospherehttp://en.wikipedia.org/wiki/Newtonian_fluidhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Bloodhttp://en.wikipedia.org/wiki/Polymerhttp://en.wikipedia.org/wiki/Non-Newtonian_fluidhttp://en.wikipedia.org/wiki/Latexhttp://en.wikipedia.org/wiki/Honeyhttp://en.wikipedia.org/wiki/Rheologyhttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=7


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[edit]Non-relativistic vs relativistic flows

Classical fluid dynamics is derived based on Newtonian mechanics, which is adequate for

most applications. However, at speeds comparable to the speed of light Newtonian mechanics is

inaccurate and a relativistic framework has to be used instead.

[edit]Magnetohydrodynamics

Main article: Magnetohydrodynamics

Magnetohydrodynamics is the multi-disciplinary study of the flow ofelectrically conducting fluids

in electromagnetic fields. Examples of such fluids includeplasmas, liquid metals, and salt water. The

fluid flow equations are solved simultaneously with Maxwell's equations of electromagnetism.

[edit]Other approximations

There are a large number of other possible approximations to fluid dynamic problems.

Some of the more commonly used are listed below.

The Boussinesq approximation neglects variations in density except to

calculate buoyancy forces. It is often used in freeconvectionproblems where density

changes are small.

Lubrication theory and Hele-Shaw flowexploits the largeaspect ratio of the

domain to show that certain terms in the equations are small and so can be neglected.

Slender-body theory is a methodology used in Stokes flow problems to estimate the

force on, or flow field around, a long slender object in a viscous fluid.

The shallow-water equationscan be used to describe a layer of relatively inviscid

fluid with afree surface, in which surface gradients are small.

The Boussinesq equationsare applicable to surface waves on thicker layers of fluid

and with steeper surface slopes.

Darcy's law is used for flow in porous media, and works with variables averaged

over several pore-widths.

In rotating systems, the quasi-geostrophic approximationassumes an almost

perfect balance between pressure gradients and theCoriolis force. It is useful in the

study ofatmospheric dynamics.

[edit]Terminology in fluid dynamics

The concept ofpressure is central to the study of both fluid statics and fluid dynamics. A pressure can

be identified for every point in a body of fluid, regardless of whether the fluid is in motion or not.
http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=8http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=8http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=9http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=9http://en.wikipedia.org/wiki/Magnetohydrodynamicshttp://en.wikipedia.org/wiki/Magnetohydrodynamicshttp://en.wikipedia.org/wiki/Electrical_conductionhttp://en.wikipedia.org/wiki/Electrical_conductionhttp://en.wikipedia.org/wiki/Electromagnetismhttp://en.wikipedia.org/wiki/Plasma_(physics)http://en.wikipedia.org/wiki/Plasma_(physics)http://en.wikipedia.org/wiki/Saline_waterhttp://en.wikipedia.org/wiki/Saline_waterhttp://en.wikipedia.org/wiki/Maxwell's_equationshttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=10http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=10http://en.wikipedia.org/wiki/Boussinesq_approximation_(buoyancy)http://en.wikipedia.org/wiki/Buoyancyhttp://en.wikipedia.org/wiki/Convectionhttp://en.wikipedia.org/wiki/Convectionhttp://en.wikipedia.org/wiki/Lubrication_theoryhttp://en.wikipedia.org/wiki/Hele-Shaw_flowhttp://en.wikipedia.org/wiki/Hele-Shaw_flowhttp://en.wikipedia.org/wiki/Aspect_ratiohttp://en.wikipedia.org/wiki/Aspect_ratiohttp://en.wikipedia.org/wiki/Slender-body_theoryhttp://en.wikipedia.org/wiki/Stokes_flowhttp://en.wikipedia.org/wiki/Shallow-water_equationshttp://en.wikipedia.org/wiki/Shallow-water_equationshttp://en.wikipedia.org/wiki/Free_surfacehttp://en.wikipedia.org/wiki/Free_surfacehttp://en.wikipedia.org/wiki/Slopehttp://en.wikipedia.org/wiki/Boussinesq_equations_(water_waves)http://en.wikipedia.org/wiki/Boussinesq_equations_(water_waves)http://en.wikipedia.org/wiki/Surface_waveshttp://en.wikipedia.org/wiki/Slopehttp://en.wikipedia.org/wiki/Darcy's_lawhttp://en.wikipedia.org/wiki/Porous_mediumhttp://en.wikipedia.org/wiki/Porous_mediumhttp://en.wikipedia.org/wiki/Balanced_flow#Geostrophic_flowhttp://en.wikipedia.org/wiki/Balanced_flow#Geostrophic_flowhttp://en.wikipedia.org/wiki/Pressure_gradienthttp://en.wikipedia.org/wiki/Coriolis_forcehttp://en.wikipedia.org/wiki/Coriolis_forcehttp://en.wikipedia.org/wiki/Atmospheric_dynamicshttp://en.wikipedia.org/wiki/Atmospheric_dynamicshttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=11http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=11http://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=8http://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=9http://en.wikipedia.org/wiki/Magnetohydrodynamicshttp://en.wikipedia.org/wiki/Magnetohydrodynamicshttp://en.wikipedia.org/wiki/Electrical_conductionhttp://en.wikipedia.org/wiki/Electromagnetismhttp://en.wikipedia.org/wiki/Plasma_(physics)http://en.wikipedia.org/wiki/Saline_waterhttp://en.wikipedia.org/wiki/Maxwell's_equationshttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=10http://en.wikipedia.org/wiki/Boussinesq_approximation_(buoyancy)http://en.wikipedia.org/wiki/Buoyancyhttp://en.wikipedia.org/wiki/Convectionhttp://en.wikipedia.org/wiki/Lubrication_theoryhttp://en.wikipedia.org/wiki/Hele-Shaw_flowhttp://en.wikipedia.org/wiki/Aspect_ratiohttp://en.wikipedia.org/wiki/Slender-body_theoryhttp://en.wikipedia.org/wiki/Stokes_flowhttp://en.wikipedia.org/wiki/Shallow-water_equationshttp://en.wikipedia.org/wiki/Free_surfacehttp://en.wikipedia.org/wiki/Slopehttp://en.wikipedia.org/wiki/Boussinesq_equations_(water_waves)http://en.wikipedia.org/wiki/Surface_waveshttp://en.wikipedia.org/wiki/Slopehttp://en.wikipedia.org/wiki/Darcy's_lawhttp://en.wikipedia.org/wiki/Porous_mediumhttp://en.wikipedia.org/wiki/Balanced_flow#Geostrophic_flowhttp://en.wikipedia.org/wiki/Pressure_gradienthttp://en.wikipedia.org/wiki/Coriolis_forcehttp://en.wikipedia.org/wiki/Atmospheric_dynamicshttp://en.wikipedia.org/w/index.php?title=Fluid_dynamics&action=edit&section=11http://en.wikipedia.org/wiki/Pressure


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Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other

methods.

Some of the terminology that is necessary in the study of fluid dynamics is not found in other similar

areas of study. In particular, some of the terminology used in fluid dynamics is not used in fluid statics.

[edit]Terminology in incompressible fluid dynamics

The concepts of total pressure and dynamic pressurearise fromBernoulli's equationand

reynold's no

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