Navier-Stokes Equation
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Navier-Stokes Equation
IWF (Göttingen)
Formal Metadata
| Title |
Navier-Stokes Equation
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| Alternative Title |
Navier-Stokes Gleichung
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| Author |
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| License |
CC Attribution - NonCommercial - NoDerivatives 3.0 Germany:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor. |
| Identifiers |
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| IWF Signature |
C 13096
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| Publisher |
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| Release Date |
2007
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| Language |
English
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| Other Version(s) | German |
| Producer |
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| Production Year |
2004
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Technical Metadata
| IWF Technical Data |
Video ; F, 4 min 45 sec
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Content Metadata
| Subject Area | |
| Abstract |
Um das Geschwindigkeitsfeld einer instationären Strömung zu bestimmen, ist die sog. "Particle Image Velocimetry" eine geeignete Methode. Mit Hilfe des zurückgelegten Weges einzelner Teilchen und der vergangenen Zeitspanne wird das Geschwindigkeitsfeld einer Strömung bestimmt. Das Verfahren wird auf eine reale Strömung angewendet, die Ergebnisse werden festgehalten. Die wichtigsten Beobachtungen kann man nun mit der theoretischen Beschreibung einer realen Strömung durch die Navier-Stokes-Gleichung vergleichen.
To determine the velocity field of a current the so-called "particle image velocimetry" is a suitable method. With the help of the distance of individual particles and the time interval the velocity field of a current is determined. The procedure is applied at a real current, the results are noted. One can compare the most important observations with the theoretical description by the Navier-Stokes equation.
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| Keywords | Strömung Particle Image Velocimetry (PIV) instationäre Strömung Geschwindigkeitsfeld Stokes, George Gabriel Navier, Claude Louis Marie Henri Navier-Stokes-Gleichungen Navier-Stokes Navier-Stokes Navier-Stokes equations Navier, Claude Louis Marie Henri Stokes, George Gabriel velocity field particle image velocimetry (PIV) current |
| IWF Classification | Mechanik Physik physics mechanics |
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Computer animation
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Elementary particle
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Map
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Direct current
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00:00
the Navier-Stokes equation but
00:13
the so called particle image velocimetry is suitable for visualizing the velocity field of an instationary flow the method is
00:28
based on the idea of putting fine particles into a fluid and
00:32
comparing successive images with each
00:35
other then the velocity of each
00:38
particle is determined with the cover distance and the time passed In the experimental set up of the method 1
00:47
uses a pulsed laser to create shop video images of the moving particles 2 successive images
00:57
are processed so that the velocity can be determined with the time passed and the covered distance here delta x 1 can illustrate
01:09
exemplarily the procedure with the Sean experiment in image 1 observes a particle at the position r 1 at the time t 1 after the time delta t 1 sees on the success of image that the particle has covered the distance that R R 1 1 obtains the velocity at the position r 1 which can be illustrated with the vector to obtain an image of the total velocity field the procedure must be repeated for many particles several times
01:51
finally 1 obtains a vector map of the flow velocity field that
01:56
varies in space and time to
02:02
show the spatial dependence of the velocity field each point of the flow is
02:06
colored according to the absolute value of the velocity 1 observes that the absolute value of the velocity varies in space this means that the gradient of the
02:20
square of you is generally not 0 that In the next step 1 compares the
02:29
directions of the velocity it's 2 different positions are 1 and R 2 1 sees also that the
02:37
direction varies in space the the the further the velocity varies in time at the position r 2 for example the partial time differentiation is not 0 according to the instationary flow here is the
03:05
velocity in a vector diagram at equidistant points in time the the
03:12
important observations can be compared with the theoretical description of a flow by the Navier-Stokes equation to set up the equation of motion for an infinitesimal volume element of a viscous fluid 1st 1 starts with a Newtonian axiom on the left side of the equation different forces are part of the total force F the the pressure force the gravitational force and the viscous force the the total time differentiation of the velocity on the right side called substantial acceleration can be splitted into Adams the partial time differentiation and for the time dependence of the velocity u at a certain position the and the term for the spatial variation which can be stated again in 2 parts the the 1st depends on the absolute value of the velocity and the 2nd depends on the direction all parts of the substantial
04:30
acceleration play a role in the show and turbulent flow
