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A '''Power-law fluid''', or the '''[[Wilhelm Ostwald|Ostwald]]–[[Armand de Waele|de Waele]] relationship''', is a type of [[generalized Newtonian fluid]] for which the [[shear stress]], ''τ'', is given by
 
:<math>\tau = K \left( \frac {\partial u} {\partial y} \right)^n </math>
 
where:
*''K'' is the ''flow consistency index'' ([[SI]] units Pa•s<sup>''n''</sup>),
*∂''u''/∂''y'' is the [[shear rate]] or the [[velocity]] [[gradient]] perpendicular to the plane of shear (SI unit s<sup>−1</sup>), and
*''n'' is the ''flow behavior index'' (dimensionless).
 
The quantity
 
:<math>\mu_{\operatorname{eff}} = K \left( \frac {\partial u} {\partial y} \right)^{n-1} </math>
 
represents an ''apparent'' or ''effective [[viscosity]]'' as a function of the shear rate (SI unit Pa•s).
 
Also known as the [[Wilhelm Ostwald|Ostwald]]–[[Armand de Waele|de Waele]] power law<ref name=OdW>e.g. [[G. W. Scott Blair]] ''et al.'', ''J. Phys. Chem''., (1939) 43 (7) 853–864.  Also the ''de Waele-Ostwald'' law, e.g [[Markus Reiner]] ''et al.'', ''Kolloid Zeitschrift'' (1933) 65 (1) 44-62</ref><ref name=Ostwald1929>Ostwald called it the de Waele-Ostwald equation: ''Kolloid Zeitschrift'' (1929) 47 (2) 176-187</ref> this [[mathematical]] relationship is useful because of its simplicity, but only approximately describes the behaviour of a real [[non-Newtonian fluid]]. For example, if ''n'' were less than one, the power law predicts that the effective viscosity would decrease with increasing shear rate indefinitely, requiring a fluid with infinite viscosity at rest and zero viscosity as the shear rate approaches infinity, but a real fluid has both a minimum and a maximum effective viscosity that depend on the [[physical chemistry]] at the [[molecular]] level. Therefore, the power law is only a good description of fluid behaviour across the range of shear rates to which the coefficients were fitted. There are a number of other models that better describe the entire flow behaviour of shear-dependent fluids, but they do so at the expense of simplicity, so the power law is still used to describe fluid behaviour, permit mathematical predictions, and correlate experimental data.
 
Power-law fluids can be subdivided into three different types of fluids based on the value of their flow behaviour index:
:{|align="left" border="1" cellspacing="0"
|''n''
|Type of fluid
|-
|<1
|[[Pseudoplastic]]
|-
|1
|[[Newtonian fluid]]
|-
|>1
|[[Dilatant]] (less common)
|}
 
<br style="clear: left"/>
 
== Pseudoplastic fluids ==
[[Pseudoplastic]], or ''shear-thinning'' fluids have a lower apparent viscosity at higher shear rates, and are usually [[solution]]s of large, [[polymer]]ic molecules in a solvent with smaller molecules. It is generally supposed that the large molecular chains tumble at random and affect large volumes of fluid under low shear, but that they gradually align themselves in the direction of increasing shear and produce less resistance.
 
A common household example of a strongly shear-thinning fluid is styling gel, which primarily composed of water and a fixative such as a vinyl acetate/vinylpyrrolidone copolymer (PVP/PA). If one were to hold a sample of hair gel in one hand and a sample of [[corn syrup]] or [[glycerine]] in the other, they would find that the hair gel is much harder to pour off the fingers (a low shear application), but that it produces much less resistance when rubbed between the fingers (a high shear application).
 
== Newtonian fluids ==
A [[Newtonian fluid]] is a power-law fluid with a behaviour index of 1, where the shear stress is directly proportional to the shear rate:
 
:<math>\tau = \mu \frac {\partial u} {\partial y} </math>
 
These fluids have a constant viscosity, ''μ'', across all shear rates and include many of the most common fluids, such as [[water]], most aqueous [[solution]]s, [[oil]]s, [[corn syrup]], [[glycerine]], [[air]] and other [[gas]]es.
 
While this holds true for relatively low shear rates, at high rates most oils in reality also behave in a non-Newtonian fashion and thin. Typical examples include oil films in automotive engine shell bearings and to a lesser extent in geartooth contacts.
 
== Dilatant fluids ==
[[Dilatant]], or ''shear-thickening'' fluids increase in apparent viscosity at higher shear rates. They are rarely encountered, but one common example is an uncooked paste of [[cornstarch]] and [[water]]. Under high shear the water is squeezed out from between the [[starch]] [[molecule]]s, which are able to interact more strongly.
 
While not strictly a dilatant fluid, [[Silly Putty]] is an example of a material that shares these viscosity characteristics. Another use is in a [[viscous coupling]] in which if both ends of the coupling are spinning at the same (rotational) speed, the fluid viscosity is minimal, but if the ends of the coupling differ greatly in speed, the coupling fluid becomes very viscous. Such couplings have applications as a lightweight, passive mechanism for a passenger automobile to automatically switch from two-wheel drive to four-wheel drive such as when the vehicle is stuck in snow and the primary driven axle starts to spin due to loss of traction under one or both tires.
 
== Velocity profile in a circular pipe ==
 
Just like a [[Newtonian fluid]] in a circular pipe gives a quadratic velocity profile (see [[Hagen–Poiseuille equation]]), a power-law fluid will result in a power-law velocity profile,
 
:<math>u(r) = \frac{n}{n+1}\left(\frac{dp}{dz}\frac{1}{2K}\right)^\frac{1}{n}\left[R^\frac{n+1}{n}-r^\frac{n+1}{n}\right] </math>
 
where <math>u(r)</math> is the (radially) local axial velocity, <math>dp/dz</math> is the pressure gradient along the pipe, and <math>R</math> is the pipe radius.
 
==See also==
*[[Power law]]
*[[Rheology]]
*[[Navier-Stokes equations]]
*[[Fluid]]
*[[First-Order Fluid]]
*[[Cross fluid]]
*[[Carreau fluid]]
*[[Generalized Newtonian fluid]]
*[[Herschel-Bulkley fluid]]
 
==References==
{{reflist}}
 
[[Category:Non-Newtonian fluids]]

Revision as of 21:29, 7 February 2014

Making a computer run quickly is pretty simple. Most computers run slow because they are jammed up with junk files, that Windows has to search from each time it wants to find anything. Imagine needing to discover a book inside a library, yet all of the library books are inside a big huge pile. That's what it's like for your computer to find something, when a program is full of junk files.

If it's not because big of the issue because we think it is very, it may probably be resolved easily by running a Startup Repair or by System Restore Utility. Again it may be because effortless as running an anti-virus check or cleaning the registry.

The PC could also have a fragmented hard drive or the windows registry might have been corrupted. It might also be due to the dust and dirt that should be cleaned. Whatever the issue, we can constantly find a answer. Here are certain tips on how to make your PC run faster.

If you feel you don't have enough income at the time to upgrade, then the number one option is to free up some area by deleting a few of the unwanted files plus folders.

When it comes to software, this really is the vital part since it is the one running a system also as additional programs required inside your functions. Always keep the cleanliness of the program from obsolete data by getting a good tuneup utilities. Protect it from a virus found on the net by providing a workable virus protection system. You could have a monthly clean up by running the defragmenter system. This technique it can enhance the performance of your computer plus for you to avoid any errors. If you think anything is wrong with the software, and you don't recognize how to fix it then refer to a technician.

The key reason why I could not make my PC run quicker was the system registry and it being fragmented. So software to defragment or clean the registry are required. Such software are called registry cleaners. Like all alternative software, there are paid ones and free ones with their blessings and disadvantages. To choose between the 2 is the user's choice.

The first reason your computer can be slow is because it needs more RAM. You'll notice this matter right away, incredibly if you have less than a gig of RAM. Most unique computers come with a least which much. While Microsoft says Windows XP may run on 128 MB, it and Vista want at least a gig to run smoothly and let you to run numerous programs at when. Fortunately, the cost of RAM has dropped significantly, plus you are able to get a gig installed for $100 or less.

So, the greatest thing to do whenever the computer runs slow is to purchase an authentic plus legal registry repair tool which would aid we eliminate all issues connected to registry and aid you enjoy a smooth running computer.