Stokes hypothesis assumptions

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Stokes hypothesis assumptions

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up. I wanted to model a real life problem using the Navier-Stokes equations and was wondering what the assumptions made by the same are so that I could better relate my entities with a 'fluid' and make or set assumptions on them likewise.

For example one of the assumptions of a Newtonian fluid is that the viscosity does not depend on the shear rate. Similarly what are the assumptions that are made on a fluid or how does the Navier-Stokes equations define a fluid for which the equation is applicable?

stokes hypothesis assumptions

Most importantly, the Navier-Stokes equations are based on a continuum assumption. This means that you should be able to view the fluid as having properties like density and velocity at infinitely small points. If you look at e. As far as I know there is no hard limit for the continuum assumption, but the Knudsen number is a useful indicator.

stokes hypothesis assumptions

Additionally there is, as ShuchangZhang mentioned, an assumption on the nature of the stress in the fluid. Although I am not sure whether you could really call this an assumption or whether it should be considered a theory like the NS equations itself. The strongest assumptions are typically not in the Navier-Stokes equations themselves, but rather in the boundary conditions that should be applied in order to solve them. To give an example, whether the no-slip boundary condition fluid velocity at the wall equals wall velocity or the navier slip boundary condition fluid velocity equals a scaled velocity gradient at the wall has been a much debated subject, in particular for hydrophobic surfaces see e.

The Navier-Stokes equations must specify a form for the diffusive fluxes e.

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The solution of the Navier-Stokes equations involves additional assumptions, but this is separate from the equations themselves e. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. What are the assumptions of the Navier-Stokes equations? Ask Question.

Asked 6 years, 6 months ago. Active 1 year, 7 months ago.The explanation stands upon a closer analysis of the effect of the terms of the complete stress tensor in which the viscosity coefficients appear. An alternative formulation of the hypothesis is proposed, which also permits to clearly identify the very particular flow conditions in which it cannot justify the experimental evidence. This is a preview of subscription content, log in to check access.

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Rent this article via DeepDyve. Serrin J. Springer, Berlin Stokes G. Rosenhead L. A Mat. Gad-el-Hak M.

Fluid Eng. ASME3—5 Markham J. Truesdell C. Rajagopal K. Nonlinear Mech. Dukhin A. Buresti G. Imperial College Press, London Emanuel G. Fluids A-Fluid 4— Fluids 6— Tritton D. Clarendon Press, Oxford Zonta F. Fluid Mech.The intent of this article is to highlight the important points of the derivation of the Navier—Stokes equations as well as its application and formulation for different families of fluids.

The Navier—Stokes equations are based on the assumption that the fluid, at the scale of interest, is a continuum — a continuous substance rather than discrete particles. Another necessary assumption is that all the fields of interest including pressureflow velocitydensityand temperature are differentiableat least weakly.

The equations are derived from the basic principles of continuity of massmomentumand energy. Sometimes it is necessary to consider a finite arbitrary volume, called a control volumeover which these principles can be applied. The control volume can remain fixed in space or can move with the fluid. Changes in properties of a moving fluid can be measured in two different ways.

One can measure a given property by either carrying out the measurement on a fixed point in space as particles of the fluid pass by, or by following a parcel of fluid along its streamline. The derivative of a field with respect to a fixed position in space is called the Eulerian derivative while the derivative following a moving parcel is called the advective or material "Lagrangian" [1] derivative.

The material derivative is defined as the nonlinear operator :. The first term on the right-hand side of the equation is the ordinary Eulerian derivative i. This "special" derivative is in fact the ordinary derivative of a function of many variables along a path following the fluid motion; it may be derived through application of the chain rule in which all independent variables are checked for change along the path i.

For example, the measurement of changes in wind velocity in the atmosphere can be obtained with the help of an anemometer in a weather station or by observing the movement of a weather balloon. The anemometer in the first case is measuring the velocity of all the moving particles passing through a fixed point in space, whereas in the second case the instrument is measuring changes in velocity as it moves with the flow. The Navier—Stokes equation is a special continuity equation. A continuity equation may be derived from conservation principles of:.

This is expressed by the following integral continuity equation:. The divergence theorem may be applied to the surface integralchanging it into a volume integral :.

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Applying Reynolds transport theorem to the integral on the left and then combining all of the integrals:. The integral must be zero for any control volume; this can only be true if the integrand itself is zero, so that:.Access to the complete content on Oxford Reference requires a subscription or purchase. Public users are able to search the site and view the abstracts and keywords for each book and chapter without a subscription.

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stokes hypothesis assumptions

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A note on Stokes’ hypothesis

You could not be signed in, please check and try again. Sign in with your library card Please enter your library card number. Search within work. Related Content In this work bulk viscosity. Publishing Information Preface.Stokes' theorem is a generalization of Green's theorem from circulation in a planar region to circulation along a surface. Green's theorem applies only to two-dimensional vector fields and to regions in the two-dimensional plane.

Stokes' theorem generalizes Green's theorem to three dimensions. For starters, let's take our above picture and simply embed it in three dimensions. The next question is what the microscopic circulation along a surface should be. Similarly, for a surface, we will want the microscopic circulation along the surace. This corresponds to the component of the curl that is perpendicular to the surface, i. You can see this using the right-hand rule. If you point the thumb of your right hand perpendicular to a surface, your fingers will curl in a direction corresponding to circulation parallel to the surface.

In summary, to go from Green's theorem to Stoke's theorem, we've made two changes. First, we've changed the line integral living in two dimensions Green's theorem to a line integral living in three dimensions Stokes' theorem. Macroscopic and microscopic circulation in three dimensions.

You can change the curve to a more complicated shape by dragging the blue point on the bottom slider, and the relationship between the macroscopic and total microscopic circulation still holds. The surface is oriented by the shown normal vector moveable cyan arrow on surfaceand the curve is oriented by the red arrow. More information about applet. Stokes' theorem allows us to do even more.

Note that moving the green point on the top slider does not change the value of either integral in the above formulas. The important point is that, even in this case, the left line integral and the right surface integral are always equal.

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There is one more subtlety that you have to get correct, or else you'll may be off by a sign. You need to orient the surface and boundary properly. The cyan normal vector to the surface and the orientation of the curve shown by red arrow in the above applet are chosen with the proper relative orientations so that Stokes' theorem applies. You can read some examples here. Select a notation system: default Marsden and Tromba Stewart. Home Threads Index About.

The idea behind Stokes' theorem. Applet loading. See also Proper orientation for Stokes' theorem Stokes' theorem examples.We do the same damn thing, hence the irritation. While they are listed as synonyms by many dictionaries, they are really not the same word. We could then assume there is sufficient market size to justify our interest. That assumption may be disastrously wrong. Perhaps those companies are buying traffic with no profit to show for it, but we are free to make that assumption and take the risk.

As you can see, all the assumptions are vague, optimistic, and untestable. The vaguer they are, the harder they are to disprove.

What makes a good hypothesis? The hypotheses above are relatively specific and we can easily see how to design an experiment to get the data that could disprove that hypothesis. To reveal hidden assumptions, there are a few tried and true generative research methods:. What have we missed on this checklist? Got a tip? Tweet me. Download Real Startup Book. I reject the idea of a success metric.

As entrepreneurs, we are biased towards our vision, towards optimizing, towards self delusion. Guard against delusion.

Difference Between Hypothesis and Assumption

Continue reading There any variety of reasons, all probably involving ramping up validity and importance. What am I expecting them to do to know this product qualifies as something they find useful? That benchmark is important to identify to know if you are aligned to the market properly so you can weed out historical defects in data, noise, technical issues, anomalies, etc.

stokes hypothesis assumptions

Knowing how to set a bench mark for traction would be important. You did setup a success metric expected in your hypothesis but its a bit arbitrary in determining what is used as criteria for easy. So that would be good to identify what people expect easy to look like as it may vary.

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The important part is to have a success metric to evaluate against that is specific and not vague so I get some of your point but just thought more specificity would bring it out more to illustrate what is important and why. What I wanted to see what context established with more specificity around your product example that was being approached with generalities versus specifics. A hypothesis is something you think is true and so is an assumption. People are using these interchangeably because of how they relate to the definition of the word.

The important point is if you assume something to be true then you must prove it to be false by evaluating the variables in a controlled experiment to validate the result you expect can be repeated when you manipulate said variables the same way over and over again. Transforming that to the business realm of success metrics which can be some behavior you expect when you manipulate a certain variable is not easy because people are missing the data points or variables they require to test.

They are also not understanding the framework either. So one challenge of your points is how to use the framework to approach an assumption so it can improve ones decision making. The other is what to test and why and where it fits into some sort of ecosystem that drives other variables that will contribute to their business model working in all parts together for a profit with the traction they need to know this is something worth pursuing.Hypothesis vs Assumption.

Hypothesis and assumption are concepts that are similar in nature and are used commonly in research and experiments. A hypothesis is a theory that seeks to explain a phenomenon or a set of phenomena.

Scientists or researchers make up hypothesis to see if they hold water.

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They conduct a number of experiments and test this hypothesis, and if the hypothesis indeed proves correct, it is deemed to have become a theory.

There is another word called assumption that is similar in meaning and confuses readers. This article attempts to highlight the differences between hypothesis and assumption. Something that has yet not been proved to classify as a theory but believed to be true by the researcher is labeled as a hypothesis.

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A hypothesis is merely a proposition that is presented or put forward by a scientist to explain a natural phenomenon. It does not become a theory until it is proved and tested under different conditions and circumstances. At best, it is an assumption that has been made working. It is rather correct to call a hypothesis a theory that needs verification and investigation.

Any statement that is put forward for the sake of argument to support an occurrence or phenomenon is called a hypothesis. Making assumptions on the basis of looks and appearance of a person is common. We take for granted the qualities in a person on the basis of his skin color, hair color, and physique. We take for granted qualities that are mere assumption and no more. An assumption is any statement that is believed to be true.

Stokes’ Law, Reynolds Number, and Measuring Liquid Viscosity

Many times, people pay dearly when they jump to conclusions based upon their assumptions. Thinking about the feelings of others is merely assumption as there is no way to tell what a person is thinking or feeling.

Coming from Engineering cum Human Resource Development background, has over 10 years experience in content developmet and management. Comments Thank you very much for clarifying the difference. Leave a Reply Cancel reply.


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