What is Stokes: Definition and 293 Discussions

In 1851, George Gabriel Stokes derived an expression, now known as Stokes law, for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid. Stokes' law is derived by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations.

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  1. F

    Is stokes vector can be a quantum state?

    Is a stokes four-vector like (1 1 0 0) being horizontal polarized vector can be treated as a quantum state? If the answer is yes, this state can be used to construct density matrix?
  2. C

    Solve Navier Stokes Eq for Vo | Don't Get Prof's Answer

    I need to solve 0=u[(d/dr)((1/r)*(d/dr)(r*Vo))] for Vo the prof gets Vo=Co*r/2+C1/r I don't get the same answer as him, does anyone know how to do this?
  3. Saladsamurai

    Navier Stokes EQ: Derivation in Integral Form

    Hello! :smile: I am doing some review and it has occurred to me that I always confuse myself when I derive the the momentum equation in integral form. So I figure I will try to hammer through it here and ask questions as I go in order to clarify certain points. I know that there are many...
  4. R

    Unpolarised light, stokes vector and image matrices.

    I was working on a project of image encryption and I got stuck at something. I'll go point-wise. 1. I need to make optical element filters like linear polariser, circular polariser, retardets etc. working in matlab. 2. I decided to use mueller calculus and stokes vectors. So, I would...
  5. S

    Stokes Parameters - Fraction of Linear/Circular Polarization

    Homework Statement The electric field of an electromagnetic wave is given by; E = Re(\frac{1}{\sqrt{13}}E_{0}(2\widehat{x}+ 3i\widehat{y})e^{i(kz-wt)}) Identify the polarization state. Homework Equations I = |E_{x}|^{2} + |E_{y}|^{2} Q = |E_{x}|^{2} - |E_{y}|^{2} U = |E_{a}|^{2} -...
  6. S

    [Calc 3] Verifying Stokes Theorem

    Homework Statement V.Field F(x,y,z)=<x^2 z, xy^2, z^2> where S is part of the plane x+y+z=1 inside cylinder x2 + y2 =9 Homework Equations Line integrals, Stokes Theorem, Parametrizing intersections... The Attempt at a Solution I found the answer to be 81pi/2 using stoke's theorem...
  7. B

    How Does Stokes' Theorem Apply to Complex Surface Integrals?

    Homework Statement Let F(x, y, z) = \left ( e^{-y^2} + y^{1+x^2} +cos(z), -z, y \right) Let s Be the portion of the paraboloid y^2+z^2=4(x+1) for 0 \leq x \leq 3 and the portion of the sphere x^2 + y^2 +z^2 = 4 for x \leq 0 Find \iint\limits_s curl(\vec{F}) d \vec{s} Homework...
  8. C

    Verify Stokes theorem for the given Surface

    Homework Statement verify Stokes theorem for the given Surface and VECTOR FIELD x2 + y2+z2=4, z≤0 oriented by a downward normal. F=(2y-z)i+(x+y2-z)j+(4y-3x)k Homework Equations ∫∫S Δ χ F dS=∫ ∂SF.ds the triangle is supposed to be upside down. The Attempt at a Solution myΔχF =...
  9. M

    NS Millennium Problem: Uniqueness & Solutions Explained

    I recently came across the NS millennium problem and I read that uniqueness for the NS equations is unknown. I have two questions. First question, if solutions are found to be non-unique, would the NS equations have to be corrected? Second question, since uniqueness is unknown, if someone...
  10. A

    Differences between Raman stokes and fluorescence

    If the fluorescence is the re-emitting of a photon with a larger wave length due to the transition from a higher energy state to a lower energy state in the case of resonance Raman (where there aren't any virtual states) seems be equal to the fluorescence. Which differences are there?
  11. T

    Is it possible to derive Divergence Theorem from Stokes Theorem?

    Is it? If so, can you show how? Thanks :smile:
  12. R

    Navier Stokes Equation Derivation and Inertial Forces

    Hi I was reading Introduction to Fluid Mechanics by Nakayama and Boucher and I got lost in their derivation of the Navier Stokes Theorem. They basically started out with a differential of fluid with dimensions dx, dy, and b. Then they say that the force acting on it F = (F_x, F_y) is F_x...
  13. S

    Question about Stokes Theorem?

    So I'm self teaching myself Multivariable Calculus from UCBerkeley's Youtube series and an online textbook. I'm up to Stokes Theorem and I'm getting conflicting definitions. UCBerkeley Youtube series says that Stokes Theorem is defined by: \int {(Curl f)} {ds} And then the textbook says that...
  14. H

    Variable viscosity in the Navier Stokes equations

    Hi, If the viscosity in the NS equations was a variable, what extra equation is used to solve the NS equations? Thanks.
  15. C

    Stokes drag of oscillation sphere

    If we consider a sphere oscillates in viscous fluid with frequency w, then sphere has velocity u=u_0*e^{-iwt} In Laudau's book, he defined the velocity of fluid is: v=e^{iwt}*F where F is a vector with only spatial variable involved. The boundary condition then becomes u=v at |x|=R, where R is...
  16. A

    Stokes' Theorem formula question

    I was wondering, how you break down dS to something with dA? I know that dS is equal to ndS. The n is equal to grad f / (magnitude of grad f) and the dS is equal to the same as the magnitude of grad f right? So is the formula the same as double integral of region D (curl F * grad f) dA?
  17. Z

    Proving Stokes Theorem for Vector Field E on Given Contour and Surface

    Homework Statement for the vector field E=x(xy)-y(x^2 +2y^2) find E.dl along the contour find (nabla)xE along the surface x=0 and x=1 y=0 and y=1 Homework Equations The Attempt at a Solution i tried the second question (nabla)xE over the surface by finding the...
  18. C

    Spatially averaging the Navier Stokes equations on a multiply connected domain

    Hi all, The problem at hand is a bubbly flow in a cylinder: I'm using an FEM to identify how the walls effect the drag on bubbles in a flow. To test my results I want to set up an infinite cylinder with randomly distributed spheres and then average the Navier-Stokes equations over the entire...
  19. P

    Solving Double Integral Using Stokes Theorem for Curl

    Homework Statement Use stokes theorem to find double integral curlF.dS where S is the part of the sphere x2+y2+z2=5 that lies above plane z=1. F(x,y,z)=x2yzi+yz2j+z3exyk Homework Equations stokes theorem says double integral of curlF.dS = \intC F.dr The Attempt at a Solution...
  20. I

    Verifying Stokes' Theorem: F=(x^2,xy,-z^2)

    this Q want to check Stokes' theorem ? for http://latex.codecogs.com/gif.latex?F=(x^2,xy,-z^2) and surface http://latex.codecogs.com/gif.latex?x^2+y^2+z^2=1 and http://latex.codecogs.com/gif.latex?z\geqslant%200 i should equal http://latex.codecogs.com/gif.latex?\oint%20Mdx+ndy+pdz with...
  21. P

    Question about Stokes' Thm and Boundaries of Surfaces

    So I'm going over Rudin's chapter on differential forms in his Principles of Mathematical Analysis and I'm looking at Example 10.36 which gives the 1 form \eta = \frac{xdy-ydx}{x^2+y^2} on the set \mathbb{R}^2-{0} and then parametrizes the circle \gamma(t)=(rcos(t),rsin(t)) for fixed r>0 and...
  22. S

    Applying Divergence Theorem to Stokes' Theorem

    Not really a homework problem, just me wondering about this: why is there a problem here? Say you want to use the divergence theorem in conjunction with Stokes' theorem. So, from Stokes' you know: Line integral (F*T ds)= Surface integral (curl(F)*n)dS. And you know that Surface...
  23. Phrak

    Determinism, Stokes' Theorem and Relativity

    I don't think these three: {Determinism, Stokes' Theorem, Relativity Theory}, are compatible. The notion of determinism, as applied to spacetime physics, means that if we know everything on an R3 spacelike hypersurface at time ta, we can predict what will be will be the state of things on an...
  24. F

    Fundamental solutions of the stokes equation.

    Homework Statement Hi, I going through my class notes for a fluids class, specifically fundamental solutions of the Stokes equations. To derive the stresslet and rotlet involves solving the following ui = (1/8*pi*μ)*(∂Gik/∂xj)*Fk*Aj Gik(x) = δij*(1/r)+(xixj/r3) We looked at it in a...
  25. C

    Calculating Stokes' Theorem Integral for c(0,2π)

    Given c(t) = [cos t, sin t, 2 + sin (t/2)] where t \epsilon [0, 2pi] and F(x,y,z) = (2-y + x2, x + sin y, \sqrt{}z4+1) --- Find \intF.dS over c(0, 2pi). I've no idea how to do this... any help would be awesome! Thanks!
  26. D

    Navier Stokes: Homework Q&A on Solution & Equations

    Homework Statement Solution and question are here: http://i51.tinypic.com/bg63qb.png Homework Equations Equations listed in image. The Attempt at a Solution I made several assumptions and there's one that I made that isn't correct but I don't understand why. My textbook lists an...
  27. V

    Navier Stokes Equation to create a Velocity Profile

    Homework Statement An incompressible, viscous fluid is placed between horizontal, infinite, parallel plates. The two plates move in opposite directions with constant velocities U1 and U2. The pressure gradient in the x-direction is zero and the only body force is due to the fluid weight. Use...
  28. jegues

    Troublesome Stokes Theorem Problem

    Homework Statement See figure attached for problem statement Homework Equations The Attempt at a Solution See figure attached for my attempt. I found this problem to be a little long and drawn out, which leads me to believe I made a mistake somewhere. Is this the case? Or...
  29. jegues

    How to Use Stokes' Theorem for Evaluating Line Integrals?

    Homework Statement Use Stoke's theorem to evaluate the line integral \oint y^{3}zdx - x^{3}zdy + 4dz where C is the curve of intersection of the paraboloid z = 2 + x^{2} + y^{2} and the plane z=5, directed clockwise as viewed from the point (0,0,7). Homework Equations The...
  30. N

    Navier stokes equeations, shear term

    Hey!, I was repeating for myself a course I had from a earlier year, fluid mechanics. I looked at the derivation of the navier stokes equations, and there is one term that does not give meaning to me. Take a look at the x-momentum equation here...
  31. F

    What Distance Negates the Dipole's Influence in Stokes Flow Around a Sphere?

    Homework Statement The flow due to translation of a sphere in a Newtonian fluid at rest is given by the following streamfunction, ψ(r,Θ) = (1/4)Ua2(3r/a - a/r)sin2Θ which consists of a stokeslet and a potential dipole. If the contribution of the dipole is less than 1%...
  32. Saladsamurai

    How to Derive 2D Navier-Stokes Equations for Steady Flow Using a Control Volume?

    Homework Statement I need to derive the 2D N-S equations for steady, incompressible, constant viscosity flow in the xy-plane. I need to use a control volume approach (as opposed to system approach) on a differential control volume (CV) using the conseervation of linear momentum...
  33. N

    Double application of Stokes' theorem to find the area of a simplex

    I'm having trouble using Stokes' theorem in order to find a simple formula for the area found within a two dimensional simplex. I know the formula, but I'm interested in the derivation. For simplicity, I've been working with a unit triangle with vertices at the coordinates (0,0), (0,1), and...
  34. W

    Stokes Theorum Surface integral

    Let's assume that I have a surface defined parametrically by a vector \mathbf{\ r}(r,\theta) Is it acceptable to simplify the Stokes theorum surface integral to: \iint\limits_D\,\nabla \times f \cdot\!(r_r\times\!r_\theta) \,\, \!r \mathrm{d}r\,\mathrm{d}\theta Where r_r and r_theta are...
  35. N

    Stokes theorem and downward orientation problem

    Homework Statement From Calculus:Concepts and Contexts 4th Edition by James Stewart. Pg.965 #13 Verify that Stokes' Theorem is true for the given vector field F and surface S F(x,y,z)= -yi+xj-2k S is the cone z^2= x^2+y^2, o<=z<=4, oriented downwards Homework Equations The Attempt at a...
  36. C

    How Do You Calculate Fluid Viscosity with Stokes' Law and Variable Formulas?

    Hi, I am doing physics coursework on finding viscosity of fluids by dropping a marble into fluids, finding terminal velocity, then using stoke's law to find viscosity. (using density of fluid, sphere, sphere diameter etc). I have completed all the practical, now just the write up However ... I...
  37. A

    Stokes' law and frictional force

    Homework Statement Derive an expression for frictional force acting on a spherical objects of radius R moving with velocity V in a continuous viscous fluid of fluid's viscosity η . Homework Equations please do not use dimension analysis to prove. The Attempt at a Solution
  38. M

    Fluids - Using Navier Stokes

    Incompressible fluid of kinematic viscosity v and density p flows in the x direction between two parallel planes at y = +-h, under the action of an unsteady unidirectional pressure gradient -p(G +Qcosnt), where G, Q, n are constants. Verify that unidirectional motion is possible and that...
  39. P

    Special case of Stokes theorem

    Do you agree that the following identity is true: \int_S (\nabla_\mu X^\mu) \Omega = \int_{\partial S} X \invneg \lrcorner \Omega where \Omega is volume form and X\invneg \lrcorner \Omega is contraction of volume form with vector X.
  40. C

    On an alternative Stokes theorem

    I find in a homework an alternative Stokes theorem tha i wasn't knew before. I wold like to know that it is really true. Any can give me a proof please? It is: Int (line) dℓ′× A = Int (surface)dS′×∇′× A
  41. A

    Solving Stokes' Law Experiment Mystery

    I am not able to understand the following situations. In stokes' experiment a tiny lead shot falls freely under gravity in a highly viscous column of liquid. When the viscous force becomes equal to the net weight of the lead shot it is said that the shot moves down with a constant...
  42. H

    Application of Stokes' theorem

    Homework Statement Evaluate the following integrals I_1 = \oint \vec{r} (\vec{a} \cdot \vec{n}) dS I_2 = \oint (\vec{a} \cdot \vec{r})\vec{n} dS where \vec{a} is a constant vector, and \vec{n} is an unit vector normal to the closed surface S. Homework Equations Stokes'...
  43. C

    How Does Stokes' Theorem Relate to Vorticity in Fluid Dynamics?

    Homework Statement Consider an imaginary circular disc, of radius R, whose arbitrary orientation is described by the unit vector, \vec {n} , perpendicular to the plane of the disc. Define the component, in the direction \vec {n} , of the angular velocity, \vec {\Omega} , at a point in the...
  44. R

    Do I understand Stokes' theorem? (Calc 3)

    Here's where I try to explain Stokes' theorem in my own words and you tell me if I'm right / what I need to clarify on. Essentially, it's a method to compute a line integral around a closed curve in three dimensions, with a given vector field F, without having to parametrize this field and...
  45. C

    Stokes' theorem Vorticity problem

    Homework Statement Consider an imaginary circular disc, of radius R, whose arbitrary orientation is described by the unit vector, \vec {n} , perpendicular to the plane of the disc. Define the component, in the direction \vec {n} , of the angular velocity, \vec {\Omega} , at a point in the...
  46. M

    Why Do Orientations Affect Stokes' Theorem Results?

    Hi everyone, I have to prove this problem but I have no idea how to approach this problem. I tried something but it seems not working... Suppose F is a vector field in R3 whose components have continuous partial derivatives. (So F satisfies the hypotheses of Stoke's Theorem.) (a)...
  47. H

    Verifying Stokes Theorem on Paraboloid z=0.5(x^2+y^2)

    Homework Statement Verify Stokes Theorem ∬(∇xF).N dA where surface S is the paraboloid z = 0.5(x^2 + y^2) bound by the plane z=2, Cis its boundary, and the vector field F = 3yi - xzj + yzk. The Attempt at a Solution I had found (∇xF) = (z+x)i + (-z-3)k r = [u, v, 0.5(u^2 + v^2)]...
  48. I

    Using stokes theorem to find magnetic field

    Homework Statement magnetic field is azimuthal B(r) = B(p,z) \phi current density J(r) = Jp(p,z) p + Jz(p,z) z = p*exp[-p] p + (p-2)*z*exp[-p] z use stokes theorem to find B-filed induced by current everywhere in space Homework Equations stokes -...
  49. J

    Reynolds Transport derivation?(or 1-form Stokes)

    Homework Statement The latex document for these equations wasnt updating correctly, so I've included them as an attachment wherever there is a ... in the text Ok, I am trying to understand the Reynolds transport theorem, but i don't understand part of it. Homework Equations This is the...
  50. R

    Did I do this right? (Stokes' Theorem, Flux)

    Homework Statement Evaluate \int\int Curl F\cdot dS where F=<z,x,y> (NOTE: the vector in my post preview is showing me the wrong one despite me trying to correct it, the right one is F=<z,x,y>) and S is the surface z=2-\sqrt{x^2 +y^2} above z=0. Homework Equations I used Stokes'...
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