# 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. ### Is the Parameterization Correct in Leithold's Stokes' Theorem Problem?

The question is a problem from Leithold's calculus book. I didn't understand the (x = 5 \cos(t)). Shouldn't it be (x = 2 cos(t))? I'm referring to item b. i tried this way. i don't know what is wrong.
2. ### Stokes' law and falling sphere method

In dire need of help, someone please explain the correct method for this, if its not possible what should i write in the conclusion for this?
3. ### I How to Calculate Surface Integral Using Stokes' Theorem?

Calculate surface integral ## \displaystyle\iint\limits_S curl F \cdot dS ## where S is the surface, oriented outward in below given figure and F = [ z,2xy,x+y]. How can we answer this question?
4. ### Computing line integral using Stokes' theorem

##curl([x^2z, 3x , -y^3],[x,y,z]) =[-3y^2 ,x^2,3]## The unit normal vector to the surface ##z(x,y)=x^2+y^2## is ##n= \frac{-2xi -2yj +k}{\sqrt{1+4x^2 +4y^2}}## ##[-3y^2,x^2,3]\cdot n= \frac{-6x^2y +6xy^2}{\sqrt{1+4x^2 + 4y^2}}## Since ##\Sigma## can be parametrized as ##r(x,y) = xi + yj +(x^2...

6. ### I Alternate forms of Stokes' theorem? Are they correct? Are they named?

The last formula is what I was going for, since it arises as the momentum flux in fluid dynamics, but in the process I came across the rest of these formulas which I’m not sure about. The second equation is missing a minus sign (I meant to put [dA X grad(f)]). Are they correct? Do they have...

11. ### Calculating the Line Integral of F over C: Stokes' Theorem and Symmetry

From Stokes we know that ##\iint_{\textbf{S}}^{}curl \textbf{F}\cdot d\textbf{S}=\int_{C}^{}\textbf{F}\cdot d\textbf{r}##. Now, we can calculate the surface integral of the curl of F by calculating the line integral of F over the curve C. The latter ends up being 0(I calculated it parametrizing...
12. ### A Green's function for Stokes equation

So I've just started learning about Greens functions and I think there is some confusion. We start with the Stokes equations in Cartesian coords for a point force. $$-\nabla \textbf{P} + \nu \nabla^2 \textbf{u} + \textbf{F}\delta(\textbf{x})=0$$ $$\nabla \cdot \textbf{u}=0$$ We can apply the...
13. ### A Integrating the Stokeslet: Solving Expression 7 from ResearchGate Publication

https://www.researchgate.net/publication/301874096_Emergent_behavior_in_active_colloids/link/5730bb3608ae08415e6a7c0a/download (expression 9 on this document derivation). I understand the need for substitution etc into the integral. What puzzles me is how the integral equals what it does. If...
14. ### [Optics] Questions on the Stokes shift

Here is my answer to this question: Stokes shift is the difference in wavelength between positions of the band maxima of the excitation and emission spectra of the same electronic transition. When Stokes shift is large, it means there is more energy loss, which is not favorable regarding...

48. ### I Why is Stokes flow time reversible?

What is the intuition behind the fact that stokes flow is time reversible?
49. ### Verifying Stokes' Theorem help

Homework Statement Verify Stokes' theorem ∫c F • t ds = ∫∫s n ∇ × F dS in each of the following cases: (a) F=i z2 + j y2 C, the square of side 1 lying in the x,z-plane and directed as shown S, the five squares S1, S2, S3, S4, S5 as shown in the figure. (b) F = iy + jz + kx C, the three...
50. ### I Proofs of Stokes Theorem without Differential Forms

Hello, does anyone have reference to(or care to write out) fully rigorous proof of Stokes theorem which does not reference Differential Forms? I'm reviewing some physics stuff and I want to relearn it. I honestly will never use the higher dimensional version but I still want to see a full proof...