Stokes Definition and 268 Threads

I know that th three dimensional case was discovered by William Thompson, but who discovered the general case?

Stokes Thm - I don't undestand this question fully Question: In Stoke's law, let v_1 = -y and v_2 = 0 to show that the area of S equals the line integral -\int_C y\,\,\,dx . Find the area of an ellipse ( x = a \cos t , y = b \sin t , x^2/a^2+y^2/b^2 = 1 , 0 \leq t \leq 2\pi ). It's...

According to Raman effect, the intensity is directly proportional to the 4th power of the wavelength. Then how come stokes lines, which have higher wavelengths than anti-stokes lines, are more intense than the anti-stokes lines?

How is stokes law related to parachutes?

Consider a stationary body within the flow of some fluid. I want to calculate pressure on the surface of the body. From the Navier Stokes (incompressible, stationary, no volume forces) equations, you would get something like: dp/dx=-rho(u du/dx+v du/dy+w du/dz)+eta(d²u/dx²+d²u/dy²+d²u/dz²)...

Here is the problem: S is the ellipsoid x^2+y^2+2z^2=10 and F is a vector field F=(sin(xy),e^x,-yz) Find: \int \int_S ( \nabla \mbox {x} F) \cdot dS So, I know that Stokes' Theorem states that: \int \int_S ( \nabla \mbox {x} F) \cdot dS = \int_{\partial S} F \cdot ds where...

I need complete assistance on this :-) Check the Stokes' theorem using the function \vec v =ay\hat x + bx\hat y (a and b are constants) for the circular path of radius R, centered at the origin of the xy plane. As usual Stokes' theorem suggests: \int_s {(\nabla\times \vec v).d\vec a =...

Check the Stokes' theorem for the function \vec v = y\hat z Here it is over a tetrahedron. Stokes' theorem suggests: \int_s {(\nabla\times \vec v).d\vec a = \oint_p\vec v.d\vec r For the right hand side I computed the line integral from (a,0,0)--->(0,2a,0)--->(0,0,a)--->(a,0,0); which...

Hello, I need the Navier Stokes equations for compressible flow (Newtonian fluid would be ok) in cylinder coordinates. Can anybody help? Thanks

I can't figure this out, help me NOW! :-p Just kidding. So anyways, here's the question: Part of stokes theorem has the following in it: \frac {\partial } {\partial x} ( Q + R \frac{\partial z}{\partial y} ) Which is written as: \frac { \partial Q }{\partial x} + \frac {...

Hi I've got this question that I've been stuck on a while now.. I am sure its really obvious but i can't see to get it: Q: with the help of stokes's theorem, show that F(r) is conservative provided that nabla X F = 0. nabla X F is the same as curl F? Cheers.

I'm not sure if this post should go here or in the Calc setion, but I figure more knowledgeable people browse this form. This question is relating to 'directionality' of doing closed loop integrals. If you have some 2D wire structure, let's image it looks like a square wave, or a square well...

Would anyone be willing to explain Stokes' Theorem to me? I have managed to grasp the concepts of grad, div, curl, and what the text calls "green's theorem", but I cannot seem to grasp the geometric meaning of "stokes theorem." I've been trying to put the theorem together based on the...

Hi folks, I'm working on the following problem... Show that the flux of the vector field \nabla \times A through a closed surface is zero. Use both Gauss and Stokes. Where can I begin? Thanks...

i thought stokes theorem (green's thm) was hard after reading it in spivak, who calls it trivial nonetheless. however lang showed it is indeed trivial in his analysis I. the same proof occurs in courant. I.e. the point is that the theorem is easy for a rectangle, where it follows...

Hello, Could anyone tell me what assumptions are made about conditions in the derivation of Stokes' law ( F = 6(pi)(eta)rv )? Also, how is the Ladenburg correction for motion in a fluid derived from/related to this? I have searched high and low on the net and in libraries, but I'm not coming up...

Hi, I'm trying to understand how to convert the cartesian form of the N-S equation to cylinderical/spherical form. Rather than re-derive the equation for spherical/cylindrical systems, I am trying to directly convert the cartesian PDE. I'm ok with converting the d/dx and d2/dx2 terms. What...

I recently came across the vector version of the Navier Stokes equations for fluid flow. \displaystyle{\frac{\partial \mathbf{u}}{\partial \mathbf{t}}} + ( \mathbf{u} \cdot \bigtriangledown) \mathbf{u} = v \bigtriangleup \mathbf{u} - grad \ p Ok, all is well until \bigtriangleup. I know...