Cylindrical coordinates Definition and 225 Threads

My question is about vector addition in cylindrical coordinates: Let A = 2x + y, B = x + 2y. In rectangular coordinates, AB = B-A = -x+y In cylindrical coordinates, x=rcosθ + θsinθ, y=rsinθ + θcosθ A =Axx + Ayy, B =Bxx + Byy Ar = Ax(x.r) + Bx(y.r)=2.236, Aθ = 0. So A = 2.236r Br...

Hey guys, Been given this formula for radial acceleration, I am not sure how they derived it. I have tried but the only forumla I know is a(radial) = v^2/r A_{r} = \ddot{r} - r\dot{\theta}^{2}EDIT - should be minus not plus

Hello all, it might be funny! but i am stuck to it! what is the vector cross product formula in spherical and cylindrical coordinates?! I know for Cartesian coordinate we have that nice looking determinant. but what about the other coordinates. I had looks to all the math books (like...

Hello, The following equation: \frac{\partial^2 u}{\partial r^2}+\frac{1}{r} \cdot \frac{\partial u}{\partial r}+ \frac{\partial^2 u}{\partial z^2} = 0 is solved by separation of variables assuming a solution of the form: u=R(r)Z(z) In other cases the assumed solution is of the...

Homework Statement A long copper pipe, with it's axis on the z axis, is cut in half and the two halves are insulated. One half is held at 0V, the other at 9V. Find the potential everywhere in space.Homework Equations \nabla^2V=0The Attempt at a Solution Alright. This is a laplace's equation...

Hello Trying to plot in MATLAB the final solution equation u(r,z) of the steady state temperatures in the circular cylinder u(r,z) is defined in cylindrical coordinates and I'm confused trying to understand also how MATLAB plots a mesh. After some simplification The final solution looks...

Consider a cylindrical shell so that the cross sectional radius is some constant a. In the first term of the divergence expression in cylindrical coordinates: \frac{1}{r}\frac{\partial}{\partial r}(rA_{r}) When I multiply the radial component by r, do I go ahead and substitute r=a...

Hey everyone, first time poster. I am looking for a general solution to poisson's equation in a cylindrical geometry for the electrostatic field. By general, I am thinking of two concentric, grounded, hollow cylinders of finite height, and the solution for the field using the green's function...

Homework Statement What current density would produce the vector potential, A = k \hat{\phi} where k is a constant, in cylindrical coordinates? Homework Equations \nabla^2 A = -\mu_{0} J In cylindrical coordinates for radial and z symmetry \nabla^2 t = \frac{1}{s^2}...

So, I have searched the globe to find the derivation of the conservation of energy equation in 3D cylindrical coordinates. I have looked in about every heat transfer, thermodynamic, thermofluid books in the library. I have spent about 4 hours on the internet trying to find something, but no...

Homework Statement Say I have line, y = - 5 in cartesian coordinates. How do I express this in cylindrical coordinates? Also, if I have a point (0,-5) in cartesian coordinates, how to I express this position vector in cylindrical coordinates? Homework Equations y = r sin (phi)...

Help! I am stuck on the following derivation: Use the conservation of mass to derive the corresponding continuity equation in cylindrical coordinates. Please take a look at my work in the following attachments. Thanks! =)

Can someone explain to me how to find the volume of the following? I am asked to use cylindrical coordinates to find the volume of the solid enclosed by the sphere r^2+a^2 = a^2 and by the cone z = r cot φ where φ is some fixed angle between 0 and pi/2? I would have thought that the volume...

Hello. To find the work of a force, I have to perform a dot product between the force and a infinitesimal displacement. If they are in cylindrical coordinates, I can't manage to make the dot product. Please, could you help me? Thank you.

I'm having some trouble understanding exactly how to graph this problem using cylindrical coordinates. The coordinates they give me is r=2cos(theta) How do I go about beginning to determine how to graph this with only the radius?

Hello. I am interested in learning the mathematical derivation from Cartesian coordinates Navier-Stokes equation to cylindrical coordinates Navier-Stokes equation. These equations have similar forms to the basic heat and mass transfer differential governing equations. I’ve tried looking...

We just started a section dealing with div/curl/grad in different orthogonal systems... before I get started doing problems involving these operations I wanted to make sure I am dealing with these operation correctly. Our first homework problem is as follows: In cylindrical coordinates compute...

Hi , I don't know how to get the edge of the cone in cylindrical coordinates. For example, we have a cone starting at the origin, of heigth 2 and the top is a circle of radius 1 (center at the origin). the edge of the cone is z=2r. but I don't know how they find it. Please can someone...

Can someone, please, show me an example of when you are better of with parabolic cylindrical coordinates than with cartesian coordinates when computing a triple integral over a solid?

I'm supposed to prove the laplacian in cylindrical coord. is what it is. I tried tackling the problem in two ways and none work! I have no idea what's the matter. The first way is to calculate d²f/dr² , d²f/dO² and d²f/dz² and isolate d²f/dx² , d²f/dy² and d²f/dz². In cylindrical coord...

How can you derive the gradient of a vector R^3 to R in cylindrical coordinates?

I'm having trouble figuring out this volume. Use the cylindrical coordinates to find the volume of the solid S bounded by z=x^2 + y^2 and z=12 - 2x^2 - 2y^2 I've included a pic of what I think the regions and the solid look like...

I have this flow field in cylindrical coordinates of which I would like to calculate the dissipation as a function of these coordinates. Now in my fluid dynamics notes I found the following expression(s) for the dissipation: 2 \mu (e_{ij} -\frac{1}{3} \Delta \delta _{ij} )^2 = 2 \mu (...

The problem says to find the volume of material cut from the solid sphere, r^2 + z^2 \le 9 by the cylinder, r = 3\sin\theta I don't know how to graph the first equation, but I can do the second in polar coordinates. How do I go about converting to use cylindrical coordinates?

Hi everybody The integral in question is the triple integral of x dV over the region E, where E is enclosed by the planes z=0, and z=x+y+3, and the cylinders x^2 + y^2 = 4 and x^2 + y^2 = 9. Well--- so far in cylindrical coordinates I know the r limits will be from 2 to 3 since the...