Cylindrical coordinate system Puns

1. In the heat transfer between the fluid flowing through a pipe and the wall; h = f (D, V, ρ, µ, k, Cp) is known to be. Accordingly, using the Rayleigh method, perform an investigation by dimensional analysis.
2. Question: Draw and show the Cartesian and Cylindrical coordinate systems

https://preview.redd.it/419jt34bj1m61.jpg?width=1708&format=pjpg&auto=webp&s=62a56b1b11857f8cb9d86206f5ffa3a7bb1d47a9

Do RGB cubic-coordinate and HSL cylindrical-coordinate systems both support same colors? Does one system support more or less colors than the other, or does one system support a color that cannot be achieved with the other system?

Help!

Edit: Thank you so much for the support guys! My exam went really well!

Hi, im working on a project whereby I need to measure the angular rotation in degrees for a shaft that is twisting. I have made a cylindrical coordinate system and am measuring deformation using those coordinates. Im wondering what the units of the coordinate system are for the angular part of the system, is it arc length, radians, or degrees?

I'm trying to fit a 3D golden spiral into a cylinder, It's been a long time since I've used cylindrical coordinates and I'm not sure how to go about it.

I know that if you spin one of these around the axis, you'll end up with a cone of some sort.

The cylinder in questions is a representation of colors by hue (angle), brightness (z), and saturation (r).

I'm only interested in the part of the spiral that is within: 0<angle<360 0<h<100 0<r<100

being able to graph it is my end goal. I want to be able to use it to pick off individual colors from the "color cylinder".

Help is greatly appreciated.

I was downvoted in my 1st post and nobody replied in 10 hours, whereas i see 2-10 comments for posts newer than mine. I apologise if i posted this in the wrong format.

I should also elaborate my objectives. I'm understanding quantum mechanics and i'd like to describe a free particle orbiting an origin.

the wavefunction i 1st tried was

Ψ = (2a/π)^(3/4) exp( -a(x-x')^2 -a(y-y')^2 -a(z-z')^2 )

substituting the transformations for x,y,z to r,θ,φ and x',y',z' for r',θ',φ' gives

Ψ = (2a/π)^(3/4) exp( -a(r^2 -rr'I(θ,φ) +(r')^(2)) )

where I(θ,φ) = J^(+)(φ)cos(θ-θ') + J^(-)(φ)cos(θ+θ')

and J^(±)(φ)= 1±cos(φ-φ')

Ι think i should start with the θ integral, but i can't seem to do it.

can anyone help?

Edit: equations in latex

[; \psi = (\frac{2a}{\pi})^{\frac{3}{4}} e^{-a(r^{2}-rr_{0}I(\theta , \phi)+r_{0}^{2})} ;]

[; I(\theta , \phi) = J^{+}(\phi) cos(\theta - \theta_{0}) + J^{-}(\phi) cos(\theta + \theta_{0}) ;]

[; J^{\pm}(\phi) = 1 \pm cos(\phi - \phi_{0}) ;]

[; \left \langle \psi\mid \psi\right \rangle = N^{2} e^{-2ar_{0}^2}\int^{\infty}_{r=0} e^{-2ar^{2}} r^{2} \int^{2\pi}_{\phi=0}\int^{\pi}_{\theta=0} e^{2rr_{0}(J^{\pm}cos(\theta \mp\theta_{0}))} sin(\theta) d\theta d\phi dr ;]

I have this last question on my homework, and I cannot seem to figure out how to convert.

Convert the rectangular equation 3x + y - 4z = 12 to (a) cylindrical coordinates and (b) spherical coordinates.

I don't know how to handle the 1st degree since all I know is that r = sqrt(x^2 + y^2) and the tan(theta)=y/x. I've tried plugging in x=rcos(theta) and y=rsin(theta) but I get stuck when trying to reduce it >.<

How are the unit vectors theta-hat and phi-hat interpreted geometrically? Are they just unit vectors tangent to the arc which subtends the angles theta or phi? Or does adding theta-hat or phi-hat correspond to rotating the angle by 1 radian? Or is there some other interpretation?

For this topic, i get confused in terms of the order of triple integration. i've written 2 methods not sure if either or neither is right

https://preview.redd.it/tl7fzaui7bx71.png?width=640&format=png&auto=webp&s=4691cd54b716e8c3829dd55ec5e8ffbc2576cddd

https://preview.redd.it/4se3n5fk7bx71.jpg?width=3024&format=pjpg&auto=webp&s=83b8fcb75566a99c0b104bb544b5a1ebcd71e893

Hey all, I want to ask if there is an online tool that graphs the volumes of specific intervals in both cylindrical and spherical coordinate systems. I want to teach these systems for some students and I'm not very good with drawing.

Like if I want to graph 1≤r≤2 , 30°≤θ≤90° and 30°≤φ≤90°, which will be a section of a sphere.

If there is no online tool to do this, is there a method to implement these examples without actually drawing them?

Thanks

Is my method correct?

So when you add the z component to the xy coordinate system, the name remains as cartesian coordinates. Yet when z is added to polar coordinates, it gets a name change. Why is this? Is there an issue with calling it polar coordinates in R^3 instead of R^2?

1. In the heat transfer between the fluid flowing through a pipe and the wall; h = f (D, V, ρ, µ, k, Cp) is known to be. Accordingly, using the Rayleigh method, perform an investigation by dimensional analysis.
2. Question: Draw and show the Cartesian and Cylindrical coordinate systems

https://preview.redd.it/ixg2pmnss8m61.jpg?width=1708&format=pjpg&auto=webp&s=29f1846fc7d16c757d61d9fc4342775b71ad6236