Differential Cartesian Coordinates Into Cylindrical Coordinates

In summary, differential Cartesian coordinates are a type of coordinate system used to describe the position of a point in three-dimensional space with measurements along the x, y, and z axes. Cylindrical coordinates, on the other hand, use measurements along the radial, azimuthal, and vertical axes. To convert from differential Cartesian coordinates to cylindrical coordinates, equations can be used. Cylindrical coordinates have advantages when working with objects with cylindrical symmetry and can be converted back to differential Cartesian coordinates using equations.
  • #1
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Has to convert B6-1 into B6-2 Source Transport Phenomenon 2nd ed -

sxgd39.jpg
 
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  • #2
I can't even start solution
No idea how to convert subscipt from vx to vr and or to vtheta?
 
  • #3
You are to find the radial component of the transport equation.

Set up the relevant quantities and relationships, then we'll help you.
 
  • #4
In the first equation: substitute Vx = Vr * Cos (theta) Vy = Vr * Sin (theta) Vz = Vz

but how do I get V(theta)
 

1. What are differential Cartesian coordinates?

Differential Cartesian coordinates are a type of coordinate system used to describe the position of a point in three-dimensional space. They consist of three measurements, typically denoted as (x, y, z), representing the distance along the x, y, and z axes from a fixed reference point.

2. What are cylindrical coordinates?

Cylindrical coordinates are another type of coordinate system used to describe the position of a point in three-dimensional space. They consist of three measurements, typically denoted as (r, θ, z), representing the distance from the origin along the radial, azimuthal, and vertical axes.

3. How do you convert differential Cartesian coordinates into cylindrical coordinates?

To convert from differential Cartesian coordinates to cylindrical coordinates, you can use the following equations:
r = √(x² + y²)
θ = arctan(y/x)
z = z
Where r represents the distance from the origin, θ represents the angle from the positive x-axis, and z remains the same in both coordinate systems.

4. What are the advantages of using cylindrical coordinates?

Cylindrical coordinates are particularly useful when working with objects that have cylindrical symmetry, such as cylinders or cones. They also simplify certain types of calculations, such as finding the volume or surface area of a cylinder.

5. Can you convert from cylindrical coordinates back to differential Cartesian coordinates?

Yes, you can convert from cylindrical coordinates back to differential Cartesian coordinates using the following equations:
x = r cos(θ)
y = r sin(θ)
z = z
Where r represents the distance from the origin, and θ represents the angle from the positive x-axis. This conversion can be useful when plotting points or solving equations in a Cartesian coordinate system.

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