Differential Cartesian Coordinates Into Cylindrical Coordinates

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SUMMARY

The discussion focuses on converting differential Cartesian coordinates into cylindrical coordinates, specifically in the context of the transport phenomenon as outlined in "Source Transport Phenomenon 2nd ed." The user seeks assistance in transforming the velocity components from Cartesian (Vx, Vy, Vz) to cylindrical coordinates (Vr, Vθ, Vz). The key relationships established include Vx = Vr * Cos(θ) and Vy = Vr * Sin(θ), but the user requires further guidance on deriving the angular component Vθ.

PREREQUISITES
  • Understanding of differential equations in fluid dynamics
  • Familiarity with coordinate transformations
  • Knowledge of cylindrical coordinate systems
  • Basic grasp of vector components in physics
NEXT STEPS
  • Study the derivation of velocity components in cylindrical coordinates
  • Learn about the application of the transport equation in fluid mechanics
  • Research the mathematical principles behind coordinate transformations
  • Explore examples of converting between Cartesian and cylindrical coordinates
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Students and professionals in engineering, particularly those specializing in fluid dynamics, as well as anyone involved in solving transport phenomena problems.

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Has to convert B6-1 into B6-2 Source Transport Phenomenon 2nd ed -

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

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

but how do I get V(theta)
 

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