Fluid Dynamics: Determining Velocity Coefficients

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SUMMARY

The discussion focuses on determining the number of independent coefficients required to uniquely specify the velocity of an incompressible, irrotational fluid represented by the velocity components v_x, v_y, and v_z. The user has utilized the divergence and curl conditions, specifically div(v)=0 and curl(v)=0, to establish relationships among the coefficients c_xx, c_xy, c_xz, c_yx, c_yy, c_yz, c_zx, c_zy, and c_zz. Further exploration of boundary conditions and potential flow theory is suggested to derive additional relationships among these coefficients.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically incompressible and irrotational flow.
  • Familiarity with vector calculus, including divergence and curl operations.
  • Knowledge of boundary conditions in fluid mechanics.
  • Basic concepts of potential flow theory.
NEXT STEPS
  • Research the application of boundary conditions in fluid dynamics.
  • Study potential flow theory and its implications for velocity coefficients.
  • Explore advanced vector calculus techniques relevant to fluid flow analysis.
  • Investigate the role of symmetry in simplifying fluid velocity coefficient relationships.
USEFUL FOR

Students and professionals in fluid dynamics, engineers working with fluid systems, and researchers focusing on velocity field analysis in incompressible flows.

nicorette
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Homework Statement


I have an incompressible, irrotational fluid with velocity v in the form:

v_x = c_xx x + c_xy y + c_xz z
v_y = c_yx x + c_yy y + c_yz z
v_z = c_zx x + c_zy y + c_zz z

The coefficients c_xx, c_xy, etc. are constants.

How can I determine how many independent coefficients I need to specify the velocity uniquely?

Homework Equations


The Attempt at a Solution

 
Last edited:
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I've used div(v)=0 and curl(v)=0 to come up with a few relationships between the various coefficients. What other conditions can I use to find relationships?
 

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