Revisiting the Von Kármán Problem with an Analytical Solution

Sebastiao Cardoso; José Manoel Balthazar; Ezio Castejon Garcia

doi:10.15866/ireme.v10i7.9723

Revisiting the Von Kármán Problem with an Analytical Solution

Sebastiao Cardoso^(1*), José Manoel Balthazar⁽²⁾, Ezio Castejon Garcia⁽³⁾

^(*) Corresponding author

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DOI: https://doi.org/10.15866/ireme.v10i7.9723

Abstract

This work presents an exact analytical solution for Navier-Stokes equations, obtained by von Kármán to study the variation of the speed and pressure of a fluid, initially at rest, close to a disk that rotates around its own axis, with a constant angular velocity. The exact analytical solution to the problem is obtained by using algebraic equations and functions of complex variables. The solutions presented here describe the behavior of the fluid near the disk. Thus, for each component of the velocity just the real part of the equations is considered because the imaginary part is included in its orthogonal component.
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Keywords

Analytical; Exact Solution; Velocity; Acceleration; Pressure; Navier-Stokes Equations; von Kármán Problem

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References

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