Abstract
In the previous chapters, the governing equations for Newtonian and incompressible fluids have been applied to internal flows, namely flows in which the fluid moves between solid walls (for example, Couette or Poiseuille motion in a channel or pipe).
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Notes
- 1.
The relations (6.49) allow to set \(\text {d}\phi =- v_r \text {d}r\) which, once integrated, yields \(\phi = - (m/2\pi ) \ln r + f(\theta )\), as well as \(\text {d}\phi =- r v_\theta \text {d}\theta \), which, once integrated, yields \(\phi = f(r)\), with \(f(\theta )\) and f(r) arbitrary integration constants. By choosing \(f(\theta )=0\) and \(f(r)=- (m / 2 \pi ) \ln r\), the velocity potential becomes: \(\phi = - (m / 2 \pi ) \ln r\).
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Soldati, A., Marchioli, C. (2024). Approximate Solutions for High Reynolds Number Flows. In: Fluid Mechanics for Mechanical Engineers. Springer, Cham. https://doi.org/10.1007/978-3-031-53950-3_6
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DOI: https://doi.org/10.1007/978-3-031-53950-3_6
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