Ringleb flow

Revision as of 08:32, 16 September 2005 by Praveen (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

$\psi = \frac{1}{q} \sin\theta$

Take

$k = \frac{1}{\psi}$

to be constant as a streamline.

Streamline equations:

$x(q) = \frac{1}{2 \rho(q) } \left( \frac{1}{q^2} - \frac{2}{k^2} \right) + \frac{1}{2} J(q)$

$y(q) = \pm \frac{1}{kq\rho(q)} \sqrt{ 1 - \frac{q^2}{k^2} }$

where

$J(q) = \frac{1}{c} + \frac{1}{3c^3} + \frac{1}{5c^5} - \frac{1}{2} \log\left( \frac{1 + c}{1 - c} \right)$

$c(q) = \sqrt{ 1 - \frac{\gamma-1}{2} q^2 }$

$\rho(q) = c^{2/(\gamma-1)}$

References

Shapiro ({{{year}}}), Mechanics and Thermodynamics of Compressible flows, {{{rest}}}.