Pressure distribution in a creeping flow around a sphere
Input(s)
\(\boldsymbol{p}_{\boldsymbol{o}}\): Pressure in the Plane \(\mathrm{z}=0\) far away from the Sphere \((\mathrm{Pa})\)
\(\rho\): Density \(\left(\mathrm{kg} / \mathrm{m}^{3}\right)\)
\(\mathrm{g}\): Gravitational Acceleration \(\left(\mathrm{m} / \mathrm{s}^{2}\right)\)
z: Direction \((\mathrm{m})\)
\(\mu\): Viscosity \((\mathrm{kg} /(\mathrm{ms}))\)
\(v_{\infty}\): Velocity as \(r\) Goes to Infinity \((\mathrm{m} / \mathrm{s})\)
\(\mathrm{R}\): Radius \((\mathrm{m})\)
r: Cylindrical Shell of Thickness (m)
Output(s)
p: Pressure Distribution \((\mathrm{Pa})\)
Formula(s)
\[
\mathrm{p}=\mathrm{p}_{\mathrm{o}}-(\rho * \mathrm{~g} * \mathrm{z})-\left(\left(\frac{3}{2}\right) *\left(\mu * \frac{\mathrm{v}_{\infty}}{\mathrm{R}}\right) *\left(\frac{\mathrm{R}}{\mathrm{r}}\right)^{2}\right) * \cos (\theta)
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 2, Page: 59.