Velocity distribution in a creeping flow around a sphere
Input(s)
\(\boldsymbol{P}_{\boldsymbol{i}}\): Input Pressure (psi)
\(\boldsymbol{P}_{\boldsymbol{o}}\): Output Pressure (psi)
L: Length (ft)
\(\boldsymbol{\mu}_{\boldsymbol{a}}\): Viscosity of A (cP)
\(\boldsymbol{\mu}_{\boldsymbol{b}}\): Viscosity of B (cP)
b: Radius \((\mathrm{ft})\)
\(\mathrm{x}\): Distance from center \((\mathrm{ft})\)
Output(s)
v: Velocity \((\mathrm{ft} / \mathrm{s})\)
Formula(s)
\[
v=\left(\frac{\left(P_{i}-P_{o}\right) *\left(b^{2}\right)}{2 * \mu_{a} * L}\right) *\left(\frac{2 * \mu_{a}}{\mu_{a}+m u_{b}}+\frac{\left(\mu_{a}-\mu_{b}\right) * x}{\left(\mu_{a}+\mu_{b}\right) * b}-\left(\frac{x}{b}\right)^{2}\right)
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Page: 59.