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.