Total force of the fluid on the sphere in a creeping flow around a sphere

Input(s)

R: Radius $(\mathrm{m})$

$\rho$: Density $\left(\mathrm{kg} / \mathrm{m}^{3}\right)$

$\boldsymbol{\mu}$: Viscosity $(\mathrm{kg} /(\mathrm{ms}))$

g: Gravitational Acceleration $\left(\mathrm{m} / \mathrm{s}^{2}\right)$

vs: Apparent Velocity $(\mathrm{m} / \mathrm{s})$

Output(s)

F: Total Force of Fluid (N)

Formula(s)

$$ F=\frac{4}{3} * \pi * R^{3} * \rho * g+6 * \pi * \mu * R * v s $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Page: 60 .