Momentum fluxes for creeping flow into a slot

Input(s)

$\mathbf{P}_{\mathrm{i}}$: Pressure input (psi)

$\mathbf{P}_{\mathbf{0}}$: Pressure output (psi)

R: Radius of sphere $(\mathrm{cm})$

к: Turbulance coefficient (dimensionless)

$\rho$: Fluid density $(\mathrm{g} / \mathrm{cc})$

$\boldsymbol{\mu}$: viscosity of fluid $(\mathrm{cP})$

$\xi$: angle of contact between two entities (rad)

Output(s)

W: Mass Flow Rate $(\mathrm{g} / \mathrm{s})$

Formula(s)

$$ W=\frac{\pi *\left(P_{i}-P_{o}\right) *\left(R^{3}\right) *\left((1-\kappa)^{3}\right) * \rho}{12 * \mu * \ln \left(\cot \left(\frac{\xi}{2}\right)\right)} $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.), John Wiley \& Sons, Page: 107.