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.