Slit flow in Bingham fluid
Input(s)
\(\boldsymbol{P}_{\boldsymbol{o}}\): Input Pressure (psi)
\(\boldsymbol{P}_{\boldsymbol{L}}\): Output Pressure (psi)
B: Breadth \((\mathrm{ft})\)
L: Length \((\mathrm{ft})\)
\(\boldsymbol{\mu}_{\boldsymbol{o}}\): Viscosity \((\mathrm{cP})\)
\(\boldsymbol{\tau}_{\boldsymbol{o}}\): Torque \(\left(\mathrm{lb} / \mathrm{ft} \mathrm{s}^{2}\right)\)
W: Width (ft)
\(\rho\): Density (ppg)
Output(s)
w: Mass Flow Rate \((\mathrm{lb} / \mathrm{s})\)
Formula(s)
\[
\mathrm{w}=\left(\frac{2 *\left(\mathrm{P}_{\mathrm{o}}-\mathrm{P}_{\mathrm{L}}\right) * \mathrm{~W} * \mathrm{~B}^{3} * \rho}{3 * \mu_{\mathrm{o}} * \mathrm{~L}}\right) *\left(1-\left(\frac{3 * \tau_{\mathrm{o}} * \mathrm{~L}}{2 *\left(\mathrm{P}_{\mathrm{o}}-\mathrm{P}_{\mathrm{L}}\right) * \mathrm{~B}}\right)+\left(0.5 *\left(\frac{\tau_{\mathrm{o}} * \mathrm{~L}}{\left(\mathrm{P}_{\mathrm{o}}-\mathrm{P}_{\mathrm{L}}\right) * \mathrm{~B}}\right)^{3}\right)\right)
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 8, Page: 260.