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.