Slit flow in Bingham fluid

Input(s)

Po\boldsymbol{P}_{\boldsymbol{o}}: Input Pressure (psi)

PL\boldsymbol{P}_{\boldsymbol{L}}: Output Pressure (psi)

B: Breadth (ft)(\mathrm{ft})

L: Length (ft)(\mathrm{ft})

μo\boldsymbol{\mu}_{\boldsymbol{o}}: Viscosity (cP)(\mathrm{cP})

τo\boldsymbol{\tau}_{\boldsymbol{o}}: Torque (lb/fts2)\left(\mathrm{lb} / \mathrm{ft} \mathrm{s}^{2}\right)

W: Width (ft)

ρ\rho: Density (ppg)

Output(s)

w: Mass Flow Rate (lb/s)(\mathrm{lb} / \mathrm{s})

Formula(s)

w=(2(PoPL) W B3ρ3μo L)(1(3τo L2(PoPL) B)+(0.5(τo L(PoPL) B)3))\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.


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