# 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.

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