Flow in a slit with uniform cross flow

Input(s)

B: Thickness (cm)

L: Length $(\mathrm{cm})$

$\boldsymbol{W}_{\boldsymbol{p}}$: Width $(\mathrm{cm})$

$v_{\mathbf{0}}$: Cross-flow Velocity $(\mathrm{cm} / \mathrm{s})$

$\rho$: Fluid Density $(\mathrm{g} / \mathrm{cc})$

$\mu$: Viscosity (Pa s)

$\boldsymbol{P}_{\boldsymbol{O}}$: Input Pressure $(\mathrm{Pa})$

$\boldsymbol{P}_{\boldsymbol{L}}$: Output Pressure $(\mathrm{Pa})$

Output(s)

A: Constant (dimensionless)

w: Mass Flow Rate (g/s)

Formula(s)

$$ \begin{gathered} \mathrm{A}=\frac{\mathrm{B} * \mathrm{v}_{\mathrm{o}} * \rho}{\mu} \\ \mathrm{w}=\left(\frac{\left(\mathrm{P}_{\mathrm{O}}-\mathrm{P}_{\mathrm{L}}\right) *\left(\mathrm{~B}^{3}\right) * \mathrm{~W}_{\mathrm{p}}}{\mu * \mathrm{~L} * \mathrm{~A}}\right) *\left(\frac{1}{2}-\frac{1}{\mathrm{~A}}+\frac{1}{(\exp (\mathrm{A})-1)}\right) \end{gathered} $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 3, Page: 110.