# 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.

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