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.