Flow in a slit with uniform cross flow

Input(s)

B: Thickness (cm)

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

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

v0v_{\mathbf{0}}: Cross-flow Velocity (cm/s)(\mathrm{cm} / \mathrm{s})

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

μ\mu: Viscosity (Pa s)

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

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

Output(s)

A: Constant (dimensionless)

w: Mass Flow Rate (g/s)

Formula(s)

A=Bvoρμw=((POPL)( B3) Wpμ L A)(121 A+1(exp(A)1))\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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