Momentum flux profile of fluids in flow of two adjacent immiscible fluids
Input(s)
\(\mathbf{p}_{\mathbf{o}}\): Pressure at Initial Point \((\mathrm{Pa})\)
\(\mathbf{p}_{\mathbf{L}}\): Pressure at point \(\mathrm{L}(\mathrm{Pa})\)
b: Distance \((\mathrm{m})\)
\(\mathbf{x}\): Distance in Cartesian Coordinate \(\mathrm{x}(\mathrm{m})\)
L : Length \((\mathrm{m})\)
\(\boldsymbol{\mu}_{\mathbf{I}}\): Viscosity of More Dense and Viscous Fluid \((\mathrm{kg} /(\mathrm{ms}))\)
\(\boldsymbol{\mu}_{\mathbf{I I}}\): Viscosity of Less Dense and Viscous Fluid \((\mathrm{kg} /(\mathrm{ms}))\)
Output(s)
\(\boldsymbol{\tau}_{\mathbf{r z}}\): Momentum Flux \((\mathrm{Pa})\)
Formula(s)
\[
\tau_{\mathrm{rz}}=\frac{\left(\mathrm{p}_{\mathrm{o}}-\mathrm{p}_{\mathrm{L}}\right) * \mathrm{~b}}{\mathrm{~L}} *\left(\left(\frac{\mathrm{x}}{\mathrm{b}}\right)-\frac{1}{2} * \frac{\mu_{\mathrm{I}}-\mu_{\mathrm{II}}}{\mu_{\mathrm{I}}+\mu_{\mathrm{II}}}\right)
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 2, Page: 57.