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.