Momentum flux profile of fluids in flow of two adjacent immiscible fluids

Input(s)

po\mathbf{p}_{\mathbf{o}}: Pressure at Initial Point (Pa)(\mathrm{Pa})

pL\mathbf{p}_{\mathbf{L}}: Pressure at point L(Pa)\mathrm{L}(\mathrm{Pa})

b: Distance (m)(\mathrm{m})

x\mathbf{x}: Distance in Cartesian Coordinate x(m)\mathrm{x}(\mathrm{m})

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

μI\boldsymbol{\mu}_{\mathbf{I}}: Viscosity of More Dense and Viscous Fluid (kg/(ms))(\mathrm{kg} /(\mathrm{ms}))

μII\boldsymbol{\mu}_{\mathbf{I I}}: Viscosity of Less Dense and Viscous Fluid (kg/(ms))(\mathrm{kg} /(\mathrm{ms}))

Output(s)

τrz\boldsymbol{\tau}_{\mathbf{r z}}: Momentum Flux (Pa)(\mathrm{Pa})

Formula(s)

τrz=(popL) b L((xb)12μIμIIμI+μII)\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.


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