Momentum flux distribution of flow through an annulus

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})

R : Radius (m)(\mathrm{m})

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

r: Cylindrical Shell of Thickness (m)

K: Ratio of Inner Pipe's Radius to Outer Pipe's Radius (fraction) (m2 kg s2 K1\left(\mathrm{m}^{2} \mathrm{~kg} \mathrm{~s}^{-2} \mathrm{~K}^{-1}\right. )

Output(s)

τrz \tau_{\text {rz }}: Momentum Flux Distribution (Pa)(\mathrm{Pa})

Formula(s)

τrz=(popL)R2 L(rR1K22ln(1 K)(Rr))\tau_{\mathrm{rz}}=\left(\mathrm{p}_{\mathrm{o}}-\mathrm{p}_{\mathrm{L}}\right) * \frac{\mathrm{R}}{2 * \mathrm{~L}} *\left(\frac{\mathrm{r}}{\mathrm{R}}-\frac{1-\mathrm{K}^{2}}{2 * \ln \left(\frac{1}{\mathrm{~K}}\right)} *\left(\frac{\mathrm{R}}{\mathrm{r}}\right)\right)

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 2, Page: 55.


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