Momentum flux distribution of flow through an annulus
Input(s)
\(\mathbf{p}_{\mathbf{o}}\): Pressure at Initial Point \((\mathrm{Pa})\)
\(\mathbf{p}_{\mathbf{L}}\): Pressure at Point \(\mathrm{L}(\mathrm{Pa})\)
R : Radius \((\mathrm{m})\)
L: Length \((\mathrm{m})\)
r: Cylindrical Shell of Thickness (m)
K: Ratio of Inner Pipe's Radius to Outer Pipe's Radius (fraction) \(\left(\mathrm{m}^{2} \mathrm{~kg} \mathrm{~s}^{-2} \mathrm{~K}^{-1}\right.\) )
Output(s)
\(\tau_{\text {rz }}\): Momentum Flux Distribution \((\mathrm{Pa})\)
Formula(s)
\[
\tau_{\mathrm{rz}}=\left(\mathrm{p}_{\mathrm{o}}-\mathrm{p}_{\mathrm{L}}\right) * \frac{\mathrm{R}}{2 * \mathrm{~L}} *\left(\frac{\mathrm{r}}{\mathrm{R}}-\frac{1-\mathrm{K}^{2}}{2 * \ln \left(\frac{1}{\mathrm{~K}}\right)} *\left(\frac{\mathrm{R}}{\mathrm{r}}\right)\right)
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 2, Page: 55.