Velocity distribution of flow through an annulus
Input(s)
po: Pressure at initial point \((\mathrm{Pa})\)
\(\mathrm{pL}\): Pressure at point \(\mathrm{L}(\mathrm{Pa})\)
\(\mathrm{R}\): Radius \((\mathrm{m})\)
\(\mu\): Viscosity \((\mathrm{kg} /(\mathrm{ms}))\)
L: Length \((\mathrm{m})\)
r: Cylindrical Shell of Thickness \((m)\)
\(\mathrm{K}\) : Boltzmann Constant \(\left(\mathrm{m}^{2} \mathrm{~kg} \mathrm{~s}^{-2} \mathrm{~K}^{-1}\right)\)
Output(s)
vz: Velocity Distribution (m/s)
Formula(s)
\[
v z=\frac{(p o-p L) * R^{2}}{4 * \mu * L} *\left(1-\left(\frac{r}{R}\right)^{2}-\frac{1-K^{2}}{\ln \left(\frac{1}{K}\right)} * \ln \left(\frac{R}{r}\right)\right)
\]
Reference(s)
Transport Phenomena, Second Edition, Bird, Page: 55.