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.