Velocity distribution of flow through an annulus

Input(s)

po: Pressure at initial point (Pa)(\mathrm{Pa})

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

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

μ\mu: Viscosity (kg/(ms))(\mathrm{kg} /(\mathrm{ms}))

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

r: Cylindrical Shell of Thickness (m)(m)

K\mathrm{K} : Boltzmann Constant (m2 kg s2 K1)\left(\mathrm{m}^{2} \mathrm{~kg} \mathrm{~s}^{-2} \mathrm{~K}^{-1}\right)

Output(s)

vz: Velocity Distribution (m/s)

Formula(s)

vz=(popL)R24μL(1(rR)21K2ln(1K)ln(Rr))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.


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