Average velocity of flow through an annulus

Input(s)

Po\boldsymbol{P}_{\boldsymbol{o}}: Pressure at Initial Point (Pa)(\mathrm{Pa})

PL\boldsymbol{P}_{\boldsymbol{L}}: Pressure at Point L(Pa)\mathrm{L}(\mathrm{Pa})

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

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

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

к: Ratio of Inner Pipe's Radius to Outer Pipe's Radius (fraction)

Output(s)

vz\boldsymbol{v}_{z}: Average Velocity (m/s)(\mathrm{m} / \mathrm{s})

Formula(s)

vz=(PoPL)R28μL[1κ41κ21κ2ln(1κ)]v_{z}=\frac{\left(P_{o}-P_{L}\right) * R^{2}}{8 * \mu * L} *\left[\frac{1-\kappa^{4}}{1-\kappa^{2}}-\frac{1-\kappa^{2}}{\ln \left(\frac{1}{\kappa}\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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