Velocity distribution of flow through a circular tube

Input(s)

po\boldsymbol{p}_{\boldsymbol{o}}: Pressure at Initial Point (Pa)(\mathrm{Pa})

pLp_{L}: Pressure at Point L(Pa)\mathrm{L}(\mathrm{Pa})

R: Radius of the Tube (m)(m)

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

L: Length of the Tube (m)

r: Cylindrical Shell of Thickness (m)

Output(s)

vzv_{z}: Velocity Distribution (m/s)(\mathrm{m} / \mathrm{s})

Formula(s)

vz=(popL)R24μ L(1(rR)2)\mathrm{v}_{\mathrm{z}}=\frac{\left(\mathrm{p}_{\mathrm{o}}-\mathrm{p}_{\mathrm{L}}\right) * \mathrm{R}^{2}}{4 * \mu * \mathrm{~L}} *\left(1-\left(\frac{\mathrm{r}}{\mathrm{R}}\right)^{2}\right)

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 2, Page: 51 .


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