Laminar flow of an incompressible power-law fluid in a circular tube

Input(s)

ρ\rho: Density of Fluid (g/cc)(\mathrm{g} / \mathrm{cc})

Po\boldsymbol{P}_{\boldsymbol{o}}: Input Pressure (Pa)(\mathrm{Pa})

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

R\mathrm{R}: Radius of Tube (cm)(\mathrm{cm})

L: Length of Tube (cm)(\mathrm{cm})

m: Power Law Constant (dimensionless)

n\mathrm{n}: Power Law Constant 2 (dimensionless)

Output(s)

w: Mass Rate (g/s)(\mathrm{g} / \mathrm{s})

Formula(s)

w=(π(R3)ρ(1n)+3)(((PoPL)R2 m L)1n)\mathrm{w}=\left(\frac{\pi *\left(\mathrm{R}^{3}\right) * \rho}{\left(\frac{1}{\mathrm{n}}\right)+3}\right) *\left(\left(\frac{\left(\mathrm{P}_{\mathrm{o}}-\mathrm{P}_{\mathrm{L}}\right) * \mathrm{R}}{2 * \mathrm{~m} * \mathrm{~L}}\right)^{\frac{1}{\mathrm{n}}}\right)

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 8, Page: 243.


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