Laminar flow of an incompressible power-law fluid in a circular tube
Input(s)
\(\rho\): Density of Fluid \((\mathrm{g} / \mathrm{cc})\)
\(\boldsymbol{P}_{\boldsymbol{o}}\): Input Pressure \((\mathrm{Pa})\)
\(\boldsymbol{P}_{\boldsymbol{L}}\): Output Pressure \((\mathrm{Pa})\)
\(\mathrm{R}\): Radius of Tube \((\mathrm{cm})\)
L: Length of Tube \((\mathrm{cm})\)
m: Power Law Constant (dimensionless)
\(\mathrm{n}\): Power Law Constant 2 (dimensionless)
Output(s)
w: Mass Rate \((\mathrm{g} / \mathrm{s})\)
Formula(s)
\[
\mathrm{w}=\left(\frac{\pi *\left(\mathrm{R}^{3}\right) * \rho}{\left(\frac{1}{\mathrm{n}}\right)+3}\right) *\left(\left(\frac{\left(\mathrm{P}_{\mathrm{o}}-\mathrm{P}_{\mathrm{L}}\right) * \mathrm{R}}{2 * \mathrm{~m} * \mathrm{~L}}\right)^{\frac{1}{\mathrm{n}}}\right)
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 8, Page: 243.