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.