# 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.

## Related

### Average velocity of flow through a circular tube

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