Buckingham Reiner equation

Input(s)

$\boldsymbol{P}_{\boldsymbol{o}}$: Input Pressure (psi)

$\boldsymbol{P}_{\boldsymbol{L}}$: Output Pressure (psi)

$\mathrm{R}$: Radius (ft)

$\rho$: Density of Fluid (ppg)

$\mu$: Viscosity of Fluid $(\mathrm{cP})$

L: Length (ft)

$\tau_{\boldsymbol{o}}$: Torque (psi)

Output(s)

$\tau_{R}$: Shear Stress at the Tube Wall (psi)

Q: Mass Flow Rate (lb/s)

Formula(s)

$$ \begin{gathered} \tau_{R}=\frac{\left(P_{o}-P_{L}\right) * R}{2 * L} \\ Q=\left[\frac{3.142 *\left(P_{o}-P_{L}\right) * R^{4} * \rho}{8 * \mu * L}\right] *\left(1-\frac{4 * \tau_{o}}{3 * \tau_{R}}+0.333 *\left(\frac{\tau_{o}}{\tau_{R}}\right)^{4}\right) \end{gathered} $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 8, Page: 260.