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.