Buckingham Reiner equation

Input(s)

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

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

R\mathrm{R}: Radius (ft)

ρ\rho: Density of Fluid (ppg)

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

L: Length (ft)

τo\tau_{\boldsymbol{o}}: Torque (psi)

Output(s)

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

Q: Mass Flow Rate (lb/s)

Formula(s)

τR=(PoPL)R2LQ=[3.142(PoPL)R4ρ8μL](14τo3τR+0.333(τoτR)4)\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.


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