Editing Lambert W function (section)

=== Time-dependent flow in simple branch hydraulic systems ===
The principal branch of the Lambert {{mvar|W}} function is employed in the field of [[mechanical engineering]], in the study of time dependent transfer of [[Newtonian fluid]]s between two reservoirs with varying free surface levels, using centrifugal pumps.<ref>{{Cite journal |last1=Pellegrini |first1=C. C. |last2=Zappi |first2=G. A. |last3=Vilalta-Alonso |first3=G. |date=2022-05-12 |title=An Analytical Solution for the Time-Dependent Flow in Simple Branch Hydraulic Systems with Centrifugal Pumps |url=https://link.springer.com/10.1007/s13369-022-06864-9 |journal=Arabian Journal for Science and Engineering |volume=47 |issue=12 |pages=16273–16287 |language=en |doi=10.1007/s13369-022-06864-9 |s2cid=248762601 |issn=2193-567X}}</ref> The Lambert {{mvar|W}} function provided an exact solution to the flow rate of fluid in both the laminar and turbulent regimes: 
<math display="block">\begin{align}
Q_\text{turb} &= \frac{Q_i}{\zeta_i} W_0\left[\zeta_i \, e^{(\zeta_i+\beta t/b)}\right]\\
Q_\text{lam} &= \frac{Q_i}{\xi_i} W_0\left[\xi_i \, e^{\left(\xi_i+\beta t/(b-\Gamma_1)\right)}\right]
\end{align}</math>
where <math>Q_i</math> is the initial flow rate and <math>t</math> is time.