Friction coefficient of an intact free liquid jet moving in air

Here, we propose a novel method of determining the friction coefficient of intact free liquid jets moving in quiescent air. The middle-size jets of this kind are relevant for such applications as decorative fountains, fiber-forming, fire suppression, agriculture, and forensics. The present method is based on measurements of trajectories created using a straightforward experimental apparatus emulating such jets at a variety of initial inclination angles. Then, the trajectories are described theoretically, accounting for the longitudinal traction imposed on such jets by the surrounding air. The comparison of the experimental data with the theoretical predictions shows that the results can be perfectly superimposed with the friction coefficient \({C_{{\text{fd}}}}=5R{e_d}^{{ - 1/2 \pm 0.05}}\), in the \(621 \leqslant R{e_d} \leqslant 1289\) range, with Red being the Reynolds number based on the local cross-sectional diameter of the jet. The results also show that the farthest distance such jets can reach corresponds to the initial inclination angle \(\alpha =35^\circ\) which is in agreement with already published data.