Closure to “Experimental Study on the Multisegment Regime of the Water Flow in Drip Emitters” by Wei Qingsong, Lu Gang, Wang Li, Zheng Jincan, Liu Jie, and Shi Yusheng

Abstract

The authors are appreciated for presenting an experimental procedure that simulates the change of emitter flow exponents with different ranges of water pressures examined. The present analysis first deals with the calculation of the emitter flow exponent, the average flow velocity, and the Reynolds numbers with regard to different phases of water pressures, then with the determination of the best choice among the pressure ranges examined for five types of drip emitters tested. For these purposes, this paper is essentially focused on three research topics: (1) change of flow exponents with different pressure segments, illustrated by the original paper’s Table 4 and Figs. 1 and 2; (2) the relationship between average flow velocities and water pressures, illustrated by the original paper’s Figs. 3 and 4; and (3) the relationship between Reynolds numbers and flow exponents, illustrated by the original paper’s Figs. 5 and 6. Although the statistical results from the present experimental research in the original paper’s “Conclusions” section are found to be satisfactory, the discusser calls attention to the following points that still require further clarification. To avoid any notation conflict, the notations or definitions are the same as those in the original paper. The paper presents Eq. (3) for the relation between the average flow velocity (v) and emitter discharge (q) in the following form: v 1⁄4 q 3.6 × 10As First, to clearly understand Eq. (3), one must know what the average flow velocity (v) means (average flow velocity inside the emitter or average flow velocity in the pipe). From the reasonable definition that it is the average flow velocity inside the emitter, it is required to derive a mathematical expression between the average flow velocity inside the emitter and the Reynolds number for the emitter flow, depending on both the pipe and the emitter geometric characteristics. Yildirim (2010) offered a simple mathematical model based on the stepwise procedure to accurately determine the pressure head profile along the lateral line. Essentially, this work extends to the previous discussion (Yildirim 2006a) on the original research of Provenzano and Pumo (2004) for a systematic comparison of different kinds of in-line/on-line emitters and various design configurations. In that paper, relative contributions of each of the energy loss components are calculated with the appropriate mathematical equation. Integrated in-line emitters cause contraction of the flow path at the upstream connection between the emitter and the lateral pipe and the expansion of the flow path immediately downstream from the emitter; thus, an additional minor friction loss must be considered (Provenzano and Pumo 2004). Integrated in-line emitters have an inner diameter, Dg (m), that is smaller than the pipe’s inner diameter,Di (m); therefore, the emitters determine higher frictional head losses because of the lower cross-section area. Emitter friction loss per unit emitter length, Je (m=m), can also be evaluated by the Darcy-Weisbach formula (Yildirim 2010):