Closure to "Simple Method for the Design of Microirrigation Paired Laterals on Sloped Fields" by Shufang Jiang and Yaohu Kang

The authors are appreciated for presenting an analytical procedure— energy-gradient line approach and the best equation form of best submain position (BSP) for designing paired laterals to meet the required water application uniformity. However, the approach taken by the authors in the paper under discussion is essentially based on the authors’ previous methods of applying the finite-element method, golden-section search method (Kang and Nishiyama 1996a), and the method of applying the lateral flow-rate equation (Kang and Nishiyama 1996b). Essentially, the approach taken in the paper under discussion incorporates three design concepts, with examples of each as indicated in the original article: (1) a design procedure to determine the BSP, in which the diameter (D), length (L), and designed emitter discharge (q) are given (Example 1); (2) a design procedure for determination of theD and the BSP when a design paired lateral with a known length (L) and designed emitter discharge (q) are given (Example 2); and (3) a design procedure for determination of the BSP and design of the length of the lateral (L) (Example 3). Although the design concepts of the simple method for paired lateral design is found to be satisfactory, the discusser calls attention to the following important points, which still need to be clarified to better understand the ability of the present technique. The notations and definitions are the same as those in the original paper. 1. Resulting from three design examples (Examples 1, 2, and 3) that focus on three design concepts, the following conclusion is presented in the section “Discussion and Summary”: “The results of these analyses revealed that the minimum pressure head of the uphill lateral was approximately equal to that of the downhill lateral.” This practical information seems very useful and enables designers to quickly evaluate the position of the minimal outflow (i.e., pressure head) and hence to determine the best solution for the design problem of the downhill sloping paired laterals that meets the required water application uniformity (qν). However, this practical evaluation could not be efficient for different types of pressure head profiles occurring along uphill and downhill sloping paired laterals. Before starting the discussion on this statement, it is useful to call attention to typical hydraulic characteristics of each type of pressure head profiles that occur along the submain line, depending on different uniform line slope situations. Essentially, there are five typical pressure head profiles (Type I, Type IIa, Type IIb, Type IIc, and Type III) under three general types (Type I, Type II, and Type III), as shown in Figs. 1(a–c) and 2(a and b) (Yildirim and Singh, unpublished report, 2010). These types can be classified (Gillespie et al. 1979; Wu et al. 1983; Barragan andWu 2005) as follows: a. Pressure profile Type I (minimum pressure at the downstream closed end of the line): As shown in Fig. 1(a), the pressure head decreases with respect to the submain length. This type occurs when the submain line is laid on zero or uphill slopes. In this condition, the dimensionless energy-gradient ratio is KS 1⁄4 S0=Sf ≤ 0. The total energy is lost by both the elevation change resulting from the uniform upslope and by friction. The maximum pressure head, Hmax , is at the inlet of the line and is equal to the operating inlet pressure, H0IðH0I 1⁄4 Hmax Þ. The minimum pressure head, Hmin , is at the closed end of the line and is equal to the downstream pressure head ðHd 1⁄4 Hmin Þ. b. Pressure profile Type II (minimum pressure along the line): As shown in Figs. 1(b and c) and 2(a), the pressure head decreases from the upstream end with respect to the pipeline length, reaches a minimum point (imin ), and then increases with respect to the submain line. The minimum pressure head is located somewhere along the line (0 < imin 1⁄4 lmin =L < 1), depending on the large interval of KS, 0 < KS 1⁄4 S0=Sf < 2.75. (1) Pressure profile Type IIa: This type of pressure profile [Fig. 1(b)] occurs under the friction and slope situation, where 0 < KS 1⁄4 S0=Sf < 1.0. In this type, the total energy gain due to uniform downslope at the end of line is less than that of the total energy drop due to friction, such that the downstream end pressure head (Hd) is still less than the operating inlet pressure (H0I). The maximum pressure head is at the inlet (Hmax 1⁄4 H0I), and the minimum pressure head is located somewhere along the line. (2) Pressure profile Type IIb (optimal pressure profile): This profile is under the friction slope situation, where the dimensionless energy-gradient ratio is KS 1⁄4 S0=Sf 1⁄4 1.0. As shown in Fig. 1(c), this profile is similar to that of Type IIa, but the profile is such that the downstream closed-end pressure head is equal to the operating inlet pressure head (H0I 1⁄4 Hd). The maximum pressure is at both the inlet (Hmax 1⁄4 H0I) and the closed end of line (Hmax 1⁄4 Hd). The minimum pressure is located somewhere near the middle section of the line. Among all types of pressure profiles, the Type II profile is considered to be the optimal (or ideal) pressure profile because it can produce the minimum pressure head difference for a given pipe length, as discussed previously (Wu and Barragan 2000; Wu et al. 1983). This profile occurs when the total energy loss due to friction is just balanced by the total energy gain due to uniform downslope (Profile IIb). (3) Pressure profile Type IIc: This profile is under the friction and slope situation, where the dimensionless energy-gradient ratio is 1.0 < KS < 2.75 for the Darcy-Weisbach (DW) or 1.0 < KS < 2.852 for the Hazen-Williams (HW) equation. This occurs when the line slope is even steeper, so the pressure at the