14.4.3: Laterals

Typically, emitters are spaced systematically along laterals in microirrigation systems. For row crops where plants are spaced uniformly in short intervals, emitters are spaced uniformly one to a few feet apart. Many laterals are currently manufactured with the emitters within the lateral itself as for single- or dual-chamber emitters (Section 14.4.4). For widely-spaced crops, like trees, emitters may be closely spaced near the tree with no emitters positioned between tree canopies. As the trees grow, additional emitters may be added. These emitter patterns apply for both surface and subsurface systems. Microspray and bubbler type emitters are also common for widely-spaced crops.

Regardless of the emitter type, the flow within the lateral decreases from the beginning of the lateral to zero at the lateral terminus. If the laterals are fairly long, it may be advantageous to decrease the size of the lateral as the flow decreases along the lateral. In most microirrigation systems, however, the laterals are relatively short so only one small-diameter lateral is used. As in Chapter 8, where friction loss and pipe size were determined for various types of irrigation pipe, the same procedure can be used for microirrigation laterals. In Chapter 8, the Hazen-William equation was used to calculate friction loss in pipes. For small-diameter, smooth-walled pipe used in microirrigation (e.g., laterals), the Hazen-Williams equation with a C value of 150 underestimates the friction loss (Keller and Bliesner, 1990). They recommend the Darcy-Weisbach equation for microirrigation laterals as was used in Table 14.1.

Table 14.1. Friction loss for small diameter PE pipe based upon the Darcy-Weisbach equation for pipe with an e (absolute roughness) = 0.0005 in.

Flow Rate, Q (gpm)	Nominal Size (in): 0.5 Inside Pipe Diameter (in): 0.622	Nominal Size (in): 0.75 Inside Pipe Diameter (in): 0.824	Nominal Size (in): 1.0 Inside Pipe Diameter (in): 1.049	Nominal Size (in): 1.5 Inside Pipe Diameter (in): 1.61
0.5	0.13	0.03
1.0	0.56	0.15
1.5	1.13	0.30	0.09
2.0	1.86	0.49	0.15
2.5	2.76	0.72	0.23	0.03
3.0	3.81	0.99	0.31	0.04
4.0	6.38	1.64	0.51	0.07
5.0	9.55	2.43	0.76	0.10
6.0	13.3	3.37	1.05	0.14
7.0		4.45	1.38	0.18
8.0		5.67	1.76	0.22
9.0		7.02	2.17	0.28
10			2.62	0.33
15			5.47	0.68
20			9.26	1.14
25				1.71

The flow rate within the lateral decreases as the flow moves past water applicators; thus, the friction loss changes. When the lateral has uniformly spaced and uniformly discharging outlets, the friction loss can be estimated by:

P_L = F L P_f

where: P_L = pressure loss due to friction for laterals with uniformly spaced and uniformly discharging outlets,

F = multiple outlet reduction factor (Table 8.3),

L = lateral length, and

P_f = pressure loss per unit length of a conveyance pipe without outlets.

For a pipe with no outlets, F = 1.0. There is a slight difference between values of F depending on the distance down the lateral from the manifold to the first outlet. If the spacing between the outlets is s, then the outlet factor is higher when the first outlet is a distance s from the manifold compared to a distance of one-half s for about the first 20 outlets on a lateral. Typical values of F are given in Table 8.3.

There are also minor pressure losses in laterals with emitters caused by flow constrictions for in-line emitters and by barbs for emitters inserted in the tubing. Keller and Bliesner (1990) present a method for estimating losses caused by in-line emitters and emitters with barbed insertions. Their method adds to the effective length of the pipe.

Example 14.3

What is the smallest recommended pipe diameter for a polyethylene lateral that is 200 ft long and has an emitter outlet spacing of 2 ft? Each emitter discharges 2 gallons per hour.

Given: L = 200 ft s =2 ft

Emitter discharge = 2 gal/h

Assume medium length insertion barbs

Polyethylene pipe

Find: Smallest pipe diameter recommended

Solution

Number of outlets, n= 200 ft/2 ft= 100 outlets

F = 0.35 (Table 8.3)

Q = n(2 gal/hr)

Q = 100(2 gal/hr) = 3.3 gpm

For d = 0.5 in: P_f = 4.7 psi/100 ft (Interpolated from Table 14.1)

Extra lateral length due to inserted barbs = 30 ft.

For d = 0.75 in: P_f = 1.2 psi/100 ft (Interpolated from Table 14.1)

Extra length due to inserted barbs = 20 ft.

P_L = F L P_f (Eq. 14.1)

For d = 0.5 in: P_L = 0.35(230 ft)(4.7 psi/100 ft)

P_L = 3.78 psi

For d = 0.75 in: P_L = 0.35(220 ft)(1.2 psi/100 ft)

P_L = 0.92 psi

If the design pressure in the lateral is 15 psi and the lateral is level, a maximum of 3 psi pressure loss would be acceptable if the criteria is that the allowable pressure variation be less that 20% of the average pressure. Thus the 0.75-inch tubing would be necessary.

Example 14.4

If microsprayers with a discharge rate of 0.5 gpm at a spacing of 8 ft were substituted for the emitters in Example 14.3, what would be the minimum recommended pipe diameter?

Given: L = 200 ft

Microspray discharge = 0.5 gpm

Assume medium length insertion barbs

Polyethylene pipe

Find: Smallest recommended pipe diameter

Solution

n = 200 ft/8 ft= 25 microsprayers

F = 0.365 (Table 8.3)

Q = n (0.5 gal/hr) = 25(0.5 gal/hr) = 12.5 gpm

For d = 1.0 in: P_f = 4.0 psi/100 ft (Interpolated from Table 14.1)

For d = 1.5 in: P_f = 0.51 psi/100 ft (Interpolated from Table 14.1)

Extra length due to inserted barbs (both tubing sizes) = 5 ft.

P_L = F L P_f (Eq. 14.1)

For d = 1.0 in: P_L = 0.365(205 ft)(4.0 psi/100 ft)

P_L = 2.99 psi

For d = 1.5 in: P_L = 0.365(205 ft)(0.51 psi/100 ft)

P_L = 0.38 psi

Using the same criteria as Example 14.3, the pressure loss of 2.99 psi in the 1-inch lateral is acceptable but only by a small amount.