14.6.2: Discharge Versus Pressure

The relationship between pressure head (h) and discharge (q_e) is an important characteristic of emitters (Equation 14.3). Figure 14.11 shows this relationship for various types of emitters. The discharge exponent, x, measures the flatness of the relationship between pressure and discharge. It shows clearly the desirability of an emitter that has a low value of x. Emitters that compensate for changes in pressure have the lowest values of x. Compensating emitters have some physical part that responds to pressure to keep discharge constant. Although having the advantage of compensating for changes in pressure, these emitters are prone to material fatigue and temperature change.

Figure 14.11. Discharge variation resulting from pressure changes for emitters having different discharge exponents. (Image courtesy of Keller and Bliesner, 1990, with permission from Blackburn Press.)

On hilly terrain the design of a highly uniform system is constrained by the sensitivity of the flow from emitters because of pressure differences in the laterals from changes in elevation. Pressure compensating emitters and pressure regulated flow in short laterals provide potential solutions. Even on level fields, the lateral length must be kept reasonably short to avoid excessive differences in pressure along the lateral.

For laminar flow emitters with a value of x near 1.0 the percent variation in pressure head results in about the same variation in discharge. Thus, variations in pressure throughout the system with laminar flow emitters should be held within about ±5% of the desired pressure to maintain water applications within acceptable limits.

For turbulent flow emitters, the change in discharge varies with the square root of pressure head; x is near 0.5. Consequently, to double the flow, the pressure must be increased four times. Thus, the pressure head for systems using turbulent flow emitters can vary up to ± 10% of the desired pressure without unacceptable variations in water applications.

Flow compensating emitters provide some degree of flow regulation as pressure changes. When x is between 0.2 and 0.35, some regulation is possible and there is still some flexibility for adjusting the discharge rate. Compensating emitters are valuable on hilly sites where it is impractical to design for uniform pressure along the laterals. Characteristics of various types of emitters are given in Table 14.4. Refer to Figures 14.8 and 14.9 for examples of the types of emitters described in Table 14.4. The exponent, x, for Equation 14.3 is given in Table 14.4 along with typical values for the manufacturers’ coefficient of variation. The remaining column in Table 14.4 indicates the flushing potential built into each type of emitter.

Table 14.4. Characteristics of various types of emitters (Keller and Bilesner, 1990).

Emitter Type	Discharge Exponent, x	Coefficient of Manufacturing Variation, v	Flushing Ability
Orifice
Vortex/orifice	0.42	0.07	None
Multiple flexible orifices	0.7	0.05	Continuous
Ball & slotted seat	0.50	0.27	Automatic
Compensating ball & slotted seat	0.25	0.09	Automatic
Capped orifice sprayers	0.56	0.05	None
Long-Path
Small tube	0.70	0.05	None
Spiral path	0.75	0.06	Manual
Compensating	0.40	0.05	None
Compensating	0.20	0.06	Automatic
Tortuous	0.65	0.02	None
Short-Path
Groove & flap	0.33	0.02	Automatic
Slot & disc	0.11	0.10	Automatic
Line-Source
Porous pipe	1.0	0.40	None
Twin chamber	0.61	0.17	None

Example \(14.7\)

The vortex emitter described in Example 14.6 is being considered for a microirrigation system to be installed in a field 1,000 feet long and sloping 1% up from south to north. The header for lateral lines is placed along the south edge of the field and the operating pressure in the header line is 15 psi. Assuming no pressure loss in the header or laterals due to friction loss, what is the difference in discharge for emitters near the header and at the north edge of the field?

Given: K = 0.24 x = 0.42
Pressure at south edge of field = 15 psi
Pressure loss at north edge of field due to elevation difference = 1,000 ft × 1% slope =1,000 ft × 0.01 = 10 ft

Find: Difference in discharge between south and north end of field

Solution

h_s = h at south end of field
h_s =15 psi (2.3 ft/psi) = 34.5 ft
q_es = Kh^x = 0.24(34.5)^0.42 = 1.06 gal/hr

h_n = h_p + h_e + h_f + h_s
where h_p = pressure head,
h_e = change in head due to elevation, and
h_f = loss in head due to friction loss
h_e is negative because the elevation is increasing in this example
h_f is assumed to be zero in this example
h_n = 34.5 ft – 10 ft – 0
h_n = 24.5 ft
q_en = Kh^x = 0.24(24.5)^0.42 = 0.92 gal/hr
Δq = q_es – q_en = 1.06 gal/hr – 0.92 gal/hr
Δq = 0.14 gal/hr

Example \(14.8\)

If a compensating, long path emitter without flushing ability is used in Example 14.5 rather than vortex emitters, what will the difference in discharge be between the north and south edges of the field?

Solution

Δq = 0, since the emitter chosen is pressure compensating.