14.6.1: Emitter Discharge

Flow variation among emitters is caused by differences in hydraulic, manufacturing, and field conditions. The discharge (qe) in gal/hr for most emitters can be described by:

q_e = Kh^x (14.3)

where h is the pressure head in feet at the emitter. The emitter discharge coefficient, K, contains the effects of the coefficient of discharge, emitter geometry, and the acceleration of gravity. The value of x, the emitter discharge exponent, characterizes the type and flow regime of the emitter. Orifice-type emitters are fully turbulent and have an emitter discharge exponent of 0.5. With long path emitters, x = 0.5 for those with fully turbulent flow and 1.0 for laminar flow. An x value of less than 0.5 indicates an emitter that compensates for changes in pressure.

To determine K and x for an emitter, the discharge must be measured at two different operating heads (h1 and h2). The x may be determined analytically from:

\(x=\dfrac{\log(q_{e1}/q_{e2})}{\log(h_1/h_2)} \) (14.4)

The value of x calculated from Equation 14.4 is used to calculate K from Equation 14.3. It is impossible to manufacture any two items exactly alike. Very small variations in emitter passage size, shape, and surface finish can result in variations in discharge. The amount of variation also depends on emitter design, construction materials, and precision during manufacturing. The coefficient of manufacturing variation for an emitter, v, is a measure of anticipated variations in the discharge for a sample of new emitters. The value of v should be available from the manufacturer. If not available, it can be determined from the discharge data of a sample set of at least 50 emitters operating at a constant reference pressure by:

\(v=\dfrac{\left[(q_1^2+q_2^2+...+q_n^2-nq_a^2)/(n-1) \right]^{1/2}}{q_a} \) (14.5)

where: n = number of emitters being tested,

q = discharge rate of an emitter, and

q_a = average emitter discharge rate.

For an emitter having a v of 0.06 and a qa of 1 gal/hr, 95% of the emitters will have a discharge rate between 0.88 and 1.12 gal/hr. As a general guide, manufacturing variability can be classified in accordance with Table 14.3. A lower standard is given for line-source tubing because it is difficult to keep both the variation and price low. Line-source tubing is normally used for row crops which are relatively insensitive to moderate variations in discharge among closely spaced outlets.

Example 14.6

Determine the discharge exponent and the discharge coefficient for a vortex emitter.

Given: From laboratory measurements:

q_e is 0.75 gal/hr when h = 15 ft

q_e is 1.0 gal/hr when h = 30 ft

Find: Discharge exponent (x) and the discharge coefficient (K)

Solution

\(x=\dfrac{\log(q_{e1}/q_{e2})}{\log(h_1/h_2)} \) (Eq. 14.4)

\(x=\dfrac{\log(0.75/1)}{\log(15/30)}=\dfrac{\log(0.75)}{\log(0.50)}=\dfrac{-0.125}{-0.301} \)

\(x=0.42\)

\(q_e=Kh^x\) (Eq. 14.3)

Solving for K yields \(K=\dfrac{q_e}{h^x} \)

\(K=\dfrac{1}{30^{0.42}}=\dfrac{1}{4.2} \)

Table 14.3. Classification for manufacturing variation, v, of emitters (Solomon, 1979)

Classification Rating	Drip & Spray Emitters	Line-Source Tubing
Excellent	v < 0.05	v < 0.1
Average	0.05 < v < 0.07	0.1 < v < 0.2
Marginal	0.07 < v < 0.11	-
Poor	0.11 < v < 0.15	0.2 < v < 0.3
Unacceptable	0.15 < v	0.3 < v