Summary Water application pattern, WAP, is one of the most important factors that determine the instantaneous and the cumulative application rates of moving irrigation machines. The mathematical background of a procedure to predict and design the WAP of moving irrigation machines is introduced. It includes a mathematical analysis of the effect of pressure head, height and spacing between emitters on the WAP, and a nomograph that presents this analysis graphically and illustrates the design procedure of the application pattern of irrigation machines.Abbreviations
P()a
water application rate at a normalized radial distance
from the emitter [m/s]
-
ka
number of linear segments needed to represent the pattern
-
s/Ra
normalized radial distance from the emitter
-
Ra
wetted radius [m]
-
sa
radial distance from the emitter [m]
-
n
j n
i/ha
normalized water application rate at point
-
j, ha
maximum water application rate [m/s]
n
j water application rate at point
j [m/s]
-
j
=
m
j/Ra
normalized radial distance of point
j from emitter
-
m
ja
radial distance of point
-
ja
from emitter [m], CWAP
- (
x)a
Cumulative Water Application Pattern: amount of water per unit area applied at a distance
-
xa
from the travel path of the emitter [m
3/m
2]
-
xa
distance from the travel path of the emitter [m]
-
T
xa
time of application at a distance
-
xa
from the travel path of the emitter [s]
-
va
velocity of propagation of the machine [m/s]
-
k
1a
the outmost linear segment that its radial distance from the emitter
-
m
k1a
is smaller than the distance of the travel path from the emitter
-
x,
T
ja
time at which the
-
j
tha
linear segment (ring) stops influencing the point located at a distance
-
xa
from the emitter
-
1,
2,
3a
dimensionless numbers derived by dimensional analysis
-
ua
water jet velocity [m/s]
-
ga
gravity acceleration [m/s
2]
-
da
nozzle diameter [m],
v kinematic viscosity [m
2/s]
-
Ha
emitters height [m]
-
, a
regression analysis coefficients
-
Paa
Pattern fit coefficient for water application
-
F(r)a
normalized desired water application pattern [1/m]
-
f(r)a
normalized actual water application pattern [1/m]
-
La
common distance on which
-
F(r) and
f(r)a
are defined [m],
SP spacing interval between emitters [m]
-
DSa
dimensionless spacing interval between emitters
-
DSa
variation of dimensionless spacing interval
-
Paa
variation of
Pa coefficient
-
Pa
pressure head [kPa]
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