Irrigation Equations
Printable List
Chapter 2
Equation 2.1
Bulk density BV = __Mass of soil = 1.3 g = 1.3 g/cm3
Volume of soil unit 1.0 cm3
Equation 2.2
Particle density = Mass of soil = 1.3 g = 2.6 g/cm3
Volume of solids 0.5 cm3
Chapter 5
Equation 5.1 lb/acre = 0.23 x Cw x Di
where,
Cw = concentration of nitrate-nitrogen in the irrigation water (ppm)
Di = depth of irrigation water applied (inches).
Equation 5.2 lb/acre = 0.23 x Cs x Bd x Dl
where,
Cs = concentration of nitrate-nitrogen on a soil basis (ppm),
Bd = bulk density of the soil (known or estimated),
Dl = depth increment from which sample was taken (inches).
Chapter 8
Equation 8.1 Ea = [Depth of water stored in the rootzone (ds) x 100 Depth of water pumped (dp) ]
where:
Ea = Average water application efficiency, %
Depth of water stored in the rootzone (ds) = Average depth of water stored in the rootzone, inches
Depth of water pumped (dp) = Average depth of water delivered from source, inches
Equation 8.2 ds = [“After” reading – “Before” reading]
where:
ds = Depth of water stored in the rootzone
Chapter 10
Equation 10.1 NLT = (WB - MB)
ETC
where:
WB = Current water balance
MB = Minimum allowable balance
ETC = Forecasted crop water use
Equation 10.2 NST = ra + dep – (TAWC – WB)
ETC
where:
ra = rainfall allowance
dep = planned effective irrigation depth
TAWC = total available water capacity
WB = water balance
ETC = forecast crop water use
Chapter 11
Equation 11.1
Average stream size (gpm) = Pump discharge (gpm)
Number of furrows flowing
Equation 11.2
Gross depth (in.) = 1155 x ave. stream size (gpm) x Time water applied (hr)
Furrow length (ft) x Watered furrow spacing (inches)
Equation 11.3
Cutoff ratio (CR) = Average advance time to end of furrow
Set time
Equation 11.4
Max. non-erosive stream size (gpm) < 12.5
Average field slope (%)
Chapter 12
Equation 12.1 A = [ π x Rs2 x Pr ] / [ 43560 ]
where,
A = irrigated area, acres
π = constant, Pi = 3.1416
Rs = wetted length of the system, feet
Pr = portion of a full circle, decimal
43560 = conversion constant, square feet per acre
Equation 12.2 Qpump = [ 18.9 x ETp x Area ] / [ Ea x Tirr ]
where,
Qpump = gross pumping rate, gallons per minute
K = 18.9 = conversion constant
ETp = peak water use rate, inches per day
Area = irrigated area, acres
Ea = application efficiency, decimal
Tirr = portion of day the system is operating, decimal
Equation 12.3 Ipeak = [ 122.5 x Qpump ] / [ Rsystem x Rsprinkler ]
where,
Ipeak = peak water application rate, inches/hour
122.5 = conversion constant
Qpump = system flow rate, gallons per minute
Rsystem = wetted length of the center pivot, feet
Rsprinkler = wetted radius of sprinklers at the end of the system, feet
Equation 12.4 Stravel = Dtraveled / Ttravel
where,
Stravel = system speed of travel, feet/min
Dtraveled = distance traveled, feet
Ttravel = travel time, minutes
Equation 12.5 Trevolution = [ 2 x π x Lend ] ¸ [ Stravel x 60 ]
where,
Trevolution = system revolution time, hours
π = constant, Pi = 3.14
Lend = distance from pivot point to the end tower, feet
Stravel = system speed of travel, feet/minute
Equation 12.6 Idepth = [ Qpump x Trevolution ] / [ 450 x Area ]
where,
Idepth = depth applied per revolution, inches
Qpump = irrigation system flow rate, gallons per minute
Trevolution = revolution time, hours
Area = irrigated area, acres
450 = conversion constant
Chapter 13
Equation 13.1 whp = gpm x 8.33 lb/gal x head (ft) / 33,000 ft-lb/min
or, since 33,000/8.33 = 3960, the equation is usually shortened to:
whp = gpm x head (ft) / 3960
Equation 13.2 head (ft) = psi x 2.31 ft/psi
This can be alternately expressed as:
Equation 13.3 psi = head (ft) / 2.31 ft/psi
Equation 13.4 Total head (ft) = Lift (ft) + Elevation (ft) + (psi x 2.31 ft/psi)
Equation 13.5 Performance. Rating = Actual Performance / NPPPC x 100%
Equation 13.6 Fuel Use /hr = whp-h