Irrigation Equations

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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)

                                   D=   depth of irrigation water applied (inches).

Equation 5.2            lb/acre = 0.23 x Cx Bd x Dl

                      where,

                                  C=    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