# Irrigation Equations

## Printable List

A printable Equation List can be found in Box: https://unl.box.com/s/xlvp35u8bi4z7fk6enk7abtk771edcrd

## 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

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