Irrigation Formulas


Water Measurement

1 gallon = 8.3 pounds
1 cubic foot = 7.48 gallons = 62.4 pounds
450 gallons per minute (gpm) = 
1 cubic foot per second (cfs) = 1 acre-inch per hour
1 acre-inch = 27,000 gallons = 1 acre flooded 1 inch deep
1 acre foot = 12 acre-inches = 43,560 cubic feet = 325,900 gallons
1 gallon = 3.785 liters = 0.003785 cubic meters
1 cubic meter = 1000 liters = 264.2 gallons 

Pressure

1 column of water 2.31 feet high exerts a pressure of 1 psi
1 pound per square inch (psi) = 2.31 feet of water
1 atmosphere = 14.7 psi = 33.95 feet of water
1 inch of mercury (hg) = 1.13 feet of water
psi X 2.31 = feet of head
Total dynamic head (TDH) in feet includes:
  pumping lift in feet
  elevation change in feet
  friction loss in feet
  system operating pressure in feet
TDH = lift + elevation change + friction + pressure 

Horsepower

Water horsepower (WHP) - power required to lift a given quantity of water against a given total dynamic head
 
WHP = Q X H
3960
Q = flow rate (gpm)
H = total dynamic head (feet)

Brake horsepower (BHP) = required power input at the pump
 
BHP = Q X H
3960 X E
Q = flow rate (gpm)
H = total dynamic head (feet)
E = pump efficiency as a decimal
(assume .75 unless known)

Water Application

Application amount (H) inches:
 
gpm
450
X time
H = QT =
A

acres

Q = flow rate in acre-in./hr = gpm/450
T = length of application (hours
A = area irrigated in time T (acres) 

Maximum application rate for outer sprinklers of a center pivot:
 
AR = Q X 122.5
R x r
Q = gpm of sprinkler system
R = length of center pivot (ft.)
r = radius of sprinkler heads at distance R
AR = application rate (inches/hr)

Furrow irrigation set size (acres): 
 
No. of rows X row width (feet) X row length (feet)
43,560

Approximate acreage covered by a pivot: 
 
Radius of pivot wetted area*,feet)2 X 3.14
43,560

*Wetted radius includes radius of end gun 

Flood irrigation set time: 
 
T= A X D
Q
T = pumping time to flood a field to depth (D), in hours
D = depth of flood (inches)**
A = area of field to be flooded (acres)
Q = flow rate acre-inches/hr = GPM

**Allow for 1" additional water for seepage and other losses on newly flooded fields.  

Maximum economical pipe flow capacities:
RULE  - Based on maximum velocity of 5 ft/sec.