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Irrigation Calculations

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Water Measurement

  • 1 gallon = 8.34 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 = 27,150 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


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 (atm) = 14.7 psi = 33.90 feet of water
1 inch of mercury (hg) = 1.13 feet of water = 0.033 atm
1 psi X 2.31 = feet of head (i.e. feet of water)

Total dynamic head (TDH) is the total equivalent height that fluid is to be pumped.
Calculation of TDH involves accounting for all factors that will oppose the flow of fluid, which includes the sum of these:

  • elevation difference between fluid level and discharge level
  • friction loss caused by pipes, fittings, and so on.
  • system operating pressure

TDH [feet] = elevation change [feet] + friction [feet] + pressure [feet]

Note: Additional head losses can occur.


Water horsepower (WHP) – power required to lift a given quantity of water against a given total dynamic head.

water horsepower

Brake horsepower (BHP) – required power input at the pump.

brake horsepower

Water Application

Application amount (H) in inches:

water application

Q = fluid flow rate (acre-inches per hour) = gpm/450
T = length of application time (hours)
A = application area irrigated in time, T (acres)

Maximum application rate (AR) [inches/hour] for outer sprinklers of a center pivot:

maximum application rate
Q = flow rate of sprinkler system (gpm)
R = length of center pivot (feet)
r = radius of sprinkler heads at distance, R (feet)

Furrow irrigation set size (acres) =furrow irrigation set size

# Rows = number of rows
Wr = row width (feet)
Lr = row length (feet)

Approximate area covered by a pivot (acres) = approximate area covered by a pivot (acres)
Pr = radius of pivot wetted area* (feet)

*Wetted radius includes radius of end gun.

Flood irrigation set time (T) = Flood Irrigation set time ()

T = pumping time required to flood a field to a depth, D (hours)
D = depth of flood (inches)**
A = area of field to be flooded (acres)
Q = flow rate of water (acre-in/hr)

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

Rule of thumb maximum economical pipe flow capacities based on maximum velocity of 5 feet per second:

pipe flow capacities

Revised by Amy M. Schmidt, Assistant Extension Professor, Agricultural and Biological Engineering, from an earlier edition by James G. Thomas.

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Form 804
Extension Service of Mississippi State University, cooperating with U.S. Department of Agriculture. Published in furtherance of Acts of Congress, May 8 and June 30, 1914. JOE E. STREET, Interim Director