Irrigation System Calculator

The FAO-56 evapotranspiration framework

The standard tool for calculating crop water requirements is the FAO Irrigation and Drainage Paper No. 56 (Allen et al., 1998), used globally by agriculture departments, irrigation district planners, and consultants. It’s based on a two-step process:

Step 1: Calculate reference evapotranspiration (ETo) — what a hypothetical short grass surface would lose to evaporation and transpiration under your weather conditions. Computed from temperature, humidity, wind, and solar radiation via the Penman-Monteith equation.

Step 2: Apply a crop coefficient (Kc) to get actual crop water need (ETc):

ETc = ETo × Kc

Where Kc depends on the specific crop and its growth stage.

Reference ETo by climate

Typical daily ETo values (in mm/day):

For exact local values, weather stations (CIMIS, AgriMet, NOAA) report ETo daily. Most state agriculture extensions publish nearby station data.

Crop coefficient (Kc) — varies by crop and stage

Crops have different water demand than the reference grass surface. Kc < 1.0 means less than reference (initial stages, after harvest); Kc > 1.0 means more (mid-season for many crops).

A corn field at mid-season in Iowa (ETo = 5 mm/day, Kc = 1.20): ETc = 6 mm/day = roughly 0.24 inches per day = 1.5 acre-inches per week (60 mm).

Gross vs net water requirement

Not all applied water reaches the crop:

Gross requirement = Net requirement (ETc) ÷ Application efficiency

A corn field needing 6 mm/day net via flood irrigation (efficiency 55%) needs ~11 mm/day applied. The same field via drip (90% efficient) needs only ~6.7 mm applied — saving 40% of water for the same crop benefit.

Drip irrigation — the math

Drip irrigation delivers water directly to root zones via emitters. Common emitter rates:

Application rate = Total emitter flow ÷ Area For a 100 m² area with 400 emitters at 4 L/h each: 1,600 L/h ÷ 100 m² = 16 mm/h application rate

If the crop needs 6 mm/day (gross), runtime = 6 ÷ 16 × 60 = 22.5 minutes/day.

Drip is the most water-efficient system because:

• Minimal evaporation (water released into soil, not air)
• No wind drift
• No wetting of leaf surfaces (also reduces disease)
• Targeted to root zones, not bare soil between plants
• Allows fertigation (fertilizer through the drip line)

Sprinkler irrigation considerations

Sprinkler systems are simpler to install but lose water to:

• Wind drift (can be 5-30% on windy days)
• Evaporation in flight (5-15% in hot/dry conditions)
• Surface evaporation from wetted soil and leaves
• Runoff if application rate exceeds soil intake rate

Best practices:

• Irrigate at night or early morning when wind is calm
• Use larger droplet sizes (lower pressure, more efficient)
• Schedule by ETc, not calendar
• Check distribution uniformity (DU) — should be > 80%

Pipe sizing — friction loss

The Hazen-Williams equation predicts pressure loss in pipes:

hf = 10.67 × L × Q^1.852 ÷ (C^1.852 × d^4.87)

Where:

• hf = head loss (m)
• L = pipe length (m)
• Q = flow rate (m³/s)
• C = Hazen-Williams roughness coefficient (varies by pipe material)
• d = pipe internal diameter (m)

Typical C values: PVC = 150, polyethylene = 140, steel = 120, concrete = 110.

For irrigation design, target pipe velocity < 1.5 m/s and friction loss < 15% of static pressure.

Practical pipe sizing chart (PVC main lines)

Under-sized pipe creates high friction loss, reduces pressure at emitters, and creates uneven distribution. Better to oversize by one nominal size than undersize.

Center pivot — the workhorse of large-scale irrigation

Center pivot irrigation covers most large irrigated acreage in the US Midwest and Great Plains:

• Standard pivot: 400-1,400 ft radius, covers 80-280 acres
• Modern LEPA pivots: drop tubes with drag-pad applicators near soil surface
• Cost: $80,000-$200,000 for new installation per pivot
• Operating cost: roughly $50-$150/acre/year for electricity + water + maintenance
• Lifespan: 25-40 years

A 130-acre pivot applying 1 inch of water:

• Needs to deliver 130 × 27,154 = 3.5 million gallons
• At 600 gpm, runs for 100 hours (4 days)
• At 1,000 gpm, runs for 60 hours (2.5 days)

This is why pivot operators run continuously during peak summer.

Subsurface drip — the future of irrigation

Subsurface drip irrigation (SDI) buries dripline 6-12 inches below soil surface. Benefits:

• 95%+ efficiency (no surface evaporation)
• No interference with field operations
• Reduced weed growth (surface stays dry)
• Excellent fertilizer placement
• 15-20 year lifespan

Drawbacks:

• Higher initial cost ($1,500-$3,000/acre)
• Hard to inspect/repair
• Requires excellent filtration

Adoption is growing in California vegetable production, Texas cotton, and high-value crops globally.

Water source — wells vs surface water

Many farms use multiple sources for resilience.

The water rights complication

Irrigation water isn’t always freely available. Different regions have very different rights systems:

• Riparian rights (eastern US, most of Europe): adjacent landowners can use water from streams “reasonably”
• Prior appropriation (western US, “first in time, first in right”): older water rights take precedence in droughts
• Mexican-American shares: cooperative water management
• State permits: required in most states for any significant pumping

A new farmer in California or Arizona may face years of waiting and tens of thousands of dollars in legal fees to secure water rights for a new well.

Bottom line

Irrigation requirements derive from ETo × Kc. Common ranges: 3-7 mm/day for major row crops in moderate climates. Apply with efficient systems (drip 85-95%, sprinkler 70-85%, surface 40-65%). Size pipes to keep velocity under 1.5 m/s. Schedule by ETc, not calendar. Modern systems (drip, LEPA pivot, SDI) reduce water use 20-50% versus older flood/sprinkler methods — increasingly necessary as water becomes scarce and expensive.