Final answer:
The total annual energy cost for irrigating 135 acres with a linear move sprinkler system with an annual net application of 69 inches, an irrigation efficiency of 77%, and energy use of 12 kWh/acre-inch is $22886.28, given an energy cost of $0.15 per kWh.
Step-by-step explanation:
To calculate the total annual energy cost for the linear move sprinkler system, we first need to determine the total volume of water required for irrigation. Using the given annual net application of 69 inches per acre and the area of 135 acres, this volume is:
- 69 inches/acre × 135 acres = 9315 inches-acres
Since 1 inch-acre is equivalent to 27,154 gallons, we can convert inches-acres to the volume in gallons as follows:
- 9315 inches-acres × 27,154 gallons/inch-acre = 253,069,710 gallons
To convert gallons to acre-inches while taking into account the irrigation efficiency (IE), we use the formula:
- Total cre-inches = (Total gallons) / (Gallons per acre-inch) ÷ IE
- Total acre-inches = 253,069,710 gallons / 27,154 gallons/inch-acre ÷ 0.77 = 12714.6 acre-inches
Next, we calculate the total energy used in kWh with an energy use of 12 kWh/ac-in as follows:
- Total kWh = 12714.6 ac-in × 12 kWh/ac-in = 152575.2 kWh
Finally, we calculate the total annual energy cost by multiplying the Total kWh by the energy cost of $0.15/kWh:
- Total annual energy cost = 152575.2 kWh × $0.15/kWh = $22886.28
This is the total annual energy cost for irrigating 135 acres of alfalfa with the given parameters.