A raw water intake pump operates 24 hours per day, pumping 2,000 GPM against a total head of 220 feet. The overall wire-to-water efficiency is 72.0% (0.72). If electric utility power costs $0.12 per kWh, what is the daily electrical pumping cost?

Formula Used: Daily Cost = [Flow (GPM) × Head (ft) × 0.746 kW/HP × 24 hrs × $/kWh] ÷ [3,960 × Wire-to-Water Eff]

Step-by-Step Mathematical Derivation:

1. Calculate theoretical WHP = (2,000 × 220) ÷ 3,960 = 111.11 WHP.
2. Calculate electrical input MHP = 111.11 ÷ 0.72 = 154.32 HP.
3. Convert horsepower to electric power: 154.32 HP × 0.746 kW/HP = 115.12 kW.
4. Calculate 24-hour kilowatt-hours: 115.12 kW × 24 hrs = 2,762.94 kWh/day.
5. Multiply by electricity rate: 2,762.94 kWh × $0.12/kWh = $331.55/day.

⚠️ Common Exam Trap: Always multiply HP by 0.746 to convert to Kilowatts (kW). 1 HP = 746 Watts = 0.746 kW.