Uncategorized

Problem 16: Water

Pump Motor – How Deep Can It Pump?

Question:
The motor on a water pump is rated at 6.6 hp. From how far down a well can water be pumped up at the rate of 220 gal/min?

Solution:

• Convert horsepower to watts:
  P = 6.6 hp × 746 = 4923.6 W
• Convert flow rate to kg/s (1 gallon ≈ 3.785 kg):
  220 gal/min × 3.785 = 832.7 kg/min ≈ 13.88 kg/s
• Use the formula: P = ṁgh
  Rearranged: h = P / (ṁg)
h = 4923.6 / (13.88 × 9.8) ≈ 36.2 m
• Convert to feet:
  h = 36.2 × 3.281 ≈ 118.8 feet

Problem 17: Fuel Efficiency and Energy Use

Question:
Suppose your car averages 30 mi/gal of gasoline.
(a) How far could you travel on 1 kWh of energy consumed?
(b) If you’re driving at 55 mi/h, at what rate are you expending energy?
(Heat of combustion of gasoline = 140 MJ/gal)

Solution:

(a) Distance on 1 kWh of Energy

• Convert kWh to MJ:
  1 kWh = 3.6 MJ
• Find energy in gallons:
  3.6 MJ / 140 MJ/gal ≈ 0.0257 gal
• Find distance:
  Distance = 30 mi/gal × 0.0257 gal ≈ 0.77 miles

(b) Energy Expenditure Rate at 55 mi/h

• Fuel used per hour:
  55 mi/h / 30 mi/gal = 1.83 gal/h
• Energy per hour:
  1.83 × 140 MJ = 256.7 MJ/h
• Convert to kW:
  256.7 MJ/h ÷ 3.6 MJ/kWh ≈ 71.3 kW