An Ocean Thermal Energy Conversion (OTEC) power plant built in Hawaii in 1987 was de-
signed to operate between the temperature limits of 86 �F at the ocean surface and 41 �F at a
depth of 2100 ft. About 13 300 gallons per minute (gpm) of cold seawater was to be pumped
from deep ocean through a 40-in-diameter pipe to serve as the cooling medium or heat sink.
If the cooling water experiences a temperature rise of 6 �F and the thermal e�ciency is 2.5%,
determine the amount of power generated. The density of seawater is approximately 64 lbm/ft3.
To determine the amount of power generated by the Ocean Thermal Energy Conversion (OTEC) power plant, we need to calculate the heat extracted from the temperature difference and multiply it by the efficiency of the plant.
Step 1: Calculate the heat extracted
The heat extracted can be calculated using the formula:
Q = (m * Cp * ΔT)
Where:
Q = Heat extracted (in BTU)
m = Mass flow rate of the cooling water (in lbm/min)
Cp = Specific heat capacity of seawater (in BTU/lbm·°F)
ΔT = Temperature rise of the cooling water (in °F)
First, convert the mass flow rate of the cooling water from gallons per minute (gpm) to lbm/min:
m = (13,300 gpm) * (64 lbm/ft^3) * (1 ft^3 / 7.48 gal) * (1 min / 60 s)
m ≈ 1,422 lbm/min
Next, calculate the heat extracted:
Q = (1,422 lbm/min) * (1 BTU/lbm·°F) * (6 °F)
Q ≈ 8,532 BTU/min
Step 2: Calculate the power generated
The power generated can be calculated using the formula:
Power = (Q * efficiency) / (BTU/min to hp)
Where:
Power = Power generated (in horsepower)
Q = Heat extracted (in BTU)
efficiency = Thermal efficiency of the power plant
BTU/min to hp = Conversion factor from BTU/min to horsepower (1 hp = 2545 BTU/min)
Substitute the values into the formula:
Power = (8,532 BTU/min) * (2.5% / 100) / (2545 BTU/min/hp)
Power ≈ 0.084 hp
Therefore, the amount of power generated by the OTEC power plant is approximately 0.084 horsepower.