ABE TUTORIALS

AGRICULTURAL AND BIOSYSTEMS ENGINEERING

PROBLEM:
ESTIMATE THE ACTUAL POWER OUTPUT IN KW FOR A RESERVOIR LOCATED 30 METERS ABOVE THE POWER GENERATING STATION. THE PIPE USED TO GENERATE POWER HAS A DIAMETER OF 2 METERS AND THE VELOCITY OF WATER FLOWING THROUGH THE DUCT IS 8 M/SEC. THE SYSTEM EFFICIENCY IS 70%.

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a. 5174 | b. 7391 | c. 7.4 | d. 5.2 | e. nota

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Step 1: Calculate the Flow Rate (Q).
Area (A) = π × (D² / 4) = 3.1416 × (2² / 4) = 3.1416 m²
Discharge (Q) = Area × Velocity = 3.1416 m² × 8 m/sec = 25.13 m³/sec

Step 2: Calculate Power Output.
Formula: P = γ × Q × H × η
Where:
γ (Specific weight of water) = 9.81 kN/m³
Q = 25.13 m³/sec
H (Head) = 30 m
η (Efficiency) = 0.70

Step 3: Solve.
P = 9.81 × 25.13 × 30 × 0.70
P = 5177.6 kW ≈ 5174 kW

Result: a. 5174