ABE TUTORIALS

AGRICULTURAL AND BIOSYSTEMS ENGINEERING

PROBLEM:
A MACHINE ORIGINALLY DRIVEN BY A 1.0 HP ELECTRIC MOTOR WILL BE RUN USING A HORIZONTAL AXIS TWO-BLADED WINDMILL. IF THE WIND SPEED IS 15 KPH, WHAT SHOULD BE THE DIAMETER OF THE WINDMILL IN METERS? (EFFICIENCY = 27.5%, AIR DENSITY = 1.2 KG/M³).

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1. What should be the diameter of the windmill in meters?

a. 15 | b. 105 | c. 47.7 | d. 11.5 | e. nota

View Solution

Step 1: Conversions.
Power (P) = 1 hp = 746 Watts
Velocity (V) = 15 kph / 3.6 = 4.167 m/s

Step 2: Solve for Swept Area (A).
Formula: P = 0.5 × ρ × A × V³ × η
746 = 0.5 × 1.2 × A × (4.167)³ × 0.275
746 = 0.6 × A × 72.34 × 0.275
746 = 11.936 × A
A ≈ 103.4 m²

Step 3: Solve for Diameter (D).
D = √ (4 × A / π)
D = √ (4 × 103.4 / 3.1416) ≈ √131.6 ≈ 11.5 m

Result: d. 11.5

2. At what speed in kph will you double the output of the windmill designed above?

a. 30 | b. 19 | c. 7.5 | d. 142 | e. nota

View Solution

Concept: Power is proportional to the cube of velocity (P ∝ V³).

Step 1: Set up the ratio.
P₂ / P₁ = (V₂ / V₁)³
Since we want to double the output, P₂ = 2P₁.
2 = (V₂ / 15 kph)³

Step 2: Solve for V₂.
V₂ = 15 × ∛2
V₂ = 15 × 1.2599 ≈ 18.9 kph

Result: b. 19 (rounded)