Final answer:
The efficiency of the tidal turbine is calculated by dividing the actual power output by the theoretical power available in the tidal stream. However, using the given values leads to an efficiency calculation of approximately 19.63%, which does not match any of the provided answer options.
Step-by-step explanation:
To determine the efficiency of a tidal turbine, we need to calculate the actual power output and compare it to the theoretical maximum power available in the tidal stream. The power available in a flow of water can be calculated using the kinetic energy formula: P = 0.5 × ρ × A × v^3, where ρ is the water density, A is the cross-sectional area of the turbine blades, and v is the velocity of the tidal stream.
First, we find the cross-sectional area (A) of the turbine blades, which is a circle area given by π × r^2. With a 12 m diameter, the radius (r) is 6 m, so A = π × (6 m)^2 ≈ 113.097 m^2. Using the given water density of 1000 kg/m^3 and the velocity of the tidal stream (1.5 m/s), the available power (P) is:
P = 0.5 × 1000 kg/m^3 × 113.097 m^2 × (1.5 m/s)^3 ≈ 382 kW.
To find the efficiency, we divide the actual power output (75 kW) by the theoretical power (382 kW) and multiply by 100 to get a percentage:
Efficiency = (75 kW / 382 kW) × 100 ≈ 19.63%.
However, none of the provided answer options (A) 39%, (B) 10%, (C) 59%, (D) 79% accurately reflect this calculated efficiency. It is possible there was a miscalculation or a misunderstanding in the question. Therefore, the correct efficiency using the given parameters would not correspond to any of the options provided.