Question

A tidal turbine with a blade diameter of 12 meters generates 75 kW of electricity in a tidal stream with a velocity of 1.5 m/s. Assume a water density of 1000kg/m³. The efficiency of this tidal turbine is most nearly

A. 79%
B. 59%
C. 10%
D. 39%

Answer 1

The efficiency of the tidal turbine is approximately 15.68%.The closest value is given in option c .

Step-by-step explanation:

The efficiency of a tidal turbine can be calculated using the formula:

Efficiency = (Power output / Power input) x 100%

First, we need to calculate the power input to the turbine. Power (P) is given by:

P = 0.5 x ρ x A x V^3, where ρ is the water density, A is the swept area of the turbine blades, and V is the velocity of the tidal stream.

Given: blade diameter (D) = 12 meters, water density (ρ) = 1000 kg/m³, velocity (V) = 1.5 m/s.

The swept area (A) can be calculated using the formula:

A = π x (D/2)^2

Substituting the values, we get:

A = π x (12/2)^2 = 113.097 m²

Now, we can calculate the power input:

P = 0.5 x 1000 x 113.097 x (1.5)^3 = 478.0815 W

Next, we can calculate the efficiency:

Efficiency = (75 kW / 478.0815 W) x 100% ≈ 15.68%

Therefore, the efficiency of this tidal turbine is most nearly 15.68%.