To solve this problem, we need to use the principle of conservation of energy. The kinetic energy of the wind before it hits the turbine is partially converted into mechanical energy by the turbine, with the rest remaining as kinetic energy in the wind as it leaves the turbine.

The kinetic energy of the wind is given by the equation KE = 0.5 * m * v^2, where m is the mass of the wind and v is its velocity. Since the mass of the wind doesn't change as it passes through the turbine, we can say that the initial kinetic energy of the wind (0.5 * m * (3.4 m/s)^2) is equal to the sum of the energy extracted by the turbine (27% of the initial kinetic energy) and the final kinetic energy of the wind (0.5 * m * v_final^2), where v_final is the velocity of the wind after it passes through the turbine.

Setting up the equation, we get:

0.5 * m * (3.4 m/s)^2 = 0.27 * (0.5 * m * (3.4 m/s)^2) + 0.5 * m * v_final^2

Solving for v_final, we get:

v_final = sqrt[(0.5 * (3.4 m/s)^2 - 0.27 * (0.5 * (3.4 m/s)^2)) / 0.5]

v_final = sqrt[(0.73 * (0.5 * (3.4 m/s)^2)) / 0.5]

v_final = sqrt[0.73 * (3.4 m/s)^2]

v_final = 3.4 m/s * sqrt[0.73]

v_final = 2.8 m/s

So, the wind velocity on the downstream side of the turbine is approximately 2.8 m/s.

Question

To solve this problem, we need to use the principle of conservation of energy. The kinetic energy of the wind before it hits the turbine is partially converted into mechanical energy by the turbine, with the rest remaining as kinetic energy in the wind as it leaves the turbine.

The kinetic energy of the wind is given by the equation KE = 0.5 * m * v^2, where m is the mass of the wind and v is its velocity. Since the mass of the wind doesn't change as it passes through the turbine, we can say that the initial kinetic energy of the wind (0.5 * m * (3.4 m/s)^2) is equal to the sum of the energy extracted by the turbine (27% of the initial kinetic energy) and the final kinetic energy of the wind (0.5 * m * v_final^2), where v_final is the velocity of the wind after it passes through the turbine.

Setting up the equation, we get:

0.5 * m * (3.4 m/s)^2 = 0.27 * (0.5 * m * (3.4 m/s)^2) + 0.5 * m * v_final^2

Solving for v_final, we get:

v_final = sqrt[(0.5 * (3.4 m/s)^2 - 0.27 * (0.5 * (3.4 m/s)^2)) / 0.5]

v_final = sqrt[(0.73 * (0.5 * (3.4 m/s)^2)) / 0.5]

v_final = sqrt[0.73 * (3.4 m/s)^2]

v_final = 3.4 m/s * sqrt[0.73]

v_final = 2.8 m/s

So, the wind velocity on the downstream side of the turbine is approximately 2.8 m/s.

Knowee AI · Accepted Answer

To solve this problem, we need to use the principle of conservation of energy. The kinetic energy of the wind before it hits the turbine is partially converted into mechanical energy by the turbine, with the rest remaining as kinetic energy in the wind as it leaves the turbine.

The kinetic energy of the wind is given by the equation KE = 0.5 * m * v^2, where m is the mass of the wind and v is its velocity. Since the mass of the wind doesn't change as it passes through the turbine, we can say that the initial kinetic energy of the wind (0.5 * m * (3.4 m/s)^2) is equal to the sum of the energy extracted by the turbine (27% of the initial kinetic energy) and the final kinetic energy of the wind (0.5 * m * v_final^2), where v_final is the velocity of the wind after it passes through the turbine.

Setting up the equation, we get:

0.5 * m * (3.4 m/s)^2 = 0.27 * (0.5 * m * (3.4 m/s)^2) + 0.5 * m * v_final^2

Solving for v_final, we get:

v_final = sqrt[(0.5 * (3.4 m/s)^2 - 0.27 * (0.5 * (3.4 m/s)^2)) / 0.5]

v_final = sqrt[(0.73 * (0.5 * (3.4 m/s)^2)) / 0.5]

v_final = sqrt[0.73 * (3.4 m/s)^2]

v_final = 3.4 m/s * sqrt[0.73]

v_final = 2.8 m/s

So, the wind velocity on the downstream side of the turbine is approximately 2.8 m/s.

The wind velocity on the upstream side of a wind turbine is 3.4 m/s. If the turbine extracts 27% of the available kinetic energy, what is the wind velocity on the downstream side of the turbine in m/s? Please include one decimal place in your answer.

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