Wind Energy Formula

Wind Energy Formula

Wind Energy Formula is the process of producing power utilising the wind. Wind turbines use the kinetic energy of the wind to generate mechanical power. 

A renewable energy source that harnesses the full strength of the wind is Wind Energy Formula. Through the usage of wind turbines, kinetic energy is translated into mechanical power, which is subsequently converted into electricity, which is used as a source of energy.

The process of converting wind energy into mechanical or electrical energy, which then can be used, is known as Wind Energy Formula. Commercial wind turbines use rotational energy to power generators, which in turn produces electricity. They consist of a rotor or blade and a nacelle, an enclosure that houses the drive system atop a tall tower. The largest turbines have rotor diameters that can surpass 162 metres (531 feet) and are installed on towers that may reach 240 metres, producing 4.8 to 9.5 megawatts of electricity (787 feet).

Wind Energy Formula

The most well-established and developed renewable energy source is Wind Energy Formula. Utilising the kinetic energy produced by the impact of air currents, it generates electricity. It reduces greenhouse gas emissions and safeguards the environment because it is a clean and renewable energy source.

The notes and solutions for the Wind Energy Formula are also made available in Hindi for students of various other boards. Comprehension of the Wind Energy Formula is made easier with the help of these notes, owing to Extramarks’ experts. The notes and solutions based on the Wind Energy Formula mimic the organisation of the NCERT books in accordance with the CBSE syllabus.

Derivation of Wind Energy Formula

Both the terms “Wind Energy Formula” and “wind power” describe the process of using the wind to generate electricity or mechanical power. This mechanical Wind Energy Formula may be used for particular tasks (such as pumping water or grinding grain) or it may be transformed into energy via a generator.

The work done W to move an object from its initial position is equal to the kinetic energy of an object with mass m and velocity v under constant acceleration. 

Rest at a distance s under a force F, i.e. 

E = W = Fs 

Newton’s Law says that we have: 

F = ma 

Hence, 

E = mas … (1) (1) 

The third equation of motion is used to: 

v2 = u2 + 2as 

we get: 

a = (v2 – u2)/2s 

Since the object’s starting velocity is 0, i.e. 

u = 0 results in: 

a = v2/2s

When it is substituted in equation (1), we learn that the 

The formula for a mass’s kinetic energy is 

E = 1/2mv2………(2) (2) 

The speed of the wind determines its power. 

a shift of energy 

P equals dE/dt = 1/2 v2dm/dt (3) 

As the mass flow rate is determined by: 

dm/dt equals Adx/dt 

Hence the formula for the rate of change of distance is: 

dx/dt = v 

we get: 

Av = dm/dt 

Consequently, based on equation (3), the power can be 

specified as: 

P = 1/2ρAv3

The notes and solutions based on the Wind Energy Formula have been curated by Extramarks’ experts after great consideration and research on the past years’ papers. The framework of the Wind Energy Formula notes designed by Extramarks experts is very easy to understand and comprehend. The Wind Energy Formula notes are extremely internet-compatible and students can also download them for offline study and reference.

Sample Problems

A form of energy is the Wind Energy Formula. The technique by which wind is used to generate power is known as wind energy. The kinetic energy in the wind is converted to mechanical power by wind turbines. 

A renewable energy source that controls the overall power of the wind is Wind Energy Formula. The wind turbines transform kinetic energy into mechanical power, and from there into electricity that serves as a valuable source.

• Example 1 

If the wind speed is 20 m/s and the blade length is 50 m, calculate the power of the wind. 

Solution: 

Given: 

wind velocity (v) = 20 m/s, 

Blade length, 50 metres, 

The density of air is 1.23 kg/m. 

The area formula provides the area. 

A = π × 2500 

= 7850 m 

The Wind Energy Formula is as follows: 

wind energy equation 

P = 38622 W is the wind power calculation.

• Example 2 

A wind turbine moves at a speed of 10 m/s and has 20 m-long blades. Identify the wind’s power. 

Solution: 

Given: 

wind velocity =10 m/s, 

Blade length, 20 metres, 

The density of air is 1.23 kg/m3. 

formula for area 

= π × 400 

= 1256 

This is how the equation has been rendered. 

The Wind Energy Formula is as follows: 

wind energy equation 

= 0.5 × 1.23 × 1256 × 1000 

P = 772440 W.