# Energy available to a wind turbine

• pgunderson
In summary, the conversation discusses the application of Bernoulli's conservation of energy equation to wind turbines. The main energies involved are kinetic, pressure, and potential. The conversation also touches on the effects of turbulence and the importance of considering pressure differentials in the application of the equation. The goal is to find the mechanical energy and power generation potential of the wind, as well as the actual power output with 30% efficiency. The approach of using Bernoulli's equation is confirmed to be correct and the importance of considering pressure changes near the blade is emphasized.

#### pgunderson

HI folks, new to this forum.

I'm in a Fluid Dynamics class and need to make a presentation on Bernoulli's conservation of energy equation as it applies to wind turbines.

I think I understand the different energies involved here: kinetic(v^2/2), pressure(P/rho), potential(zg)... I want to make sure I am applying the equation right and comprehending the concepts.

It seems to me that in an airstream we've basically only got KE operating for us. The velocity entering the blade assembly is fast, energy is extracted by the turbine, and the air leaving the assembly is then slower.

But someone pointed out to me that if you think about the area really close to the plane of the swept area, there is also a pressure differential.

Is this small enough to be ignored? It seems the problem I'm to use as an example doesn't consider this possibility. The only givens are: steady windspeed of 12 m/s, blade assembly of 50m diameter, and use air density of 1.25kg/m^3.

I'm to find the mech. energy of air/unit mass (ok) and the power generation potential (ok) and the actual power assuming 30% efficiency (ok).

Is my assumption correct that the only available energy is the KE of the wind's velocity? What happens with turbulence? If there's a pressure differential at some point, can that be causing the airstream to take on a shape that is not similar to a tube with cross-sectional area equivalent to the swept area of the blades? What rules can I apply to ensure that this really is a conservation problem?

Any conceptual help will be very much appreciated!

patti

Yes, your benoulis approach is correct.
there is a pressure rise near the blade (wheel).
the Z diff=0
upsteram air V > down stream air V
Work done/mass flow rate = KE1-KE2
Power = massflow rate x (V1^2 -V2^2)/2g
= 1/2g * rho * Area * Vtur *(V1^2-V2^2)
Pmax (possible) = 8/27g *rho * Area * V1^3 (optimised one after differentiation)

Hi Patti, welcome to the forum! It's great that you're exploring the application of Bernoulli's equation to wind turbines in your Fluid Dynamics class.

First of all, your understanding of the different energies involved in wind turbines is correct. The kinetic energy of the wind is what drives the blades and is ultimately converted into mechanical energy and then electricity. The pressure differential, as you mentioned, is also a factor in the operation of wind turbines.

To answer your question, the pressure differential near the plane of the swept area is not negligible and cannot be ignored. This is because the air near the blades experiences a decrease in pressure as it passes through the blades, which helps to drive the rotation of the blades.

In terms of turbulence, it is important to consider the effects of turbulence on the wind flow and the blades. Turbulence can cause variations in wind speed and direction, which can affect the performance of the wind turbine. However, most modern wind turbines are designed to handle turbulent winds and still operate efficiently.

To ensure that this is a conservation problem, you can apply the principles of conservation of mass, energy, and momentum. This means that the total mass, energy, and momentum of the air entering the blades must be equal to the total mass, energy, and momentum of the air leaving the blades.

I hope this helps to clarify your understanding of the energy available to a wind turbine. Good luck with your presentation!

## 1. How is the energy available to a wind turbine calculated?

The energy available to a wind turbine is calculated by multiplying the power or capacity of the turbine (in megawatts) by the number of hours it operates in a year. This will give you the total amount of energy in megawatt-hours that the turbine can produce annually.

## 2. What factors affect the energy available to a wind turbine?

Several factors can affect the energy available to a wind turbine, including the wind speed and direction, the size and design of the turbine, the altitude and location of the turbine, and the efficiency of the turbine's components.

## 3. How does wind speed impact the energy available to a wind turbine?

Wind speed plays a crucial role in determining the energy available to a wind turbine. The higher the wind speed, the more energy the turbine can produce. This is because wind turbines rely on the kinetic energy of the wind to turn their blades and generate electricity.

## 4. Can a wind turbine produce more energy than it uses?

Yes, it is possible for a wind turbine to produce more energy than it uses. This is known as a net positive energy output. However, this is dependent on various factors such as wind conditions, turbine efficiency, and maintenance.

## 5. How does the location of a wind turbine affect its energy production?

The location of a wind turbine has a significant impact on its energy production. Turbines placed in areas with consistent and strong winds will produce more energy than those in areas with inconsistent or weak winds. Additionally, the terrain, altitude, and surrounding structures can also affect the energy available to a wind turbine.