Turbines / conservation of energy

[kalamater]

Wind turbines / hydroelectric turbines - I think the same fundamental Physics applies to my question. The fluid (water or air) prior to meeting the turbine has kinetic energy, after the turbine the flow must be the same (or there would be a 'build up' of fluid) - so it has the same KE as before ?, yet the turbine 'extracts' energy. Where has the energy which the turbine has produced come from ?

 

[Diferencialdex]

The flow (kg/s) is constant. In the physical model we use power, not energy. To calculate energy, we just multiply power by time. The kinetic power is what changes, just because the velocity does, E = 1/2 G (V1-V2)^2, where G is the flow. The power that generate the turbine is just because the change of the velocity in that part of the fluid. The flow remains constant because the area of the section changes according with that. Was that your question?

 

[gmax137]

In the case of a hydro turbine, the water is falling through the turbine - the elevation of the liquid surface upstream is higher than the elevation downstream. So the energy extracted into turning the shaft comes from the potential energy of the upstream liquid - in other words, gravity is powering the turbine.

 

[Topher925]

In the case of a wind turbine, you can think of the flow following the bath of a diffuser. As the air passes through the wind turbine disc it slows down and expands out word because of its slower velocity. This is analogous to the down wash of a helicopter which the flow becomes more narrow do to an increase in velocity. The kinetic power extraction limit of a wind turbine is modeled using the Betz Law.

http://www.windpower.org/res/turbtubx.gif

 

[russ_watters]

What changes from one side of the turbine to the other is pressure. Power in a turbine is mass flow rate times pressure.

 

[kalamater]

Many thanks everyone, yes some good ideas to pick over here, I'll chew on the power and pressure ideas. The hydro argument over potential I like, guess if there was no turbine in the way, the ejected water would be at a greater velocity, all (or nearly all) the PE being converted to KE. I generally feel happy now about the hydro idea but will have to think on about the wind generators. Thanks

As an aside, I was told some time ago that the tidal barrage scheme in North France would result in the slowing of the Earth's rotation by some 0.25 seconds in 1 million years (I haven't actually bothered to do the calculation myself) - presumably as we move more and more to 'renewables' such as wind generators, we'll slow down the rotation a bit more - after all we don't get energy for nothing, it has to come from somewhere.

 

[kalamater]

Thanks also for Betz law and the link - time to go away and do a bit of thinking!

 

[Topher925]

As an aside, I was told some time ago that the tidal barrage scheme in North France would result in the slowing of the Earth's rotation by some 0.25 seconds in 1 million years (I haven't actually bothered to do the calculation myself) - presumably as we move more and more to 'renewables' such as wind generators, we'll slow down the rotation a bit more - after all we don't get energy for nothing, it has to come from somewhere.

What!? How exactly do wind turbines or changes in tide affect the rotation of the earth? The only thing we can do to change its rotational speed is move mass outwards away from the surface of the earth. All the satellites and garbage in space will have a greater affect than anything France does.

 

[kalamater]

Sorry, not accusing France of anything, but I was given to understand that any tidal energy schemes result in slowing of the Earth's rotation by reducing it's rotational KE, after all the energy has to come from somewhere - if not the Earth's rotational KE then where else ?

Betz law in Google seems to answer my original questions though - thanks again.

 

[rcgldr]

The fluid (water or air) prior to meeting the turbine has kinetic energy, after the turbine the flow must be the same (or there would be a 'build up' of fluid) - so it has the same KE as before.

Only the mass flow remains the same. In the case of a wind turbine, the air flow is diverted "outwards" by the turbine blades, slowing the air and changing it's direction.

http://en.wikipedia.org/wiki/Wind_turbine

Most water turbines are "reaction turbines". The water flow is contained in pipes so it won't expand under pressure. If the turbine's axis is horizontal, then pressure of water decreases as it flows through the turbine, converting pressure energy into mechancial energy. If the axis is vertical, then gravitational potential energy is also converted into mechanical energy.

http://en.wikipedia.org/wiki/Water_Turbine