# Energy conversion in a hydroelectric dam

1. Nov 17, 2013

### kimau79

(this is the first time I post. hope this is in the correct board)

So I want to know about how the internal energy of water has been converted into electrical energy when the turbine is rotating at a steady speed.

I have read several textbooks and they all give me several answers:
1. GPE of water ==> KE of water ==> KE of turbine ==> electrical energy
2. GPE of water ==> work done again electromagnetic force (force from water pressure) ==> electrical energy

I know that if the turbine is starting up, then answer 1 makes sense, but it does not seem valid when the turbine is rotating steadily (since it not gain KE). answer 2 makes more sense in that case, but I am just not sure whether GPE of water will turn into KE of water before becoming the work done against electromagnetic force.

So which one is correct? thank you

PS. in case the abbreviation is different, GPE refers to gravitational potential energy

Last edited by a moderator: Nov 17, 2013
2. Nov 17, 2013

### Staff: Mentor

Both are correct. The water pressure forces water through the dam's turbines at a certain velocity, performing work on them and producing electrical energy. The whole process converts the gravitational potential energy of the water into electrical energy. Note that for water to enter the damn it MUST be accelerated, turning GPE into KE.

3. Nov 17, 2013

### kimau79

Thanks Drakkith.

Just to clear things up, the energy conversion is
(when turbine starting up) GPE of water ==> KE of water ==> KE of turbine ==> electrical energy
(when turbine running at steady speed) GPE of water ==> KE of water ==> work done against electromagnetic force ==> electrical energy

Am I correct?

4. Nov 17, 2013

### Bandersnatch

Not entirely. Both answers are simply parts of a more detailed answer. It goes like this:

1.Water with certain GPE falls down accelerated by the gravitational field, losing GPE and gaining KE.
2.High-speed water hits the turbine blades, performing work on them. It loses KE and the turbine gains KE(work is the transfer or change of energy in a system).
3.The rotating blades are slowed down by the generator. They perfom work(transfer the KE) on the generator, which gains(produces) electrical energy.

Or,

GPE of water =(work by gravity)=> KE of water =(pressure forces do work on the turbine)=> KE of turbine =(work by EM forces)=> electrical energy

Each of the two original answers skips some details, possibly because the authors thought the omissions to be obvious or unimportant. After all, if you simply wrote:
GPE of water =(some work is done here)=>electrical energy
it'd still be correct, if not entirely informative.

5. Nov 17, 2013

### kimau79

Thanks bandersnatch, that clear things a lot. But still I have a little bit more to ask. This is the complete paragraph from one of the textbooks I read:

One of the end-of-chapter exercises also stress again on that the conversion "loss of GPE of water ==> gain in KE of water (or turbine blades) ==> Electric potential energy" is INCORRECT (it should be "Loss in GPE of water ==> work done against friction ==> electric potential energy" according to what they say).

So according to what you mentioned, does the textbook make a mistake here? or just because they are playing with the wording? (they explanation to the answer is that since there is no "gain" in water or turbine blades during the process)

Thanks again.

6. Nov 17, 2013

### OmCheeto

I'm not sure I like the wording surrounding "accelerated", when in steady state mode. If one were to model the river as a pipe, with the same diameter as the turbine inlet, I'm pretty sure you'd get the same power output. The fact that water flows faster through the turbines, than the river flows, is just an artifact of the design.

hmmm... That's weird. In my system, the kinetic energy of the fluid doesn't change, until it reaches the turbine blades. So where did this extra energy at the turbine come from?

So there is more energy available at the turbine, simply because there is a column of water sitting above it.

I suppose the horizontal flow of the river becoming more vertical is a change in direction, which implies an acceleration, but not a change in speed, nor mass flow rate.

7. Nov 17, 2013

### OmCheeto

I would guess that no one has made any mistakes. It is simply difficult to describe in words, which can only be described mathematically.

P = ρhrgk

8. Nov 17, 2013

### Staff: Mentor

I was taking the water as standing still in the lake and being accelerated when it enters the dam.

9. Nov 17, 2013

### OmCheeto

Ok. That makes sense.

I think there are too many ways to model this problem in ones head. I've gone from hydraulic levers, to stacked bowling balls, to bicycle chains on a frictionless surface, to a tarp collecting rainwater in my back yard.

And now I've got your model in my brain......

10. Nov 17, 2013

### Bandersnatch

Well, there you go. In my head I was envisioning something closer to a waterwheel design, hence the acceleration of water as it falls.