TBR: Energy from Making it Rain

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justadream

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TBR Physics I page 161

In this energy generator, rain (falling from a great height) is used to spin a turbine to generate energy.

I have 2 questions
1) Does the fact that rain is funnelled REDUCE the amount of energy generated? It seems to me that the rain that does not go through the small hole in the center (but that instead hits the funnel) loses a great amount of kinetic energy?

2) TBR says that increasing the number of paddles on the turbine to catch the water wouldn't help since it would increase mass and thus increase friction. But what about efficiency? Doesn't having more paddles increase the total net amount of water that is taken up. For example, if you have 5 paddles, you'll probably catch more of the total water than if you have 2 paddles.

3) I didn't show it but there are multiple turbines (imagine a second one just below the one I drew). TBR says (in question 27) that placing that turbines farther apart vertically would result in faster rotation of the turbines. But doesn't this decrease the amount of PE in the upper turbines (those closer to the sky)?

fVDfK.jpg

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Yes - I would agree that funneling the rain will reduce the kinetic energy through loss to friction/heat. It seems that it would be the only way to guarantee the rain falls on the turbine though.

This system seems highly inefficient as it is! Increasing the number of paddles would likely have no net effect - as I think the machine is modeled to collect all rainfall. So if you have more paddles, each will receive less rain - so it will be a neutral effect. As you also stated, increasing the number of paddles will increase the moment of inertia of the turbine - resulting is more force required to rotate it.

I think that it is assuming you keep the upper turbine in place and lower the second one. This will increase the PE of rain falling to the second turbine and have no effect on the first one. The height of the first one is limited by the placement of the funnel.
 
@Cawolf

With regard to 2), okay I guess we were supposed to assume that.

With regard to ""it is assuming you keep the upper turbine in place and lower the second one", how do you assume that?

If anything, you should keep the lower one in place and raise the first one. After all, the ground level is constant (unless you start digging below the ground)?
 
I was assuming that that the funnel was a fixed height and the turbines could be moved. If the upper turbine was as close as possible, then the lower turbine would be moved downwards.

If the system was as you described, then the upper turbine would be moved upwards and the total rainfall distance would be the same - with no net gain. I had that passage narrowed down to that one as the best answer - so I modeled my explanation as to why that seemed to be a logical choice.

Though if there was room to move the upper turbine only, then that would be an incorrect answer.
 
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@Cawolf

I thought both the choices about movement of the turbines were bad because I didn't know if they were changing the average vertical placement of the turbines.

But I think TBR's explanation mentioned something about momentum being greater if you spread out the turbines more.

So which will generate more energy
Scenario 1: 1 turbine at 6 meters above the ground, the second at 4 meters
Secnario 2: 1 turbine at 7 meters above the ground, the second at 3 meters

Note that the average vertical height is the same.
 
Well - if we assume the rain falls at a terminal velocity, then the second scenario would be the greatest.

I hadn't considered that before, but it is likely the height of the first turbine will not have much effect, due to drag force on the rain drops.

So if the height of the first turbine has no effect, then we want the greatest distance between the two - so scenario 2 would be the most effective.
 
@Cawolf

Okay, that makes sense.

With regard to 1), I ask because in question #39 TBR asks why this generator is inefficient.

The answer is that the surface area required would be too large. What came to my mind though (not one of the answer choices) was that too much of the energy would be lost from collisions with the funnel. How much relatively speaking (e.g., 20%? 50%? 80%?) of the energy would the collisions with the funnel reduce the energy that could be used to spin the turbine?

To me, I thought it would be like 80% because the water might back up (creating a small pond) in which case the PE becomes the depth of the water in the bond. Of course, that might not happen if the opening in the funnel is large enough.

And even if the funnel's opening were really small, we might have to consider momentum conservation (the rain hitting the top of the water in the funnel would transmit that energy through the layers of water to the bottom, thus increasing pressure at the bottom?)
 
For that question - all of the other answers are really silly, leaving the surface area choice as the only plausible answer.

As far as the numbers and percents - I have no idea. This isn't a realistic design, so one can't really speak about those things.
 
@Cawolf

Okay thanks.

As you can see, when I do these questions, a million different possibilities/assumptions/things to consider pop up in my mind.
 
Makes sense - it obviously works well for you.

All of your proposed ideas are rational - but without making wild guesses about the size, components, and function of the machine - any solid numbers are really just conjecture.
 
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