Hydro in the Gutters

[wdyasq]

Occasionally, one gets what they perceive as a brilliant idea. An idea that comes up regularly is 'Can I put hydro-turbines in my downspouts and make power'. I answered one of these on the IRC channel recently and thought I should post the math here. In this manor, my math, it it is wrong, will get corrected and Wooferhound can stick this thread in the unseen FAQ section.

We will start win a 1000SF roof and a 12 inch/1 foot rain in an hour. I realize this is absurd but, putting turbines in gutters is in the same league so just bear with this a bit. We will also use a 10' drop or 'head' for our figures.

On to the numbers:

We have 1000SF area getting 1 foot of water so we have 1000 cubic feet of water at 62.4 pounds a cubic foot or 62,400 pounds of water. This will fall 10 feet so we have 624,000 foot pounds of energy in one hour time. As power is in 'foot pounds a minute', we divide this by 60 and get 10,400 foot pounds of energy a minute.

We take the 10,400 foot pounds of energy and divide by 33,000 foot pounds of energy in a horsepower and get .31HP. At this time we have no inefficiencies or loses due to friction or anything else. I think if we got 20% efficiency out of our turbine for such a small one we would be doing very well. We end up producing .062HP for the hour.

This we need to convert to our International Watt or Kilowatt so we can converse with the world. 1HP = 746 Watts and .062 X 746 = 46.25W. Since we got this over an hour this is .046kWh for every foot of rain.

Just to finish the thinking, I'll take an example of a 3500SF roof here in North Central Texas where we get about 30" (2-1/2') of rain per year.  In a year, if one had a place to store the 63,000 gallons of water, the electrical production would be ~.4kW. That is $0.07 worth of electricity/year at $0.16 kWh rate (one of the highest in the nation).

Ron

Yeah, woofer should stuff this in the often unread FAQ / WIKI.

[spinningmagnets]

Can this be grid-tied?

"All I asked for was a few sharks with freakin lasers mounted to their heads, is that really too much to ask for, people?" -Dr Evil (Austin Powers)

[TomW]

Golly, Ron.

No fair injecting reality into a really good idea.

Tom.

[PeterAVT]

I gotta admit, the math looks good. Even up here in the Northeast, it isn't really feasible. But I would save the basic math ideas for a real FAQ.

[DamonHD]

Now you got me thinking... that's 1Wh for every mm of rain on my roof (~50m^2)!

Rgds

Damon

[elvin1949]

  Ron

 About 1 time every 50 years i get slam dunked by a Hurricane here.

 So you can multiply that by 50 on those rare occasions.   HEHEHE

later

Elvin

[tecker]

If you get enough rain to warrent the expense you can collect water in a tank and work out the details using a down spoute will back up water in the gutter and overflow to the soffit .

[Norm]

If only the ones that thought up this brilliant

idea would look at their water bill?

   Roughly speaking 100 gallons of water cost me

a $1 (our new sewerage is included....ever gallon

of their water you use goes down their drains)

   We use 200 gallons a day.

   Now if I put a (free)55 gallon plastic barrel

at the 4 corners of my 36' x 24' house, they would

be filled in a couple of hours during just an average rainy day....

   So just flushing the toilet using 50 gallons

of water a day and it rains just enough so I use

this amount 10 days out of a month....

   I could be saving $5 a month...double that

by learning to save on the water.

[wooferhound]

so payoff of the $600 system would be in 8571 years

or

it would never pay to even keep batteries updated

this has been discussed briefly several times, along with ideas like,

I want to pump water uphill using my dumpload power . . .

[wdyasq]

Sorry Norm,

I haven't figured out how to make people think.....

Ron

[Norm]

That's okay Ron...no one is perfect...

Ah well....

[rossw]

Ahh, Ron, you missed a key ingredient. Head.

If you dug a deeep hole (say, 90' deep) you would increase (substantially) the pressure of your water flow and increase your yield. With a mere 90' deep hole, you now have 100' head - or 10 times your output power (neglecting losses)

If you happen to live really high up say on a mountain......

(grin)

[vawtman]

Hi Ron,

 These homes can't use the scheme anymore.

http://www.620wtmj.com/news/local/19662404.html

[richsuka]

hydro from city water supply 70-100psi every time u turn on the water.

Needs to be setup before it come into home.

At lest you get head pressure (head ache)all the time.

File this one tooo.

Rich

[MattM]

I think your figure for total foot pounds is too generalized.  Gravity accelerates at a negative 32 odd feet a second square.  So its not really 10 foot pounds for a single pound dropping 10 feet, more like 25 foot pounds if my finger counting is right and so that should be more like 3/4 hp.

If your house is on the top of a 65' cliff and you put an extension on your 10' downspout down the cliff (for a 75' total) then you only triple the kinetic energy, right?

[wdyasq]

Feel free to recalculate and post your findings.

Ron

[MattM]

Actually, if you calculate the gravity and velocity of the water in 100' its a little more than 3 times the power of a 10' drop.

[joestue]

I hope you were being sarcastic. ROFLMAOAAPMP!

what is the definition of one joule? hs physics. one newton meter.

I suppose since the water is traveling three times faster it's going to give the waterwheel three times the momentum too..

[pyrocasto]

Well if any of you would use your brain you'd realize why not use some of the power you make, to pump the water back up, and generate more. You wouldnt even need a constant rain. Just one to get you started, recycle the water, and then you could power some of your house with the extra!

I think you could do the same with solar. Just use some power to power a lightbulb in front of the panels. You could make power at night!

I think I might start prototyping this sometime this month.

[richsuka]

Using the rain water can save you money ,not in making energy but used as a supply a solar water heater. Or it can be diverted back to your water supply line to the house, with the simple filter. or a new water line just for washing cloth or bath water, lawn and garden watering cost me 25.00 monthly. If you are still thinking on using it as a power source, watch TV because it would take the rain fall that has cause flooding in the north over the last week or so to give you any measure or energy vs dollars spent. Save you money on this one.

rich

[MattM]

No, I was calculating power - a product of time - whereas you are calculating work potential.

Maybe we had different physics classes.

[joestue]

it would still be 10 times the power

[MattM]

My math was probably off because I was only figuring velocity.

Here's a new calculation.

1. foot-pound per second = 0.001818 horsepower
   
1000. cubic feet of water is equal to 62,400 pounds
      
62. ,400 pounds over one hour is 17.333 pounds per second
    
17. 333 gallons per second times 0.001818 horsepower is 0.031512 horsepower
    
    

Now this is for one foot displacement per pound without the effects of gravity.  Let's factor in gravity...  Using math we can figure the time necessary for the water to fall 10 feet by using the equation for the distance that the object falls in a given time. This equation is d = gt²/2

where

    d is the distance the object falls

    g is the acceleration due to gravity

    t is the time considered

    t² is t times t or t-squared

    gt²/2 is g times t-squared divided by 2

so 10 feet = (32.17 feet/seconds²)t²/2

    (32.17 feet/seconds²)t² = 20 feet

    t² = 20 feet / 32.17 feet/seconds²

    t² = .6216972 seconds²

    t = .78847795 seconds

Now we need to figure the average velocity for the object in order to figure out the force it will have at the 10 feet mark.  We know the distance and the time travelled, therefore we can calculate the distance over the time.  At the .78847795 seconds mark the water is travelling at 12.68266 feet/second.

17.333 pounds per second times 12.68266 feet per second is equal to approximately 220 foot-pounds per second, which is also .4 horsepower.

Is this a little better or did I fudge something here?

[MattM]

Using math we can figure the time necessary for the water to fall 75 feet by using the equation for the distance that the object falls in a given time. This equation is d = gt²/2

where

    d is the distance the object falls

    g is the acceleration due to gravity

    t is the time considered

    t² is t times t or t-squared

    gt²/2 is g times t-squared divided by 2

so 75 feet = (32.17 feet/seconds²)t²/2

    (32.17 feet/seconds²)t² = 150 feet

    t² = 150 feet / 32.17 feet/seconds²

    t² = 4.6627293 seconds²

    t = 2.1593354 seconds

75. feet / 2.1593354 seconds = 34.732909 feet / second
    
17. 333 pounds / second * 34.732909 feet / second = 602 foot-pounds per second, which is also 1.09 horsepower.
    
    

Correct my math where it went wrong.

[MattM]

Ooopps, you were saying 10 times for 100 feet and I calculated 75 foot.  Here's 100 foot.

100 feet = (32.17 feet/seconds²)t²/2

    (32.17 feet/seconds²)t² = 200 feet

    t² = 200 feet / 32.17 feet/seconds²

    t² = 6.116208 seconds²

    t = 2.47309683 seconds

100. feet / 2.47309683 seconds = 40.435133 feet / second
     
17. 333 pounds / second * 40.435133 feet / second = 700 foot-pounds per second, which is also 1.27 horsepower.
    

[joestue]

man, i really don't know what you are trying to figure out.

time to fall 100 feet will be square root of ten times as long as the time to fall 10 feet.

energy is 1/2 Kg (m/s)^2

gravitational potential energy is mgh.

[bastardization] gravitational potential power would be (kilograms/second)x(9.8m/s^2)x(height in meters)

[MattM]

joestue said, "it would still be 10 times the power"

I have shown that the power for 100 foot drop is not 10 times more than for a 10 foot drop.  Are you arguing about the math or the whole concept in general?

[thirteen]

You mentioned holding water, a couple of large buried tanks might help you. Maybe you could collect all of the rain water into large tanks and have a longer running flow of water using some floats inside the tank. When full it opens valves and thus letting the water out for generating purposes. Also depends on the slope of the land you have to work with. If you could keep all of the water maybe you could make a pond and raise fish. Just a idea

[DamonHD]

I think it's pretty certain that 10 times the height in a constant gravitational field has 10 times the potential energy.

Rgds

Damon

[joestue]

The flow rate didn't change - a logical assumption, water flow = available source.

Further more the time required to fall doesn't matter.

If i drop a 10 Kg ball one meter, just before it touches the ground, it's moving 4.427 meters per second and it has 98 joules of kinetic energy.

If i drop a 10 Kg ball ten meters, just before it touches the ground, it's moving 14 meters per second and it has 980 joules of kinetic energy.

If i drop [one] 10 Kg ball per second, then i have an average energy dissipated at the bottom of 98 watts, and 980 watts respectively.

The definition of work is Fd force x distance.

ask yourself where did the energy go,

it is obvious it takes 10 times the energy to lift that water 10X height.

[MattM]

The energy did not go anywhere, joe, you're intermixing "energy" with "power".

Horsepower is a unit of power, not energy.  Pound-force per foot is the relative unit of energy.

[joestue]

Please try to piss me off, it's not going to work.

I am not mixing up energy and power

energy is mgh

power is mgh/seconds

one thousand kilograms of water falling 100 meters is 980,000 joules.

I don't care how long it takes to fall.

you can figure the math out.

100 feet = (32.17 feet/seconds²)t²/2

    (32.17 feet/seconds²)t² = 200 feet

    t² = 200 feet / 32.17 feet/seconds²

    t² = 6.116208 seconds²

    t = 2.47309683 seconds

 100. feet / 2.47309683 seconds = 40.435133 feet / second   [average speed!]

  17. 333 pounds / second * 40.435133 feet / second = 700 foot-pounds per second, which is also 1.27 horsepower.

If the energy didn't go anywhere, then it should work backwards.

700 foot pounds/second will lift 7 pounds of water 100 feet per second.

you started with 17.33 pounds per second.

KISS 17.33 pound/second x 100 feet. = 1733 foot pounds per second or 3.15 horse power.

[MattM]

But when you fall its not at just one static velocity.  Your height displacement affects the overall velocity, which then makes the time nonlinear relative to the displacement.  If the velocity is constant your formula works.  Once you add in the acceleration due to gravity things are not so cut and dry.

Piss you off?  Please.  If pointing out the facts piss you off then so be it.