[daveshorts]

Now it seems that you're suggesting that a tree is doing something impossible!

According to your figs 0.11g per second * 60 * 60 * 24 = 9504g or 9.5 liters a day!

9.5 liters a day doesn't come close to what a tree tries NOT to do!

That is 9.5 litres per square metre, for a large tree 10m across so about 100 square metres that is 950 litres - a bloody good estimate if I do say so myself

As I said earlier I'll go though most of the math with regards to estimating how much water we can raise.

 we estimated earlier than we can increase this by a factor of a hundred, recently we've begun to think than we can increase this natural evaporation rate by closer to three hundred.

I would very much like to see your maths...

[YourUncleBob (OP)]

excellent point Dave,

Yes, per square meter, silly me, now if only a tree looked like a 100 square meter pool of water, the math would pan out.

As I said a tree doesn't 'want' to release this water, and at night would continue to release this water if it didn't close its stomata.

Physics has to explain nature.

Have you ever wondered what experimental apparatus was used to get the figure of 2.2mj of energy to evaporate 1 kg of water.

Energy is required to break the hydrogen bonds between the individual water molecules so that they may eventually leave their liquid siblings and take flight.

Why do those H2O molecules on the surface leave first, because obviously they have half the bonds to break.

Does it take the same amount of energy to evaporate 1 kg of water when it is in a cube shape as it does when it is spread out a few molecules in depth with a huge surface area?

Blaine

[daveshorts]

Does it take the same amount of energy to evaporate 1 kg of water when it is in a cube shape as it does when it is spread out a few molecules in depth with a huge surface area?

The water molecules always evaporate from the surface so to a first approximation they will be eqiuvalent

If you are getting more subtle:
If you spread out the water on a hydrophobic surface you are doing work against surface tension to stretch the water out so you are giving the water some energy before you try and evaporate it, so the energy required would be slightly less...
However
Water won't spread out over a hydrophobic surface, the reason that water will spread out over such a large surface on a tree is that the tree's surface is very hydrophilic - the water molecules bond to the tree probably better than they do to other water molecules - so you are going to need at least as much energy if not more to evaporate a kilogram of water from your tree, than from a bucket.

In fact because energy must be conserved in your design the difference in energy to evaporate a kilogram of water from the leaves of the tree 300m up and from a bucket on the ground. must be at least the change in potential energy of the water as it rises the 300m. So it will definitely require more energy to evaporate water from your tree than from a bucket.

Although if the energy is available the larger surface area of the tree will mean a higher rate of evaporation. But if the energy isn't being added by the sun as fast as it is being lost though, your tree will cool down until the rate of energy loss equals the rate of energy input.

[lyner]

This is in imperial units and the the '11.8' is used to convert units of feet and seconds into kilowatts per hour.

If we can have kilowatts per hour why not per minute?

Kilowatt Hours (Power times time) is the unit of energy - not Kilowatts PER Hour (Power divided by time). There is a huge difference between the two and you can't just gloss over such an error.
Basics basics basics!

[lyner]

The power available to the tree to do this work will come from the thermal energy 'absorbed' by the leaves at the top. This can be from the Sun or from the surrounding air (clothes dry in the shade as well as in direct sun, although not so quickly).
The details of the actual evaporation process, although important, are not as important as the Energy consideration. With bigger or smaller leaf area and a different surface chemistry, the same Energy budget would apply.

[lyner]

In any case, where is this thread going?
Are we discussing
1.how a tree gets enough energy to supply what is needed for self irrigation (it clearly gets enough energy)
or
2. whether this is a system which could be looked upon as a possible Energy Resource for electricity generation (not in a million years - there just isn't enough power input)?

It isn't clear.

[YourUncleBob (OP)]

Sophie Dave,

I wish I could devote more time on here, hopefully soon, in the meantime let me clarify where this thread is hopefully going.

Two questions need to be addressed.

1) How much power can be generated from the falling water 800,000 liters falling 250 meters through a 20 cm diameter pipe?

2) Can our Artificial Trees lift that much water?

We have a lot of confidence in our Artificial tree's ability to lift the water. Which as I alluded to earlier has to do with the apparatus used in the experiments to measure the energy required to evaporate 1 kg of water. Did any of you check it out? (remember water is not a good conductor of heat)

Question 1 has been very confusing, have you guys checked the link I gave for the formula I used? If not please check their example, I'll copy and paste it below.

If you could kindly point out the errors I made when working through the formula with our numbers I would be very grateful.

Below is the example reprinted from this website http://www.wvic.com/hydro-works.htm [nofollow]

Power = (10 feet) x (500 cubic feet per second) x (0.80) / 11.8 = 339 kilowatts

To get an idea what 339 kilowatts means, let's see how much electric energy we can make in a year.

Since electric energy is normally measured in kilowatt-hours, we multiply the power from our dam by the number of hours in a year.

Electric Energy = (339 kilowatts) x (24 hours per day) x (365 days per year) = 2,969,000 kilowatt hours.

The average annual residential energy use in the U.S. is about 3,000 kilowatt-hours for each person. So we can figure out how many people our dam could serve by dividing the annual energy production by 3,000.

People Served = 2,969,000 kilowatts-hours / 3,000 kilowatt-hours per person) = 990 people


Kind Regards
Blaine

[daveshorts]

Question 1 is not confusing, it is trivial to put an upper bound on.

800 000kg of water raised by 250m by mgh has about

800 000kg * 10kgm/s² * 250m
2GJ of energy
which is 555kWhr of energy.

assuming this is  what your system can lift in a day (which will mean it has an area of about 8 hectares)

you will be producing an average of 23kW

about 50ish people assuming a 100% efficient conversion from potential to electrical energy, this is probably nearer 80% so you are talking about 18kW average.

[lyner]

Yes, Y U B, question 1 is triv.
This system works on evaporation of some of the water to provide energy for lifting all of it.
I have a suspicion that all this energy transfer could produce a significant modification to the microclimate. The air would be full of evaporated water and it could mean an increase in rainfall (admittedly, some of this rainfall would find itself back in the system again.)
This process is not unlike the normal water cycle, which uses the GPE of water which has been lifted there by solar energy via the clouds. 
I would need some more information before accepting that an area of artificial tree covering 8 hectares would produce the quoted level of power output. It would depend, greatly, upon the actual location on the Earth and the existing climate. A cold Northerly wind would put the mockers on it, I feel.

[daveshorts]

The 8.5ha is the minimum possible area at the equator if all the sun's energy falling onto those 8ha was used to evaporate water and then all the water was condensed again (with some mysterious immense heat sink) 250m up.

As a comparison 8ha of 12.5% efficient solar cells on the equator would produce nearer 80 000*30W/m² 2.4MW - I think rather better than 20kw, and probably also far cheaper to build as they don't involve thousands of 205m tall 'trees', with giant glass domes at the top, and huge pumps to move cold seawater in order to cool your condensing surfaces which would probably use more energy than your turbines produce.

[lyner]

My original point about the system that trees use is that it does a particular job excellently. The available power just suits the requirement and doesn't allow for TV, heating or lighting.