How much energy does it take to raise the Earth's average daily rainfall into the sky?
It's said that 500,000 km3 of rain falls on the Earth in any given year.
(http://en.wikipedia.org/wiki/Rain)
500,000 km3 per year = 1,382 km3 per day.
Converted to metres cubed,
1.38261E+12 m3 of rain falls on the Earth per day, on average.
As 1 litre of water is equal to 1 kg, 1 m3 of water equals 1 tonne (1000kg).
So 1.38261E+12 tonnes of water falls on the Earth in 1 day.
How much energy does it take to raise that water up into the sky from where it falls?
It takes 9.8 joules of energy to raise 1 kg of water (or anything) 1 metre (google).
Therefore, to raise 1 tonne 1 km it takes 9800000 joules of energy
1 gigajoule is equal to 1 billion joules. (http://en.wikipedia.org/wiki/Joule)
Converting above, it takes 0.0098 gigajoules to raise 1 tonne 1 km.
What's the average height at which rain falls from? Google doesn't help with that so I'm going to take a guess at 1.5 km.
Energy required to raise avg daily rainfall 1.5 km
= 0.0098 x 1.38261E+12 x 1.5
= 20,324,435,318 gigajoules
Sounds big, but how much is it really?
Nuclear warheads are rated in kilotons and megatons. 1 kiloton is equivalent to 1 tonne of TNT. 1 megaton is 1000 kilotons.
Energy in 1 kiloton is 4.184 gigajoules. (http://en.wikipedia.org/wiki/Kiloton)
The Little Boy Hiroshima nuke was rated at 15 kilotons, thereabouts.
20,324,435,318 / (4.184 * 15) = 324 million.
The energy required to raise the volume of water which falls on the Earth in 1 day is equivalent to 324 million Little Boy nuclear weapon blasts.
Or putting it another way.
1 watt = 1 joule per second.
The highest rated US nuclear power plants can produce 1300 MWs (mega, million watts) at peak.
(http://en.wikipedia.org/wiki/MWe#Electrical_and_thermal_watts)
That would be 1.3 billion joules energy per second. Or 1.3 gigajoules per second.
How long would such a nuclear plant have to run to raise the volume of water which falls on the Earth in one day 1.5 km?
We need the plant to produce 20,324,435,318 gigajoules, and we know it can output 1.3 gigajoules every second.
(interestingly, the energy in Little Boy was equivalent to 48 seconds worth of output of the US's largest nuclear plant at full output)
20,324,435,318 / 1.3 = 15,634,181,013 seconds.
= 495 years.
It's said that 500,000 km3 of rain falls on the Earth in any given year.
(http://en.wikipedia.org/wiki/Rain)
500,000 km3 per year = 1,382 km3 per day.
Converted to metres cubed,
1.38261E+12 m3 of rain falls on the Earth per day, on average.
As 1 litre of water is equal to 1 kg, 1 m3 of water equals 1 tonne (1000kg).
So 1.38261E+12 tonnes of water falls on the Earth in 1 day.
How much energy does it take to raise that water up into the sky from where it falls?
It takes 9.8 joules of energy to raise 1 kg of water (or anything) 1 metre (google).
Therefore, to raise 1 tonne 1 km it takes 9800000 joules of energy
1 gigajoule is equal to 1 billion joules. (http://en.wikipedia.org/wiki/Joule)
Converting above, it takes 0.0098 gigajoules to raise 1 tonne 1 km.
What's the average height at which rain falls from? Google doesn't help with that so I'm going to take a guess at 1.5 km.
Energy required to raise avg daily rainfall 1.5 km
= 0.0098 x 1.38261E+12 x 1.5
= 20,324,435,318 gigajoules
Sounds big, but how much is it really?
Nuclear warheads are rated in kilotons and megatons. 1 kiloton is equivalent to 1 tonne of TNT. 1 megaton is 1000 kilotons.
Energy in 1 kiloton is 4.184 gigajoules. (http://en.wikipedia.org/wiki/Kiloton)
The Little Boy Hiroshima nuke was rated at 15 kilotons, thereabouts.
20,324,435,318 / (4.184 * 15) = 324 million.
The energy required to raise the volume of water which falls on the Earth in 1 day is equivalent to 324 million Little Boy nuclear weapon blasts.
Or putting it another way.
1 watt = 1 joule per second.
The highest rated US nuclear power plants can produce 1300 MWs (mega, million watts) at peak.
(http://en.wikipedia.org/wiki/MWe#Electrical_and_thermal_watts)
That would be 1.3 billion joules energy per second. Or 1.3 gigajoules per second.
How long would such a nuclear plant have to run to raise the volume of water which falls on the Earth in one day 1.5 km?
We need the plant to produce 20,324,435,318 gigajoules, and we know it can output 1.3 gigajoules every second.
(interestingly, the energy in Little Boy was equivalent to 48 seconds worth of output of the US's largest nuclear plant at full output)
20,324,435,318 / 1.3 = 15,634,181,013 seconds.
= 495 years.
