Does a 1m2 solar panel really provide more power than 1l/s of water falling 1m?

Question

I'm trying to develop an intuition for small scale power, in the context of off-grid power.

Are these sums correct?

• A 10% efficient solar panel, of one square meter, with incident 1kW sunlight, will produce up to 100W of power (only while normal to direct sunlight).

• a flow of 1l/s of water (1kg/s) falling 1m, driving a 90% efficient pelton wheel, will produce 9.8 * 0.9 = 8.8W of power.

• a tiny computer, like a Raspberry Pi can use 1A @ 5V, which is 5W.

• raising 1l of water 1 degree per second (to boil in just over a minute) requires 4,200W.

• a 100Ah car battery will provide, or store, 12 * 100 / 24 = 50W for a day.

The reason I'm asking this question, is that I am surprised that this amount of solar power provides more than that amount of water power. (I had expected them to be roughly similar.)

I'm also surprised that it would need as much water-flow as 500l/s (two baths per second) falling 1m to run a 4.2kW kettle.

Therefore, I think that I may have made mistakes.

Answer 1

The calculations seem right.

Yes, it is surprising how much energy it takes to heat water, or how much energy sunlight can produce.

When heat is involved the energy is high (sunlight can feel very hot sometimes).

So, for example, if you wanted to reduce your household energy bill, turning off a radio would make almost no difference, but turning off an electric fire would reduce your bill.

Also energy efficient light bulbs don't generate as much heat as the traditional type, and so use much less energy.