I wrote in a recent post about how I love finding links between different facts that I have learnt. I also thoroughly enjoy linking this with some quick "number testing".
Last Saturday, I was driving from Dehradun to Delhi with my family when my father said, "We had gone to see an old hydel power project that takes water from a river. They have built a tunnel through the mountain for this and all the equipment is buried in the earth. Though it was built in the 1970s, it is in good condition and looks very impressive. The tunnel is about 15 feet across and the total head of water is about 100 meters of height. The plan was to generate about 100 MW through 3 stages, of which 2 have been built."
My first reaction was, "100 MW through just a 15 feet tunnel? That's too much!"
Then I began to calculate. 15 feet is about 5 meters, say. That is, 2.5 m radius. Or area of about 6Pi or 18 sq m approximately.
Now every meter length of the tunnel contained 18 tons of water (one ton of water is 1000 kg). This was falling 100 meters. Work done is force x distance. Force here is 18000 kg mass into 9.8 m/sec sq acceleration (due to gravity) or 180,000 Newtons. So if this acts for 100 meters, we are talking of 18 million Joules of potential energy from 1 meter of water.
What would be the speed of the water? We have all seen how water rushes out of such hydel tunnels. 20 meters going out in a second is not inconceivable IMHO. So we have a possibility of 18*20 million Joules/second or 360 MW. So we are in the same ballpark.
Now, there will be a loss due to conversion efficiency etc. The tunnel may not be full. So a 100MW generation is plausible.
I hope my calculations are correct (I am now a rusty engineer!) My estimates may also be off by a bit, so the numbers might be quite inaccurate. But here I'm emphasizing more the need to start to cross check these calculations - whether in engineering or in business or in general life - rather than just accepting what is given to you. I think this is an important trait of the best executives.
I'll give some more examples in the next post.