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.
7 comments:
Hello Sir,
Thank you for this quick and wonderful calculation, though calculations are not my cup of tea.
but I have learnt one thing from this insightful post of yours that always cross check whatever we recieve.
Thank you
Pankaj Gangwani
Yes, I agree. It is important to know enough to check whether what you are checking is in the ballpark of where it needs to be...
Only one comment on your calculations, not sure how you came up with the 20 m/s number for the exit velocity of the water.
If we are using acceleration due to gravity to calculate the force, then the velocity attained for free falling 100m would be in the ballpark of 40-50 m/s...
Loved the calculation nevertheless.
Dear Sir,
It was a nice use of maths with data. I inspired to use it more in future.
Regards,
Proton Ashok Kumar
Fall' 08
Dear Sir,
I totally agree to the point that manager (weather he/she is an engineer or not)must have the ability to cross check the things in numbers. Maths is a universal language and if we can master in using it for our benefit then we can be a good manager.
Thanks & Regards
Hi Vaibhav, the 20 m/sec was to calculate the volume of water. I don't know what this horizontal velocity really is but I assumed it was around 60-90 kmph by imagining the water gushing out at the other end of the tunnel. Just a guess as to what the maximum value could safely be.
Hi Manas, I was just saying that since you used gravity to calculate the force for the water (i guess you assumed that the water is going to fall vertically) - i was using the same simplification to get an idea at the velocity at which water would be moving at the end of the 100 meters when being accelerated at 9.8 meters per second square.
Of course, the ulterior motive for sticking with this point is to apply your teaching in the post - always make sure that you double-check what you read :D.
Cheers.
Sir,
It’s very important to work with no. and have a rough estimate.
When we are crosschecking a thing it’s easy to manipulate things as per the ans. required, like we had taken the overall efficiency roughly as 30% but missed out the 3 stage concept. The decreasing energy of water is further used in stage 2nd and 3rd to generate more energy which counts to overall 100 MW.
Since we were knowing the ans., our assumptions were manipulated, but what when we have no idea of the ans., should we go for such calculation in that case also?
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