Maximum power available for a windmill with cross sectional area A exposed to wi
ID: 1638009 • Letter: M
Question
Maximum power available for a windmill with cross sectional area A exposed to wind at speed v expressed to be Pmax = (1/2)(row)(A)(v3 ) where here, (row) represents the density of air.
You have been called in to settle a debate. A small town in a rather windy area would like to use that wind to supply electricity to the town. ACME has provided a prototype windmill so the city engineers could conduct some on site tests. One of the city’s engineers has estimated that the prototype would supply about half of the present electrical need. She suggests that the city install the windmill atop a nearby hillside where the average wind speed is twice as large as the original test site wind speed. Another city engineer points out that there will be additional costs that need to be considered in building the site remotely. According to his calculations, the hillside installation would cost as much as a second windmill. He suggests that the city just install a second windmill at the test site. The ACME representative confirms both sets of calculations. Help the mayor decide which option would be best for her city. Explain reasoning and incorportate equation if possible.
Explanation / Answer
I would recommend that windmills should be installed in the city instead of mill on the hillside.
Reason:
The girl engineer is right that installing windmill on hillside would produce more electricity because of the wind factor. On the other hand the installation charge would be almost double . BUT we can increase the number of windmills by double( keeping the cost constant) if we use the idea of the male engineer. So in this way both ideas are equally likely to be eligible for the execution. But there is one factor we are missing, that is repairing and servicing of the windmill. It is evident that you cannot just install a windmill and hope it will supply you electricity forever . You will have to service it , there could be manufacturing defects. These things would be difficult to rectify in the hillside because of the extrimities and also it will take much more labour and money to do the repair in the hillside as compared to the mill installed in the city. If the town is crowded then it will be ok to install the windmill on the hill. But since it is a small town so the windmill should be installed in the town because of the reason i mentioned above.
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