Yes, to get the same pressure on the tank, total area has to be 1000x.
area is proportional to diameter squared.
A=PI/4 (D^2)...
so if the diameters were 20 cm, then the new diameters should be 20sqrt(1000)
This is based off of the paper "Scaling -- The Physics of Lilliput", but I think the following questions can be answered out of context:
1. Based on the Lilliputian reading:
A) A rectangular water tank is supported above the ground by 4 pillars 5.0 cm long whose diameters are 20 cm. If the tank were made 10x longer, wider, and deeper, how much more would the tank hold?
--> I already figured out that the answer is 1000x, which is correct.
B) In units of meters, what diameter pillars would be needed to support the weight of the new tank?
--> I am told this has to do with the pillar's cross-sectional area. If I'm not mistaken, the CSA of the pillar increases 1000x as well, but I'm not sure how you use this knowledge to determine the diameter of the new pillars.
Thanks so much in advance for any help I can get!
1 answer
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