Fluid Mechanics Problem:
A manufacturer is investigating a new type of straw. The marketing department asks the engineers to examine the possibility of a straw with a square cross section. However, the cost of the material must be the same, i.e, the perimeter of the square straw must be the same as the currently manufactured circular straw. The engineers tell the marketers that the square straw is a silly idea, because it is much more difficult to suck water through.
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Assume flow is laminar, and f = 56.9/Re for square pipes. For a given length L and flow rate Q, what is the relative pressure drop across each type of straw? If the marketers tell the engineers to design a straw where the pressure drop is the same for each geometry, how much more material would be required to make the square straw?