Math CentralQuandaries & Queries


Question from JYOTI, a student:

three pipes of varying diameters can fill the vessels of 1,2,and 3 L in 4,18,and 48 min respectively. what is the ratio of their diameters?(assume that speed of the flow is same in all the cases)

Hi Jyoti.

If the flow rates are the same, as indicated, then the ratio of the areas of the cross-section of the pipes is the same as the ratio of the times.

Since the area of a circle varies as the square of the diameter, the diameter of a circle varies as the square root of the area.

Thus, the ratios of the diameters must be the square root of the ratios of the filling times.

Hope this helps,

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