2 round holes, one is larger than the other, in a round tankwith an open top, th

Question

2 round holes, one is larger than the other, in a round tankwith an open top, the center of 1 hole is twice as low as theother, the flow coming out is the same, which hole is closest tothe top? what is the ratio of smaller hole to thelarger? I know the larger hole is higher, but I can't figure out theratio. 2 round holes, one is larger than the other, in a round tankwith an open top, the center of 1 hole is twice as low as theother, the flow coming out is the same, which hole is closest tothe top? what is the ratio of smaller hole to thelarger? I know the larger hole is higher, but I can't figure out theratio.

Explanation / Answer

flow rate = speed * area    and the flow rates are the same. So... .       speed * area of largerhole   = speed * area of smaller hole. .     frombernoullis,      speed = 2gd            and you are told   d is depth of the larger hole,while 2d is the depth for the smaller hole. .    Now...     speed forlarge / speed for small   =   areaof small / area of large . This is the ratio you are asked to find... but notice theratio of the areas is the same as the ratio of the speeds. . So... .           area of small / area of large = 2gd / 2g*2d = 2gd/4gd = 0.5 =   0.707    is the ratio of the areas.

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