Two circular holes, one larger than the other, are cut in theside of a large wat

Question

Two circular holes, one larger than the other, are cut in theside of a large water tank whose top is open to the atmosphere.Hole 1 is the larger hole, and hole2 is the smaller hole. The center of one of theseholes is located 7.07 times as far beneath the surface of the wateras the other. The volume flow rate of the water coming out of theholes is the same. (a) Decide which hole(1 or 2) is located nearest thesurface of the water. (b) Calculate the ratio ofthe radius of the larger hole to the radius of the smaller hole,rA/rB. Thank you to anyone who can help with this. Two circular holes, one larger than the other, are cut in theside of a large water tank whose top is open to the atmosphere.Hole 1 is the larger hole, and hole2 is the smaller hole. The center of one of theseholes is located 7.07 times as far beneath the surface of the wateras the other. The volume flow rate of the water coming out of theholes is the same. (a) Decide which hole(1 or 2) is located nearest thesurface of the water. (b) Calculate the ratio ofthe radius of the larger hole to the radius of the smaller hole,rA/rB. Thank you to anyone who can help with this.

Explanation / Answer

(a) the largerhole is closer to the top, smaller hole is lower. This isbecause the flow rates are the same, and flow rate is area timesspeed. So the smaller hole must have greater speeed. It is lower,where the pressure is greater to create faster speed. . (b) use Bernoullis toget:       v = 2gd        where   d is the depth of the hole below thesurface. .     Since the smaller hole is 7.07 timesdeeper, we know it's speed is   7.07 =   2.6589 times greater than the speed at the tophole. . This means that    large area / smallarea = 2.6589             or        r for large / r forsmall = 2.6589 =   1.631 .    So theratio of large radius to small radius is  1.631

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