I'm having a problem starting and solving the following problem:

Fluid Mechanics

My attempt at the solution was to realize you need to balance the upward forces with those of the downward forces in which case you have a buoyant force, for the upward force. And downward is the weight of the ball and the pressure of the ball at that height it's at. So then to solve it I assume you equate both and then you can find the specific gravity?



You are close. The forces on the ball are 1. Gravity 2. Water pressure, and 3. air pressure from the hole at the bottom. For convenience you can assume the air pressure is 0, or you can keep it in, it will go away from the final answer. Not the trick is that the water pressure would produce a net booyant force given by Archimedes principle, IF it was completely surrounded by water. But it is not completely surrounded. You need to subtract from the bouayant force, the force that would come from the area over the hold, if the hold were also full of water. Since the hold is small compared to the ball, you can probably just estimate this as the area of the hold times the water pressure at the bottom of the tank. And there you go.


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