Would a bucket with a hole in the bottom being filled at different rates with water come to to different equilibrium levels with in the bucket? Or would at any fill rate above initial flow rate of the hole cause the bucket to overflow?
An answer with more math is preferred.
If flow rates of water into bucket less than initial flow rate of hole then water level stays at or below height of hole in bucket.
If water flow rates begin to increase, so does the depth of the water above the hole then since the product of the hole's size and pressure is positively proportional to flow rate, the water leaving and coming reach a equilibrium point with in bucket x height above hole.
If water entering bucket becomes to fast then a equilibrium point in the size of the current bucket can not be reached, so the bucket over flows.