When water flows out of a fountain, the continuity equation tells us that the flow rate must remain constant - the same amount of water is moving every second. That means if you make the opening smaller, the water speeds up to compensate. It’s the same reason pinching a hose makes the stream shoot farther. A faster jet of water has more kinetic energy, so it arcs higher and travels farther before falling. That’s why covering part of the fountain’s hole makes it much easier to fill a bottle - the stream gains enough speed to clear the edge instead of dribbling short.
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