It is a common experience that water shoots higher when we block a garden hose outlet by our thumb. But what causes this? How high does the water go? Does water from our neighbor's garden hose reach the same height? Is there an optimum outlet blockage that results in the greatest height that water can reach? Here, we show that a competition between viscous friction along the hose and the viscous dissipation at the thumb-generated constriction results in a variable water shooting height. Through systematic analysis, we demonstrate that depending on the municipal water main pressure, and length and diameter of the hose, the maximum water height may increase, decrease, or gain an optimum as the blockage ratio of the outlet varies.

中文翻译：

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如果我们部分堵塞花园水管出口，为什么水会冲高？

通常的经验是，当我们用拇指挡住花园水管出水口时，水会喷得更高。但是是什么原因造成的呢？水流到多高？我们邻居的花园水管中的水是否达到相同的高度？是否有最佳的出口堵塞，导致水可以达到的最大高度？在这里，我们显示出沿软管的粘性摩擦与拇指产生的收缩处的粘性耗散之间的竞争导致了可变的注水高度。通过系统分析，我们证明，取决于市政供水主压力以及软管的长度和直径，随着出水口堵塞率的变化，最大水位可能会增加，减少或获得最佳值。