So when you put a thumb over a garden hose you reduce the size of the opening and to keep the same flow rate the water goes out faster, right? So why can’t you (or can you) achieve arbitrary speed with that method (something like water jet cutting)? If you move your thumb to let less and less space for water to pass, shouldn’t that increase the speed of the water even more since the flow rate needs to get higher and higher? But that obviously doesn’t happen. So what determines the max speed of water? I assume the water pressure would have to be involved somehow.
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One step that is often missed is that the water doesn’t get faster because you are constricting it, it is getting faster at the point of constriction because it is getting slower elsewhere in the hose. This means that there is less friction between the water and the walls of the hose, decreasing how much energy is lost while the water is flowing. The theoretical maximum speed can be found from the Bernoulli equation*, speed=sqrt(2*Pressure/density)
*Once your speed approaches the speed of sound in water, this stops working, and you need more complicated maths
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