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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The maximum speed at any particular pressure is the same speed an object would reach falling from the height *h* needed to create to create that pressure due to gravity *g*. The formula is √(2*gh*). Domestic water pressure can be due to a head of water of up to 50 m, i.e., that’s how far the surface of the water in your local supply tank is above the level of your house. Plugging that number and *g*=9.8 m/s^2 into the formula gives 31 m/s or 70 mph.
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