why water can’t get really fast when you put a thumb on the garden hose?

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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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It only increases so much as the pressure from inside the tube can build up. At some point the opening is so small that you reach max pressure from the pump that makes the water flow inside the tube

Spraying nozzles do exactly that.

You can reach some higher speed but it depends on the water pressure. If the hose is too long and the pump too weak and the hight between the pump and the hose end too much, there will only be a little increase in speed.

Going to assume it’s something to do with how much pressure is behind the flow, pressure washers need an extra pump inside then to function, thats why you can’t just attach the nozzle to any old hose.

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&#8239;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&#8239;m/s^2 into the formula gives 31&#8239;m/s or 70&#8239;mph.

You can’t make energy out of nothing.

When you constrict a nozzle you essentially force the pressure energy in the fluid to be turned into kinetic energy, but you only have so much pressure energy that you can convert, how much depends on your pump, and once you’re out of pressure energy that’s it, if you further constrict the flow you’ll just chocke the pump, i.e. the pump will simply start pumping LESS wate to compensate for the blockage.

And even with an arbitrarily powerful pump, you are still limited to the speed of sound, since a contracting nozzle can neverr accelerate a fluid past it’s speed of sound, you need converging – diverging nozzle for that