Always thought water increases its speed when you shrink the pipe, not the other way around
At a bottleneck, the water that gets through is moving faster, but the total volume of water going through is lower.
It's a classic EE analogy, so people tend to shorthand it. One good and thorough explanation of the full bit is here: http://science.howstuffworks.com/environmental/energy/questi...
What happens if you increase the pressure in the tank? You probably can guess that this makes more water come out of the hose. The same is true of an electrical system: Increasing the voltage will make more current flow.
Let's say you increase the diameter of the hose and all of the fittings to the tank. You probably guessed that this also makes more water come out of the hose. This is like decreasing the resistance in an electrical system, which increases the current flow.
This is incorrect because the volume of water will be the same under I3 flow (called I-cube flow: Incompressible, Inviscid and Irrotational).
Due to conservation of mass, we have
mass = density x volume = density x area x speed x time
Measuring the amount of volume for the same time with changing area, the only quantity that can change is the speed (recall that we have fixed the time and already assumed incompressible flow, hence density does not change).
So, more area means lower speed and vice versa. But the volume always is the same under stated assumptions.
Not exactly. It increases its speed when you shrink the nozzle. If you shrink the pipe and don't change the supply pressure the water will slow down.
The nozzle is special because it's a transition from high pressure (inside the pipe) to zero pressure (the world outside).
If you keep the flow rate of the water unchanged then shrinking the nozzle means the water must flow faster in order for the flow rate to remain unchanged.
But if the nozzle feeds into a high pressure part of the pipe then things just slow down.