# Why water can fly faster (then slower) when you press the water hose with your thumb?

If you press your thumb on a water hose, you can make the water flow faster, but if you try to make the hole even smaller, you will find that the water velocity starts to decrease. Why?

Also, the velocity of the water should be

$v = \sqrt{\frac{2P}{ρ}}$
where P is water pressure and $ρ$ is water density.

This means that the water pressure must increased when you decreased the hole area, but shouldn't the water pressure be independent to the flow rate?

$$A_{1}V_{1}=A_{2}V_{2};$$
where $$V_{2}$$ is the hose velocity. If you reduce the area $$A_{2}$$, $$V_{2}$$ increases.