if by Poiseuille’s Law, the greater the radius/diameter of a tube the faster the flow, why does water flow faster out of a hose when you put your thumb over the nozzle?
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Flow in terms of Poiseuille’s Law is a measure of current. It is how much total volume of fluid can traverse the pipe/tube.
However, what you are describing when you put your thumb over the nozzle is **pressure.** Flow can actually be higher in a low pressure system. Like if you dump a bucket, it has more flow than a hose for the amount of time that the water is leaving the bucket, but the pressure is very low.
Alternatively, when you put your thumb over the end of a nozzle, you are actually **reducing the flow**, by decreasing the total volume of water that comes out of the hose, but because there is less space at the end for the water to come out, the pressure increases. This is actually an offshoot of Bernoulli’s principle, dealing with speed and pressure as opposed to flow.
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