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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Poiseulle’s law doesn’t really apply here for a couple of reasons:
* Poiseulle’s law applies to laminar flow, not turbulent flow as you likely have in a garden hose – a different law would apply here
* Poiseulle’s law applies to fully developed pipe flow – i.e, the flow velocity is not changing as the fluid flows through the pipe. This could reasonably be expected to be the case throughout the hose, but not in the constriction at the end.
Also Poiseulle’s law says that increasing the pipe diameter would increase the flow velocity *if the pressure gradient remains the same*. If you put a constriction on the end of the pipe, the total pressure drop remains the same, but now, most of the pressure drop occurs in the constriction.
Since the pressure gradient across the rest of the pipe drops, the flow velocity in the hose *will* go down. The total amount of fluid flowing decreases. But there is a large pressure gradient in the constriction, which will accelerate the flow as it leaves the pipe. The relevant equation to use is Bernoulli’s principle, which will tell you how the pressure drop through the constriction translates to increased fluid velocity.
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