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?
In: 7
Poiseuille is for the entire hose. You’re changing the end only.
https://www.physlink.com/education/askexperts/ae185.cfm#:~:text=When%20you%20put%20your%20finger%20over%20the%20tip%20of%20the,water%20flowing%20out%20a%20constant).
https://physics.stackexchange.com/questions/384972/why-water-can-fly-faster-then-slower-when-you-press-the-water-hose-with-your-t
As the other poster said, you might be confusing the stream velocity for the volumetric flow rate. Another thing that comes into play is that if the flow in the hose is reduced because of the nozzle, the frictional losses in the hose are less.
To find the flow rate, you multiply the pressure by the velocity. When you put your thumb over the hose, you obstruct the flow area, and the flow velocity goes up.
Same amount of water through a narrower space, with the same amount of pressure behind it (your thumb does technically push back, but negligibly) means the water has to move faster to flow out.
There’s a restriction in flow before the water enters the hose, so with nothing blocking the end, the pressure in the hose is very close to air pressure.
If you put your thumb over the nozzle, the pressure can increase up to whatever the pressure is inside the water pipes before the earlier restriction. The velocity of the water increases, but the total flow decreases, because the cross sectional area is smaller.
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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