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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Water in your pipes is intentionally pressurized by the water provider. Water will flow out any pipe/hose opening no matter what direction it’s facing, within reason. This is to the point that any leak is just automatically a disaster to your home.
There’s more a of a conservation-of-work thing going on here, in the style of hydraulic systems. A certain amount of pressure is coming from the water provider, and out a certain size hole it will come out with a certain speed to get the quantity of water out that it’s aiming for. By obstructing the pipe, to get the same quantity out, the speed out the smaller hole has to be higher.
It sound like Poiseuille’s Law has more to do with the viscosity of the fluid. Like if you suck water through a straw then compare that with a straw that’s two times the diameter, it’s almost the same but if you suck a milk shake through the same straws, there will be a bigger difference.
Edit, from wik “Poiseuille’s equation describes the pressure drop due to the **viscosity** of the fluid”
“The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of **constant circular cross-section** that is substantially longer than its diameter; and there is **no acceleration of fluid** in the pipe.”
By putting your thumb over the end, you’re changing the cross section and accelerating flow. Also you’re comparing the two with the same viscosity water.
It doesn’t flow any faster. It’ll still take the same amount of time to fill a given container. What putting your finger over the end does is increase the pressure at which the water leaves the hose. The volume of water is still the same.
Reread the law – it has a lot to do with pressure. Specifically, very little pressure. I’m not extremely familiar with fluid dynamics (more than average tho) but I don’t think this law applies to the situation you are mentioning.
When you put your finger over the end of the hose you are decreasing the cross section for the same volume of fluid – thus skyrocketing the pressure.
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.
there is a difference between flow rate (liters per second) and flow speed (meters per second)
eli5, if you have big buckets you can move lots of water without running, if you have tiny buckets you have to run really fast to keep up
Poiseuilles Law describes flow through a pipe. What squirts out the end of the hose is not in a pipe so Poiseuilles Law doesn’t really describe it.
It doesn’t flow faster out of a hose when you put your thumb over the nozzle, it just blows with more pressure because you are decreasing the size of the hole.
To add on to everyone else’s answers, a good way to visualize the difference is to fill buckets. Fill one with your thumb covering the tip of the hose, and fill one uncovered, and time both. This will show you the difference between velocity and volumetric flow rate.
I had this same problem in a fluids class in the early 90s and it stumped me too! When you put your thumb over the end of a hose you restrict the flow of water. Cover it completely and the flow stops entirely. There is then no flow, and no ‘drag’ on the walls of the hose. The pressure is then the same all the way from the source/manifold/pump/whatever to the tip of the hose. Open it a bit and viola! High pressure creating a powerful jet at the hose tip. Open it more and the flow rate, and hence viscous flow-induced drag, increases. Your hose doesn’t squirt quite as far.
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