Friction + Bernoulli's Equation

[ShamelessGit]

I was watering my garden the other day, and I noticed (obviously), that the water came out of the hose faster if I stuck my thumb at the end of the hose. Then I suddenly remembered that in physics class, I was taught that gravity-powered water pressure should result in an exit velocity which was only dependent on the height of the water. Our water comes from a water tower, so I was confused about why putting my thumb on the hose should make a difference to the velocity. I asked my father if there was a water pump in between the water tower and our house, and he insisted that there was not. Then I asked him about this physics problem, and he said that he was sure that friction in the pipe was the cause of the behavior of the water in the hose.


I have attached a word document in which I modeled friction. I got an answer which (qualitatively) fits reality. I just thought it was interesting that I (and I assume many other people too) have relied on pinching the hose to get water to come out faster for a long time without ever thinking about how it happened.

 

[BOAS]

I'm on a mobile device and haven't looked at your document but I think I can help.

The reason that the velocity of the water increases when you decrease the size of the hole it leaves by is actually to conserve mass!

You can look up the continuity equation, but it basically says that the volume of water flowing into a pipe must equal the volume of water flowing out of the pipe. This assumes a non compressible fluid and a rigid pipe.

So, let's say that the amount of water flowing into your hose is constant. If the nozzle is constricted then water must leave faster to empty the same amount.

Going through the derivation from first principles of bernoullis equation would probably make this even clearer.

Hope that helps!

 

[russ_watters]

The way I explain this is by the source of the pressure loss:

With the pipe open, the flow is high and the losses happen throughout the pipe, resulting in the exiting water having near zero total pressure.

When you put your thumb over the end, you create a large restriction, lowering the flow. With low flow, there is almost no pressure loss anywhere else but at your thumb, so all of that available pressure gets used to accelerate the small amount of water past your thumb.

So your father's explanation is basically correct.

 

[ShamelessGit]

Russ Watters explanation is exactly how I modeled it in the document. By the way, I made a sign error mistake in the word document, but apart from that I think it is correct.

 

[PJC01]

I find your observations and questions very interesting. The behavior of water in a hose is actually a combination of both Bernoulli's equation and the effects of friction. Bernoulli's equation states that as the velocity of a fluid increases, its pressure decreases. This is due to the conservation of energy principle in fluid flow. In the case of your garden hose, when you put your thumb at the end, you are essentially creating a smaller opening for the water to flow through, causing it to speed up and therefore decrease in pressure.

However, the effects of friction cannot be ignored. As water travels through the hose, it encounters resistance from the walls of the hose, which slows it down and causes some energy to be lost. This results in a decrease in velocity and an increase in pressure. When you put your thumb at the end of the hose, you are essentially reducing the amount of space for the water to flow through, which increases the amount of friction and therefore decreases the velocity even further.

It is also important to consider the source of the water. While your father may be correct in saying that there is no water pump between the water tower and your house, there may be one at the water tower itself. This pump would increase the pressure of the water, causing it to flow faster through the hose and resulting in a higher velocity even without your thumb at the end.

Your modeling of friction in a word document is a great way to visualize and understand the effects it has on the behavior of water in a hose. It is a great example of how science can help us understand everyday phenomena that we may take for granted. Keep up the curiosity and exploration, it is what drives us to discover and learn more about the world around us.