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Q & A: hose nozzle speeds

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Most recent answer: 01/13/2011
One evening,a husband and wife are working in their garden. While watering the grass, the wife holds the hose horizontally and the water flows from the end of the hose. She twists the nozzle of the hose to partially close it and suddenly the water shoots farther from the end of the hose. This seems odd to her husband, who wonders, "Why does the stream of water travel farther, since it appears that less water is flowing from the end of the hose?" My challenge is to give a scientific explanation for this unnatural phenomenom.
- venus (age 34)
Nice question.
The flow through the hose is limited both by how hard it is to push the water through the hose and how hard it is to push it out the nozzle. The nozzle is much shorter than the hose, so when open it provides only a little bit of the resistance to flow. As you start to narrow its opening its resistance goes up, but not enough to slow the total flow much, because the hose resistance is still bigger.

Now let's look at the water flow as it leaves the nozzle. When the nozzle is wide open (say 1 cm2 opening) a flow of 1000cm3/second would require the exit velocity to be 1000 cm/s. If the nozzle is narrowed to say 0.5 cm2 the flow will drop a little (maybe to 900 cm3/s) but the exit velocity now must be 900/0.5=1800 cm/s. So the stream will go farther.

This description is a little over-simplified, but I think you get the idea.

Mike W.

(published on 10/18/2008)

Follow-Up #1: water momentum conserved

The phenomenon could have been more easily explained using law of conservation of momentum. The mass of water exiting the hose nozzle gets reduced when squeezed, so the law requires that its velocity must increase. Same thing happens when space rockets dispense with their burnt out fuel tanks. Isn't it?
- Indrajit Kuri
New Delhi, India
The momentum of the water isn't really conserved here, because there are forces on the water stream from the nozzle and from the pressure from the water source. As the nozzle is shut down, the total flow falls to zero, so the momentum is not a fixed number.

Rockets are in a way simpler, since other than gravity they typically have no external forces on them.

Mike W.

(published on 01/13/2011)

Follow-up on this answer.