Will all four jets produce fountains at the same height?

[solarblast]

Suppose I have say a 40' long 3/4" garden hose stretched out linearly on a level surface. One end is attached to a faucet with maybe 30 psi. At 10', 20', 30', and 40' there are small vertical pipes from which will shoot water when the faucet is turned on. The end of the hose is capped. There's no friction in the hose. Will all four jets produce fountains at the same height? Suppose instead I had a faucet with circular attachment to which I could insert four 10' hoses with a jet at the end. Using the same pressure, would the jets be as high as the first example?

 

[Studiot]

There's no friction in the hose.

But you have entitled this 'Practical...'

 

[boneh3ad]

Including friction (which is, of course, practical) produces a very different answer from neglecting it.

 

[solarblast]

It is practical. It came about because a friend had a lawn problem similar to the first example. I happen to have a lawn sprinkler somewhat like the second example, and was curious about the distribution of water. Shrinking the problem to its barest form sometimes leads to insight for the real problem.

 

[256bits]

It is practical. It came about because a friend had a lawn problem similar to the first example. I happen to have a lawn sprinkler somewhat like the second example, and was curious about the distribution of water. Shrinking the problem to its barest form sometimes leads to insight for the real problem.

Sometimes but not always.
One could model the friction to a very low, negligable value by substiuting a large enough hose so that the velocity of the water in the hose is practicly reduced to zero. But then you would not have a garden hose anymore, but maybe something closer to the size of a fire hose or larger. In which case all 4 jets would rise to the same height.

With a real garden hose the height of the jets would diminish from the first to the last. Depending upon the amount of water flow from each jet, the last could become a mere trickle..

In other words if each jet was the size of a pinhole in the garden hose, all jets should reach the same approximate height. As the size of the hole increases, the difference in height of each jet will become more pronounced from first to last.

 

[boneh3ad]

It isn't practical because it doesn't give a solution that is practically useful. Ignoring friction would say that in your first example, the jets would all be the same height. However, if you look at the situation in reality, they would not be the same height but instead would get progressively shorter as you go downstream.

For the second situation, without friction they would all be the same height (nominally) as the fountains from the original example. In real life, they would all be approximately the same height as the first jet from the first example minus a little slop from the pressure loss due to friction in your manifold you describe.

So in short, it absolutely matters if you include friction. Without friction, this particular problem is not practical at all since it doesn't answer the fundamental questions you have correctly.

 

[solarblast]

What spawned this question was a friend who lives 150 miles from here. He had landscapers put in a watering system for his backyard, about 40x80'. It had four stations, sprinkler valves, put around the area. His psi was measured at 86(!). When all four stations were turned on, the arrangement was insufficient. It did not cover the area well. He called the city to see if they agreed that it should do the job. Yes, he had more than enough pressure. 3/4" underground pipes. It was finally resolved by pairing up to stations for one time of the day, and other pair for another part of the day.

Nevertheless, he was curious why such a high psi failed to water simultaneously. The landscapers and the city fellow had no idea. The first abstract example was intended to provide some reasonable insight into the answer. Is there an answer provided by some physics model?

BTW, I once had an irrigation problem for an area probably 4 times bigger than his area. I took the problem h/w store, and in about 20-30 min, the h/w store guy figured out adequate sizes for it, and used handbooks on flow, pipes, friction and pressure to work it out--successfully.

 

[Studiot]

Folks are often suprised how quickly the flow rate drops off in small(ish) bore pipes, even with high pressure, when you have multiple branches.
You need proper manifolds or tanks for this, which provide the necessary buffering, or pumps.