Water Hose and Pressure
I was watering my lawn recently when I noticed that if the water
pressure is too great, the end of the hose will flop around.
I am assuming that this is the only way the hose can find to
dissipate the excess energy created by the water pressure.
My question is first, am I correct in my assumtion? Second, can the
pattern of oscillation be predicted or is it a fairly random process?
A fire hose with high water pressure in it is "unstable". that is, if you
the hose out straight, and put water pressure in it, it is ok, it will stay
straight. but if even a slight amount of bending occurs along the length of
the hose, then the water pressure will act in such a way to make this kink
bigger. Any little kink will do to start things out, so it pretty much always
happens, once the pressure in the hose reaches a certain point relative to the
sturdyness of the hose (bigger, beefy hoses take more pressure).
You can see this yourself. Draw an imaginary hose. Make the lines of force
along the hose, straight lines of force. As the water gushes out the end, it
would push the hose straight back. Now pretend that there is a slight bow in
the hose, our kink. Now the lines of force (pressure) have a component
pointing to make part of the kink move further out, and the other side of the
kink to make the hose move the other way. if the hose cannot resist even this
small initial kinking force, it will kink all the more, the pressure will then
be pointing to make the kink even worse etc etc.The hose will flop around.
I think this is even called in mechanics books a "fire hose" instability.
My guess is that the end of the hose flops around because of the water
rushing out. If your hose is like most, it is not perfectly straight at
the end. This means that the water coming out the end of the hose is not
traveling in exactly the same direction as it was right before it reached
the end. This change in direction is a change in velocity (a vector
quantity), and consequently a change in the momentum of the water. By the
law of conservation of momentum, something else must experience a momentum
change of the same magnitude but opposite direction. In your case, that
something else is the hose. If the hose were firmly clamped, or if you
were to hold it tightly so that it dod not move, the earth itself would be
the something recoiling from the water (the effect would be so slight it
could not be noticed, but it is there all the same). This is the same
force that makes those whirlygig lawn waterers go around in circles.
Whether the oscillation of the end of your hose is predictable is not a
simple answer. Most likely, there are conditions of water flow and
positioning of the hose for which the hose will trace out a repeating
pattern. It is also likely that under other conditions, the hose can water
weenie along forever without once repeating itself (being at the same
position, pointing in the same direction, and moving in the same speed and
direction as at any time before). This is a condition known as
"deterministic chaos" or simply "chaos," a phenomenon that has received
intense study over the last decade. Many systems display "chaotic"
behavior, and your hose is probably one of them.
Richard Barrans Jr., Ph.D.
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Update: June 2012