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Pop quiz

October 2, 2007

You need to refill your water bottle, so you go to a nearby pair of drinking fountains, one of which is closer to the ground to permit easier access by children, people in wheelchairs, et al. To fill your bottle as completely as possible, you should use…
A. the higher fountain
B. the lower fountain
C. whichever one has a better stream, which you can’t know until you’ve tried both

Until recently, I had never thought carefully about this question. That must be why I’ve gotten it wrong hundreds of times over the past 15 years or so. Almost invariably, I’d activate the higher fountain, be disappointed by its sad little trickle of water, try the lower fountain, and receive a stronger, higher-arching stream that could be more easily directed into the bottle. I never learned anything from this experience because I always attributed the better flow of the lower fountain to “luck.” Such a scientific mind, eh?

Then last week it occurred to me that pressure is needed to drive water through the fountains, and that the higher the water climbs against gravity, the more the pressure will dissipate. The water is under higher pressure when it exits the lower fountain, so it’s ejected more forcefully.

I don’t know why it took me so long to realize such a simple truth, but the reason probably relates to the fact that I’m a biologist rather than a physicist.

6 comments

  1. Ha! I don't think I've ever thought about it either. Now that I am thinking about it…the lower one has more kid slobber though.


  2. I'm inclined to pick neither. Icky, gooey, nasty stuff is probably all over that park fountain. Whether it's kid slobber on the bottom or adult nastiness on the top.Ew.


  3. Being short, I naturally go for the lower one. But now it makes more sense why the stream is bigger. I usually hold the bottle way out to avoid the slime. Besides, a little slime is good for the immune system! Keeps it working!I think I saw you at Cougar today and should have said hi. You were getting Phil out of the car (I had the kayak racks – or 'lawn chairs' on top of my car). Anyway, thanks for being out there!


  4. sometimes one is amazed by the most simplest discoveries that expand beyond the depths of what we have learned in grad school. I often find these discoveries about nature when running on trail. For instance, why do geese lead in a (V) formation? Why not some other shape? Why does every flock do a (V?). Maybe somethings are left unknown.


  5. Oh…like you, Mr Bernoulli would answer C; but, Mr Bernoulli's equation would tell you the pressure of the water exiting the lower and higher fountains is virtually the same. The lower fountain has a higher velocity when it exits and therefore rises higher above the fountain exit than for the higher fountain!Now can you give me the equation that tells me how to run sub 5 min miles?


  6. Al:Thanks so much for this comment as well as your subsequent offline comments. I'm embarrassed that my entry was so vague with respect to the forces involved.I initially had trouble understanding what you meant, since the Bernoulli equation has so many forms and applications. I like the version that you sent me:P1 + 0.5*rho*v1^2 + rho*g*h1 = P2 + 0.5*rho*v2^2 + rho*g*h2where rho is the fluid's density, v is the fluid's velocity, g is acceleration due to gravity, and h is the fluid's height.As you explained to me, the simple P term is the the external force on the matter at the boundaries of the control system; the 0.5*rho*v^2 term is the dynamic pressure (corresponding to the kinetic energy of the fluid); and the rho*g*h term is the hydrostatic pressure (corresponding to the potential energy of the fluid).Applying this equation to the two fountains, let's say that the left side of the equation refers to the lower fountain and the right side to the higher fountain. You point out that, for all practical purposes, the atmospheric pressure is the same for both (P1 = P2). However, you add, the water exiting the lower fountain has a higher velocity (v1 > v2) and thus a higher dynamic pressure, which it has gained at the expense of a lower hydrostatic pressure (h1 < h2).The whole problem thus boils down to the interconversion of potential energy and kinetic energy — how one can be gained at the expense of the other. I sure wish I had framed the issue that way originally!



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