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Picture two liquid spray nozzles spaced vertically by some distance. Both nozzles are connected via flexible tubing to a single valve via a tee. Once the nozzle lines are full of fluid how can i prevent the fluid from draining out the bottom nozzle when the valve is shut. Would routing the lower nozzle tubing to the same height as the higher nozzle work? Some other physics magic I could employ? I prefer not to use check valves, two valves, or any additional hardware.

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Add another valve onto one of the tees? Inject an air-gap into the lines (with an appropriate configuration of lines)?

Once you have a continuous and unbroken line of liquid that is free to move, the entire system simply acts as a container in which the liquid will find the lowest level (and draw air in at the highest).

So without additional control hardware of some kind, you cannot allow the nozzles to remain in a configuration where they are at differing levels once the pressure is turned off, if you want the supply lines to each nozzle to retain unvented liquid.

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Let me see if I understand your setup. You have two nozzles in a vertical plane, one above the other, and connected by a t-section of pipe to a common valve: the setup

And you wish to keep a fluid from dribbling out of the lower nozzle (B) when the valve is closed, with no additional hardware, and preferably with some 'physics magic'?

Ok. I have two solutions for you:

1. Use your thumb

Plug the top nozzle (A) with something. I recommend your thumb: use your thumb

As long as the lower nozzle isn't too big, the fluid won't be able to escape assuming: $$h \lt \frac{P_a}{\rho g}$$

where $h$ is the height between nozzles, $\rho$ is the density of the fluid and $P_a$ and $g$ are atmospheric pressure and gravitational acceleration at sea level. If you are pumping a water-based fluid through the nozzles, then $h$ < 10.3 meters, or 33 feet 9-1/2 inches. Sadly, if you are spraying mercury, the distance is much less: 0.76 meters or 2-1/2 feet. (You might want to wear a glove if it is indeed mercury you are spraying before you use your thumb).

2. Thumbs count as 'additional hardware'. Enter the accelerating reference frame:

This is my preferred answer, as it is more "pure" and requires no additional hardware*. You can re-orient, or even eliminate, gravitational effects by accelerating the the nozzles. Then the apparent gravitational acceleration will be: $$ \vec g_a = \vec g - \vec a$$

$g_a = 0$ when $a = g$, so apparently free-fall induces weightlessness. No fluid weight, no pressure differential between nozzles A and B and no annoying dribbles. I recommend a free-fall with a modest tangential velocity around ~9000 m/s at a height of about 300,000 m for starters.

*You will need to start a rocket company first, however (so don't wait too long). angel emoji

In all seriousness. Can you not put plugs over the nozzles?

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This apparatus is for a cattle sprayer... the cattle walk through, a sensor is tripped and the valve opens and then closes when the cow exits.

The accelerating frame isn't feasible because I don't want to have to teach the cows zero gravity ambulation.

I've decided to use a check valve on the upper nozzle, kinda like your 'thumb' on top of a straw.

Thanks

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  • $\begingroup$ A solution should be as simple as possible - but no simpler! $\endgroup$ – Steve Feb 7 '18 at 13:03

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