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Method of determining volume of water in an arbitrary container

  1. Sep 11, 2013 #1

    I'm trying to work through a problem in my head and am looking for a little guidance.

    I want to build a system that can be used to measure the volume of water inside a container of arbitrary size and shape. The application, in case you're curious, is the drinking water tanks of a sailboat. They tend to be shaped to conform to the hull, and moreover, they're subject to quite a bit of sloshing around.

    The traditional method of doing this is to use a float, but the result is that you're measuring water *level*, not water *volume*. If you want to convert to volume, you need an accurate model of the shape of the tank. You're also subject to the imprecision due to the water moving around in the tank.

    At first I thought that I could use a water pressure sensor at the bottom of the tank, but of course that would be measuring just the water column height - it would be agnostic to the shape of the vessel and therefore not useful in determining volume.

    What I really want is a way to measure the volume of the water inside the vessel, but I'm unsure how to do that practically. For my purposes, directly measuring either the mass or weight of the water would be close enough. But I can't use a scale in this application (remember, this is a water tank that's affixed to the hull of a boat), and I'm a little unclear how I would measure weight (force) directly.

    If anyone has any pointers, I'm all ears.

  2. jcsd
  3. Sep 11, 2013 #2
    I'm not sure if you can do this or not given what you described but could you use the concept of buoyancy at all? This boat is going into water correct? If you have the dry weight of the boat then technically the buoyancy can give you the wet weight and from there you can get the volume of water?
  4. Sep 11, 2013 #3
    That would work in theory, but in practice there are a bunch of other variables - not the least of which is whether there are people onboard - that affect buoyancy too. Good thought, though!
  5. Sep 11, 2013 #4


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    Maybe a dumb question, but why can't you just put a flow meter on the end of a hose, fill up the tank, and see how much water it took?
  6. Sep 11, 2013 #5


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    Most people are satisfied with tank tables which give capacity versus water level. Insofar as sloshing is concerned, you eyeball the average location of the water level. If it's sloshing too much, you should be paying attention to other things besides the water level in the tank.

    You don't necessarily have to calculate these tables. In harbor, when it is calm, you can prepare your own tables by calibration: after draining the tank, put a known quantity of water in the tank (say a gallon or 5 at the time) and record the corresponding level.
  7. Sep 11, 2013 #6
    Those are all great ideas! My goal is really to develop this into a system that would be plug-and-play, though, and would give just the information the user actually wants - what volume of water is in his tank. Calibrating tank level to volume tables is fine if it's one boat, but optimally I'm looking for a system that could be installed on any boat, with repeatable results and relatively straightforward installation.

    Re: sloshing: Agreed, but if a boat is under sail for a long period of time - say, on a oceanic passage - then it might be difficult to find a time when the hull was level and even remotely stable. Knowing how much water you have would be nice on trips like this, where rationing can become an issue.

    It's likely that I'm chasing an impossible goal... but thanks for the responses so far!
  8. Sep 11, 2013 #7


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    I think I've answered my own dumb question - you want not just the total volume of the tank, but how much water is in it at any one time.

    I think car fuel gauges, which have a similar problem in that the shape of the gas tank varies to conform to the space available in the car, just use a float, and then do a one-time calibration of the float to how much fuel is in the tank. They then have a circuit that translates the float level to the amount of fuel left. Couldn't you do something similar?
  9. Sep 11, 2013 #8
    well the only ways that I see to calculate the volume of water is either know the volume of the container and use a float like thing as described which you don't want to do, or you can determine the weight of the water which you can't use a scale for. Ultimately you may just have to suck it up and go with an option that is less ideal but will still give you the results you want like the float idea. Going back to phyzguy's idea though about the flow meter concept, couldn't you monitor how much you put into the tank and then also monitor how much is leaving the tank as you empty it to keep a running total? That could work as well.
  10. Sep 11, 2013 #9
    There isn't any practical way of measuring it directly so you use something like this.
  11. Sep 11, 2013 #10


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    Read SteamKing's post.
  12. Sep 11, 2013 #11
    Was that directed at me? I'll rephrase:

    There isn't any practical way of measuring it directly so you need to use some kind of calibrated conversion from level to volume, either manually as SteamKing suggested or automatically using something like this meter described here in exactly this application.
  13. Sep 11, 2013 #12
    Lower an appropriate sensor into the tank, and bounce waves off the walls in different directions. This can be used with appropriate software to measure the shape of the tank. If the sensor is below the water level, then the wave will be reflected off the surface of the water, and the surface will appear flat. The software can be set up to calculate the volume.
  14. Sep 12, 2013 #13
    Could you drop the float into an empty tank and monitor the volume as you fill it to calibrate the float?
  15. Sep 12, 2013 #14
    There are body fat measuring devices that measure the volume of the human body using pressure variations induced by a simple loudspeaker within a sealed chamber. The one I've read about has a large egg shaped chamber just big enough to hold a person. The person climbs in and the door is sealed air tight. As the speaker cone pushes into and out of the chamber, the volume of compressible air space changes slightly. A large person leaves less residual airspace volume and therefore the pressure changes faster when the speaker cone changes the volume. Flexibility in the walls, such as is likely with a flat wall, might defeat this measurement system.
  16. Sep 12, 2013 #15


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    There are several reciprocal dilution methods.

    Ignoring density changes. Trap x litres of water from the tank, heat it to y°C above the tank temperature, then mix it back into the tank, measure the change in temperature of the tank water as dTemp. That is a reciprocal function of tank volume.

    Put one kg of neutral density plastic beads, (say 1mm diameter) into the tank. Fit a fine mesh at the outlet to retain the beads in perpetuity. Stir the tank. Then either; View the density of beads low down in the tank.

    Or trap one litre of the mixed water with beads in a chamber, pump that litre through a sight tube with a mesh to retain the beads in the sight tube. View the column length of beads. Reverse the pump to clear the tube prior to the next measurement. Beads should pass freely through the pump.

    As above, but empty the sample through an insulated membrane with one small hole. Count the beads as they pass through the hole by monitoring the change in electrical conductivity across the membrane as the individual beads pass through.
  17. Sep 16, 2013 #16
    Have a float as in a regular car gas tank.

    Also have a separate calibrating mechanism that pumps up a measured amount of water/ submerges a wight of known volume, and checks what impact this has on the level of the float. This will give you a cross section of the tank at that point.

    You'd have to run this calibrating mechanism under controlled conditions in a harbor. Or you could continuously have the mechanism run the test and average the results at sea. Over time, it would build up a picture of the volume of the tank. I guess.

    Or maybe have a "submarine Roomba" type robot that swims around in the tank and maps out its shape?
  18. Sep 16, 2013 #17
    Strain gauges and accelerometers. Accelerometers measures the motion of the boat in rough waters to account for fluctuations in the data acquired by the strain gauge(s) on the tank mounts. Calibrate strain gauges in calm water using known volumes and then create a model to adjust readouts based on increased/decreased strain gauge readings during acceleration when pitching and rolling.

    Or, use an air compressor with metering to determine how much air it takes to pressurize the tank to some pressure when empty. Fill the tank, use the compressor to maintain tank pressure. As the tank empties, the air fills the void and is metered. As a known quantity of air has entered the tank, a known volume of water must have exited.
  19. Sep 18, 2013 #18


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    The one way I can think of is use an innocuous dopant that dissolves and monitor concentration at outlet. That'd allow an initial calibration of an arbitrarily shaped partially full tank and would be agnostic of sloshing.

    Trick is to choose the right dopant. Hopefully trace quantities, and easily dispersible and sensitively detected.

    Probably minute amounts of a radioisotope for a fuel tank or some innocuous molecule for a water tank.
  20. Sep 18, 2013 #19


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    Horrible idea on a boat. You'd report a massive hull leak as a full tank. :)
  21. Sep 18, 2013 #20


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    A modification of this idea that does away with the need for a metering compressor:

    Inject a tiny but accurately known aliquot of a gas into ullage space (not that hard; e.g. use a autoinjector with a microsyringe or a vial or something similar) . Wait.

    Choose gas so that it is innocuous, stable, insoluble in water & whose concentration is easily measured. That won't be so hard: Thermal conductivity, IR spectra, ionization and lots of ways to very accurately detect a gas concentration.

    You know conc. and moles injected. You can easily estimate ullage volume and hence the liquid volume.

    After a reading a blower can easily exhaust the probe molecule to be ready for next measurement. Alternatively just use a step change in conc. after pre measurement of baseline concentration.
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