Science Buddies: "Ask an Expert"

My son's science fair project is to measure the time it takes for water to empty from one bottle to another when inverted (set up like an hour glass). He has roughly 6 different shapes of bottles to use. His hypothesis is that the larger the bottle, the faster it will take. I am stuck on offering him advice on research (his teacher said it would be tough - but failed to offer him any suggestions). Does anyone have any suggestions on what topics/principles to research. I barely remember something from high school referencing the size of an oriface affecting flow rate. Any suggestions would greatly help as he has spent two evenings on the computer and has gotten now where (and I have spent one evening and am no further along).

Thanks for the help,
Paul

Fluid Dynamics is a very large subject area. See http://en.wikipedia.org/wiki/Category:Fluid_mechanics as a starting point.

If your son only uses a single fluid (tap water at the same temperature and barametric pressure) in all experiments, then lots of variables become constant and it is much easier to predict the fluid behavior. Read up on the Scientific Method on this site to understand why one should eliminate variation in a well constructed experiment.

The height of the water in the inverted bottle and the size of the opening in the bottle will dramatically affect the pressure and force involved and thus the instantaneous flow rate.

You and your son also need to consider that in order for a fluid to be drained from a container, its volume must be replaced by something, usually another fluid, air. Getting two fluids to flow in opposite directions through a single opening smoothly will likely have a huge effect on the fluid exchange rate. Modeling this mathmatically with a fluid dynamic model is well beyond what any engineer wants to tackle.

If the container is thin walled and will deform, then the likely flow will be something like:
As the container volume decreases because of deforming, water exits the opening. Once the spring constants of the sides matches the force exerted by the remaining water, the container will start to expand and air will enter the container increasing its volume until the spring force reduces and the water forces again dominates and causes the container volume to shrink as water leaves. This cycle repeats and changes in frequency as the water leaves.

If you take a look at the design of gallon milk jugs, the hollow handle loop when on top provides a way for air to smoothly enter the jug as long as the jug angle doesn't cause the entire opening of the jug to be closed off by the liquid. Even when the opening is completely closed, the distance the air has to travel to reach the handle loop is shorter than the distance to reach the inside of the rest of the container. If you orient the hollow handle loop down, the behavior of how liquid exits the bottle will change.

I suspect that inserting a small diameter hose to the bottom of most bottles filled with water and holding the external end of the hose near the bottom and then inverting the bottle thus providing a smooth entry path for the replacement fluid air will cause the bottle to empty faster because the fluid exchange is smooth and not cyclical. Modeling fluid exchanges when the exchange path is not shared is considerably simpler because the pressures and forces aren't oscillating, but even this is well beyond the grade level.

His hypothesis is that the larger the bottle, the faster it will take

As worded, this hypothesis is flawed. A larger bottle can hold more liquid. Taken to extreme, a full 5 gallon gasolene can is going to take longer to empty than a full 1 gallon gasolene can using the same pour spout. How do you define larger? If you don't utilize the same amount of liquid in each experiment, then you have a variation that may or may not dominate and control the outcome. On the other hand, a one quart wide mouth canning jar and a one quart squeeze ketchup bottle hold the same volume; however, I suspect they won't empty in the same amount of time when inverted.

If your experimental method involves capturing all of the fluid from one bottle into an identical bottle, then you need to consider how you are going to seal the two bottles together so that there isn't any variation in the leakage to the outside between test samples. If the seal is permanent or semi-permanent, this methodology has the advantage that it maybe able to be exhibited without having to deal with open liquid. A simpler method of just using a large catch basin or sink might provide results faster and without the complication of having to come up with a good sealing method suitable for a variety of containers. I'm guessing that you won't be allowed to demonstrate this at exhibition, something about not wanting to provide an opportunity for others to get people wet.

Coming up with a testable hypothesis is the key to a good science fair project.

Craig,
Thank your for your reply. I guess I should have been more clear in my first post. He is using a variety of different shaped bottles, but all are at least 0.5L. In all tests, the fluid will be .5L of room temperature tap water (with 5 drops red food coloring to make it easier to observe). Most are between 1L and 1/2 gallon. Where the bottles are joined will be well sealed with rubber tape and duct tape as to eliminate (or drastically reduce) any leakage. We will probable have to insert a small straw as you stated (gotta figure out to do that). I'm not sure what would be appropriate reasearch for a 6th grader....what kind of key words should he be looking for? Is there a basic principle involved?

Hi aliesdad,

I believe that Poiseuille's equation is what you're looking for:

http://hyperphysics.phy-astr.gsu.edu/Hb ... s.html#poi

This would apply to the "pipe" section of your system -- the part with the narrow diameter where the necks of the bottles join, which hopefully has a constant radius. If the neck narrows gradually, or if your containers have varying geometries, then you really need to combine it with Bernoulli's equation to represent the whole system:

http://www.ac.wwu.edu/~vawter/PhysicsNe ... ation.html
http://hyperphysics.phy-astr.gsu.edu/Hb ... r.html#beq

(You can google either of those terms for additional explanations.)

One of the things that Craig is getting at is that there are a number of variables affecting the flow rate, and you want to control things so that you only vary one of them. "Bottle size" doesn't directly correspond to any one of the relevant variables, so you will probably need to modify that description in order to have a well-designed experiment. The pressure driving the flow will change depending on the depth of the water above the junction, which depends on both how much has already flowed through and the geometry of the bottle on top. Here are two possibilities:

--Keep the bottle geometry constant (cylindrically shaped would be ideal) and vary the diameter of the junction.
--Keep the junction diameter constant and vary the bottle geometry, ideally in one way, such as using cylinders of different diameters rather than some cylinders, some cones, etc. (A cylinder is only special in this case because its cross-sectional area is constant along its height, so you could also use a cube, but cylindrical bottles seem to be more common.)

Also, instead of providing a path for air to move between the two bottles to equalize the pressure, you can separately allow them to equilibrate with outside air. Just punch a hole in the bottle somehow in an area that won't be underwater (if they will be less than half-full, then the middle would work), insert a straw (maybe sticking into the bottle an inch or so so that water running down the sides won't enter it), and secure the straw and seal the area around with some kind of putty. Of course, you'll want to be careful not to introduce a large crack in the bottle.

Hope that helps,
Amanda