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Name: Peggy
Status: educator
Grade: K-3
Location: MD
Country: N/A
Date: 4/22/2005


Question:
Does the shape of an object make a difference in the amount of water it displaces? For example, if a lump of clay in the shape of a cube or sphere displaces 10 ml of water, would the same clay flattened displace the same amount of water? (My class tried this and in its flattened form, the clay displaced only 5 ml of water)


Replies:
A body submerged in a liquid displaces a volume of liquid equal to its volume, regardless of shape. However, there are some "practical" considerations. If the body is porous, or has air entrapped inside it, its gross geometric volume is less than the actual volume of body material. So in your case it is possible that the original lump of clay had trapped air inside that you "worked out" in flattening the clay. But the underlying principle is: Two solid or liquid insoluble materials cannot occupy the same space at the same time.

Vince Calder


Very mysterious! A certain amount of clay has a definite mass and, if the density is constant, it then must have a definite volume regardless of its shape. In some materials, the water could penetrate the surface and so for shapes with larger surface area the material would absorb more water and therefore displace less water. However, I would think that clay does not absorb much water.

If the clay is in the shape of a sphere, it has the smallest possible surface area. Of course, it is possible that the sphere is hollow, in which case it would clearly displace more water. If you do a careful measurement, I would bet a fair number of pennies that you would find the amount of water displaced is the same for all shapes within the experimental error. Let me know!

It would be interesting to know if the volume displaced in the case of a sphere is larger than the volume of the sphere or if the water displaced by the flattened clay is less than the volume of the clay if your measurements continue to get the same results..

Best, Dick Plano, Professor of Physics emeritus, Rutgers University


If there are not any empty volumes inside the shape, then the shape does not matter. If there are empty volumes (for example, if you make a hollow ball) then the clay can displace up to its own weight in water.

Tim Mooney


Peggy,

I am really sure that the shape does not make any difference. But it is pretty hard to make displacement measurements work accurately for small numbers of milliliters.

The problem is the meniscus: it can bulge upwards from your measuring tub by a variable amount. Suppose you are using a cooking pot 8 inches in diameter. For one measurement the water is perfectly flat before displacement draining and bulged-up afterwards. For the other measurement the water happened to be bulging before and flat afterwards. The bulge can be 0.5 mm high, and the area is 3.14 * (10cm)^2 = 314 cm2, so the volume of your possible error is 314 cm2 * 0.05 cm = = 15.7 cm3 =16 ml in any one measurement. If you had opposite errors in two measurements you could lose 30 ml.

I know that if you are careful you can do better than that most of the time, and you probably did. Your errors appeared to be about 5ml.

One way to evaluate errors is to repeat the experiment a lot. They might average away.

Personally, I would simply use 100 ml of clay, not 10 ml. That would solve your problem and be easy. Then if you get the same 5 ml discrepancies in your measurement, they will not be such a substantial percentage of the measured values..

But you could pursue making a more accurate measurement:

It helps to use a container with the smallest open top area you can easily fit your test samples into.

It might help to make the pouring-spout, where you want the water to spill out, more wettable. Water-wetting follows micro-grooves fairly well. So you could sand-paper across the rim-top and down a 1/4" streak on the outside wall for about 1" down. Do not sand-paper the inside wall at all. (We do not want the water to start siphoning and drip forever.) Then you have to declare the spilling done when the dripping gets to some slowness, like 10 seconds since the last drop.

It might help to invent ways to look at the mirror-like water surface to tell when it is exactly flat around the edges, neither bulging nor concave.

Better containers for displacement-measuring have tight-fitting flat-bottomed lids, so you can press the lid on and squeeze out any bulging water. The shape and size of the fully-enclosed water in a hard container can have errors much less than 0.1mm, instead of 0.5mm. If you are using a small metal cook pot with a slightly domed lid, turning the lid upside down may make it usable for you. This lid has the advantage that when you lift it up, all the dripping goes back into the pot and is not lost from the measurement.

Jim Swenson

PS- I am wondering how you control the amount of water clinging to the outside of the clay after the first time you immerse it. Perhaps some clays are easy to dry off.


Peggy,

There are several things you must be careful of in such an experiment. One item is of course that all of the clay is underwater. The second is absorption. When the clay is first submerged, it can absorb a great deal of water. In fact, the clay might eventually dissolve. If the clay is submerged a second time, water remaining within the clay can cause a problem. Also, air bubbles in the clay cause trouble. When molded into a cube, small air bubbles can form. When pressed flat, these bubbles can be squeezed out.

I suggest one of two things. You can wrap the clay in something like Reynold's Wrap to keep the water out. You can start with two identical lumps of clay. Form one into a cube and one into a pancake. Submerge each of them in identical water containers. See whether there is much difference.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College


Assuming you do not have any air pockets captured in the material then the amount of water displaced will be independent of the shape when the material is fully submerged.

In your experiment, is it possible that your cube or sphere was hollow? Did someone remove some of the clay while it was being flattened?

Greg Bradburn



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