# Marine Discussion: Physics of the fish tank

#### sumthin fishy

##### I eat spam
joephys said:
Light is basically elector-magnetic radiation................. vary efficient...
Those are the only errors Ive found. You are right, most of this was totally irrelavant to me, but interesting enough that I read the whole thing. Put in the simplest possible terms, I was able to understand the majority of it. GREAT JOB :thm:

#### vidiots

##### AC Members
Water Displacement

5. While we are still on the topic of water, lets talk about water displacement. I remember a post once where someone asked if, since water displaces the weight of an object, does that mean that rocks weigh less? Well, the short answer is no.

Archimedes principle states that an object displaces its weight in water if it is floating (and only floating). Basically if something that is 10 lbs is floating, then it displaces 10 lbs of water. The volume of the water displaced is the same volume of the amount of the object under water. That is why ice is mostly under water when it floats (its just slightly lighter than water). When an object doesn’t float, its weight is being supported by the bottom of the tank, and not the water, so it displaces its volume, not its weight. Thus rocks weigh the same in the tank as they do outside of it.

An explanation of #5, with a few more details. The answer that the true mass of the object is fixed, is correct. If you were to take a 1000g steel weight with a density of 8.0g/cm3 and add it to an aquarium that was sitting on top of a scale the weight of the aquarium would increase by 1000g. However if you were to place the scale inside the aquarium and put the 1000g weight on the scale you will find that the scale would indicate slightly less than 1000g. The buoyancy effect is still there even if the object sinks. The downward force of the 1000g weight on the submerged scale would be decreased by the weight of the water that it is displacing.

1000g / 8g/cm3 = 125 cm3 (volume of 1000g weight)

The volume of the 1000g weight is equal to the volume of the water that it is displacing. Water has a density of 1.0g/cm3

125cm3 * 1.0g/cm3 = 125g (weight of displaced water)
1000g - 125g = 875g (value indicated on the scale)

The scale submerged in the aquarium would indicate that the 1000g weight was only 875g. This is because the pan of the scale would be supporting 875g of the total weight and the water would be supporting the other 125g.

Being a metrologist I have to compensate for the buoyancy effect in air when making precision mass measurements. The math works the same only the density of air is approx 0.0012g/cm3.

As for what floats, any thing with a density less than water (<1.0g/cm3), and any object with a density greater than water will sink.

#### vidiots

##### AC Members
Pressure Measurement

A simple way of measuring water pressure is using a ruler to measure its verticle height or depth. Most unit converters will have inches of water listed as a pressure unit to select.
If you wanted to be ultra precise 1 psi is approximately equal to 27.73 inches of water at 20°C.

#### partsrep

##### Go Yankees!
joephys said:
Cylinder:
Find the distance across the tank and divide by 2 (R).
Find the height of the tank (H).
V= 3.14 x R^2 x H (Note: R^2=R squared, or RxR)

Bow fronts can be difficult to measure. If the bow is perfectly circular or parabolic then it maybe possible to calculate the volume, but it is a lot of work and more easily done in different coordinates. I don’t want to get into that since I said that I would keep the math on the easier side.
So I believe a quarter round corner tank would use the same equation as a cylindrical tank divided by four. Would you agree?

Excellent article Joephys.

#### born2lovefish

##### AC Members
Only error I found was "they" and I think it should have been the. Other than that nice article. I am in physics right now and some of that stuff makes sense. Very interesting.

#### joephys

##### AC Members
Thanks for the proof read sumthin fishy.

Vidiots, thanks for pointing that out. After reading that I agree I do need to explain it a little better. To me weight=mass x acceleration due to gravity, so the situation you described, I would call the apparent weight in the water. I will update it in a bit.

You would be correct partsrep.

I am glad that people are finding it at least some what interesting, and that I did an ok job keeping it in simple terms. I think that is the thing that keeps people away from science, I looks and sounds more difficult than it actually is.

#### beblondie

##### grand high exhalted poobah
Overall good article 3 probs i noticed
1.Proper volume needs to be inside measurements (if this was mentioned I missed it)
2. you need the weight of the empty tank+water weight (see chart here http://www.all-glass.com/services/index.html)
3. for every 50 lbs of decoration substrate,rocks etc etc. you will displace 2.2 gallons of water

#### vidiots

##### AC Members
At work I try to avoid using the word "weight" because it can lead to confusion. Instead I try to use "Mass" or "Force". It's difficult because we were all brought up using the word "weight" to mean both of these.

#### Bigbob55

##### AC Members
I'm a physics-EE major in college, a very well written article.

Most relevant things in there, not much that isn't important. A good read.

"3. for every 50 lbs of decoration substrate,rocks etc etc. you will displace 2.2 gallons of water"

that may be an average... but if something sinks completely, it will displace whatever volume it has. Remember in physics or chemistry when you wanted to find the volume of an irregularly shaped object you place it in a graduated cylinder or the likes and measure the difference in water level. Weight has almost nothing to do with displacement, provided the object sinks. A fiber-glass decoration which wieghs 5 lbs and displaces .5 cu. ft. will displace the same as a .5 cu. ft. chunk of iron weighing much more.
(didn't get any exact measurements of that , just pulling some examples from my head for principle)

BTW, what are your credentials, Joephys?