[mark-r]

I once worked with a guy who had just bought a surplus cylindrical water tank, and wanted to get an idea of what it would weigh when filled. I asked him for the dimensions and multiplied each by 2.5 to convert to approximately centimeters. Then I multiplied the diameter by 3, approximating pi. I converted each to the nearest power of 2 so I could multiply by adding the exponents. Assuming 1 cubic cm of water is 1 gram, I had the log2 weight in grams. Then I subtracted 10 to divide by 1024, getting approximate kilograms. Then added 1 to get approximate pounds. Finally took 2 to the power of the result. By the time he finished telling me the dimensions, I had an answer for him.

[jessaustin]

How would one use the diameter to determine weight? Do we square it then divide by four?

[mark-r]

In metric, the weight of water in grams is equal to the volume in cubic centimeters, by definition. The volume of a cylinder is the area of the circle times the length. The area of a circle is pi * r^2. So my description above skipped a step or two.

[zokier]

> In metric, the weight of water in grams is equal to the volume in cubic centimeters, by definition.

Just to clarify this is not exactly true. It was the original idea, but pretty quickly they realized that it wasn't a practical definition and kilogram ended up being defined by a standard reference object which was carefully stored in a vault in Paris and thus being disconnected from the meter and the density of water. Finally in 2019 kilogram was redefined again in terms of natural constants in the great SI unit upheaval. Although sadly the new definition is not very intuitive to understand.

[mark-r]

I'm sure the updates to the Kilogram definition tried to keep it as close to the original as possible, right? The difference pales in comparison to the other shortcuts I was taking.

[abduhl]

I have no idea what the GP is doing but you would just do

Pi * D^2 / 4 * H * 62.4

Where D is tank diameter in ft H is tank height in ft and 62.4 is the unit weight of water in lbs per cubic foot. Divide by 144 of D is in inches and 12 if H is in inches.

Or if you want to be real lazy you can see Pi/4*62.4 is ~49 and round to 50.

[Symbiote]

Do most people know 62.4 lb/ft³?

The equivalent metric factor is 1 g/cm³ or 1 kg/L [1] so with D and H in centimeters the calculation is

  π D²/4 × H

kilograms of water.

[1] Assuming we're talking about a normal water tank, not a space rocket. Density varies with temperature, it's 0.9970474 g/cm³ at 25 °C.

[abduhl]

The unit weight of water being 62.4 pcf is probably not known by most people - most people don’t think in cubic feet. The more likely (and less useful) number most people know is ~8 lbs per gallon.