This morning I worked out the equation relating light intensity to tank size and bulb wattage. It isn't that difficult to do, if you can do integral calculus. The explanation is:

Tubular fluorescents usually produce a fixed amount of light per inch of length, consuming a fixed amount of watts per inch of length. Four foot long T12 bulbs are 40 watt bulbs, 10 watts per foot. 2 foot T12's are 20 watts, etc. So, a tubular fluorescent bulb is a length of light above the tank with about the same brightness per inch all along its length. Do a mind experiment: Take a four foot long tank, with a four foot long bulb above it. Now insert a pair of opaque dividers in the tank so that there is two feet between them and only two feet of the bulb lights the substrate between them. Same bulb, same tank, but the light intensity at the substrate drops considerably. That is because that section no longer gets light from the blocked off ends of the four foot long bulb. Move those opaque dividers close together, so they are an inch apart - the substrate in that section is almost dim, but it is still the same bulb up there.

The reason a ten gallon tank needs more wattage of light to get the same light intensity is that it doesn't have as long a bulb above it shining light from the whole length of the bulb on every spot on the substrate.

Now to the math: (only the solution, not the process)

The light intensity from a bulb producing a fixed amount of light per inch of length on a substrate at a distance "D" from the bulb, where the tank is "L" long is proportional to the natural log of the following ratio: [L/2 + the square root of D squared plus L/2 squared] divided by D.

Figuring all of that out for various tank sizes gives the following table:

This table shows that a ten gallon tank gets only about a quarter as much light intensity at the substrate as a 55 gallon tank, when both are lighted with T8 or T5, etc. bulbs. It also shows that a 125 gallon tank gets about 30% more light intensity at the substrate as a 55 gallon tank when both are lighted with T8, T5, etc. bulbs.

So, if a 55 gallon tank needs one 54 watt T5 bulb to get adequate light at the substrate, a 10 gallon tank would need about 40 watts of T5 light for the same light intensity.

Being a retired engineer, I find this fascinating.

EDIT: Another question that comes up is how much more light do we need for a deep tank, like a standard 90 gallon tank. This analysis gives that answer too. For a 90 gallon tank we only need about 15% more bulb wattage than for a 55 gallon tank to get the same light intensity at the substrate.

This analysis only works for a tubular light that extends the length of the tank. It doesn't work for any light fixture that has a bulb shorter than the tank, including HQI or Power Compact bulbs which are shorter than the tank is long.