This question (and the links I found for my answer)
Can a "dune" worm actually swim in sand?
got me thinking about how a sandworm might reduce friction while "swimming." One idea I hit on would be natural glass scales, lubricated with some kind of oil. There's only one species that forms silica shells, and while we're not entirely sure how diatoms do it, we have identified the proteins that are probably involved in the process.
https://en.wikipedia.org/wiki/Diatom#Silica_uptake_mechanism
This is kind of similar to this question,
How would or could a creature with a crystalline sail evolve?
but I'm not looking for evolutionary reasons for the scales. I know from experience that glass can be heavy. I'm wondering how thick the scales would have to be (maybe it's even a silica coating on a substrate?), and if something the size of a blue whale could support that much weight.
(Now, if you'll excuse me, I'm off to listen to this soundtrack...https://www.youtube.com/watch?v=yNY0D4z5FJ4&list=PLB066CAAD43DD2047&index=19&t=0s
You're welcome.)
Edit: When I first wrote this question, I used "blue whale" as a shorthand for "as big as the books make it sound." It's led to Frostfyre's excellent answer, but I can also see that I need to be more specific about physical dimensions. So instead of whales, let's try scaling up a green anaconda, since it already has the body shape we're after.
Assumptions for the average, real world anaconda, a cylinder with:
Length = 4 meters
radius = 0.1524 meters
Volume = 0.39 meters^3
surface Area = 3.98 meters^2
Mass = 50 kilogams
density (p) = 128.205 kg/m^3
weight (N) = 490 N
resting pressure (Pa) = 490 / 3.98 = 123.116 Pa
To stay in the ballpark size I was thinking of, we'll round the average blue whale's length up to 28 meters, making our multiplier 7. As per the Square-Cube Law...
This makes the assumptions for an imaginary giant sand worm, a cylinder with:
L = 4 * 7 = 28m
r = 0.1524 * 7 = 1.0668 m (not the widest mouth*)
V = πr2L = π * 1.0668 * 2 * 28 = 100.11 m^3or 0.39*7^3 = 133.77 m^3
A = 2πrL+2πr^2 = 194.83 m^2or 3.98*7^2 = 195.02 m^2
assuming density (p) remains the same, = 128.205 kg/m^3
M = pV = 128.205 * 100.11 = 12,834.6 kgor = 128.205 * 133.77 = 17,150 kg
N = 9.8 * 12,834.6 = 125,779.08 Nor = 9.8 * 17,150 = 168,070 N
resting Pressure = 125,779.08 N / 194.83 = 645.584 Paor 125,779.08 N / 195.02 = 644.955 Pa ...or 168,070 / 194.83 = 862.649 Paor 168,070 / 195.02 = 861.809 Pa
...................................
*Recalculating with a wider radius of 2.1336 gives us:
L = 28m
r = 2.1336 m
V = πr2L = π * 1.0668 * 2 * 28 = 400.44 m^3
A = 2πrL+2πr^2 = 403.97 m^2
assuming density (p) remains the same, = 128.205 kg/m^3
M = pV = 128.205 * 100.11 = 51,338.4 kg
N = 9.8 * 51,338.4 = 503,116.32 N
resting Pressure = 503,116.32 N / 403.97 = 1,245.43 Pa
...............................
So, back from dinner, and the Dune wiki says:
By anyone's standards, Sandworms could grow to an enormous size. Dr. Yueh cited that specimens "up to 450 meters long" were spotted by observers in the deep desert. To make a comparison, the largest animal on earth was believed to be a Blue whale measuring in at only 33 meters, or about 7% of a large sandworm's length.
...Some people believe that worms from 700 to even 1000 meters existed in the southern pole regions. This was neither confirmed nor denied.
However there is some contention regarding these estimates as Harvester Factories were said to be 120 meters long and still ... the sand displaced by its maw) was described as twice that width. Although this particular specimen was stated to be a large example of the species, a Sandworm with jaws 240 meters in diameter would exceed in size even those of myth which could supposedly be sighted in much deeper desert than the typical spice mining region.
http://dune.wikia.com/wiki/Sandworm
So let's try increasing the size even more to make a mythic sandworm.
L = 1000 m
r = 120 m
V = πr2L = π * 120 * 2 * 1000 = 753,982.2 m^3
A = 2πrL+2πr^2 = 844,460.1 m^2
Let's round density (p) up, = 130 kg/m^3
M = pV = 130 * 753,982.2 = 98,017,686 kg
N = 9.8 * 98,017,686 = 960,573,322.8 N
resting Pressure = 960,573,322.8 N / 844,460.1 = 1137.500 Pa
