1. Lecture # 10: Hydrostatic Skeletons

2. Body Plan Evolution 1 cell cellular sheet cellular bilayer one way gut
bilayered canister
ecto-
derm
endo-
one way gut
mouth
anus
cephalization
mesoderm

5. Body Plan Evolution 1 cell cellular sheet cellular bilayer one way gut
bilayered canister
ecto-
derm
endo-
one way gut
mouth
anus
cephalization
mesoderm

8. coelom
ectoderm
mesoderm
endoderm
gut
coelom

9. pseudocoelom
ectoderm
mesoderm
endoderm
gut

20. How does stress in a worm depend on geometry?
Consider a hollow spherical animal….
slice in half d r P
P= internal pressure
r = radius
d= thickness P P
what is stress in wall?
Define tension, T, as force/length
then T = s x d
= r p / 2
T = ½ r p
s = force/area
= (p r2 p) / (2 p r d)
= (r p) / (2 d)
disk area ~ p r2
rim area ~ 2 p r d
LaPlace’s Law: Tension in wall of sphere is proportional to radius and pressure.

21. Consider a cylindrical animal….
2) slice in half
1) longitudinal slice
Equivalent to spherical case,
Thus longitudinal tension, TLis same as in sphere of equal radius:
TL = ½ r p
3) cap with
hemisphere

22. Consider a cylindrical animal….
1) transverse wedge r sc d
slice area
=2rd
rim area
=2 d d
sc = force/area
= (2 r d p) / (2 d d)
= r p / d
Again, TC = sc x d
TC = r p
Circumferential or ‘hoop stress’
is twice than longitudinal stress.
TC = 2 x TL

23. P Implications of LaPlace’s Law:
Small worm withstand greater pressure than large worms.
Large worms should have thicker walls.
Square cross sections should be rare. P P P P
Pierre-Simon Laplace
tension
is infinite

24. L
Consider a helical worm: L
Volume = p r2 L
Solve for volume in terms of q (helical angle):
D = L cos q
r = D sin q /(2 p )
Solve for dV/dq:
Maximum volume at q = 54.73o
V = D3 sin2 q cos q
4 p

25. muscle action
V = d3 sin2 q cos q
4 p
Permissible
Morpho-space
elliptical
profile
circular
section

28. Ontogenetic scaling of burrowing forces in the earthworm Lumbricus terrestris
Kim Quillin
J Exp Biol 203, (2000)