Formula conventions and energy question

[tony873004]

** edit: did I forget how to use tex, or is there a system bug? I'll type the formulas normally below the tex
I'm reading through a textbook on natural disasters. There are some formulas that don't look right. Let me get some opinions here.

The velocity of tsunami waves depends on the water depth and gravity:
$${\rm{C}} = \sqrt {g{\rm{D}}}$$
C=sqrt(g D)
where
C = velocity in meters per second
D=depth in meters
g=gravitational acceleration (9.8 m/sec²)

I know the letters used are just man-made convention. I could say
$${\rm{j}} = \sqrt {y{\rm{Z}}}$$
j=sqrt(y/Z)
as long as I define what each variable or constant stands for. But it seems like most literature has adopted a common convention which is not followed here. I've never seen C used to represent velocity, unless its the speed of light, in which case I believe it should be lower case c. Velocity is usually lowercase v. Also, it seems to me that the common convention is that variables and constants are italicized while units are not. So it would seem to me that common convention should give this formula as
$$v = \sqrt {gd}$$
v=sqrt(gd)
The next formula in question is:

the period (P) of the pendulum, or total time for a back-and-forth smovement, is equal to the square root of the pendulum length (L):
$$P = \sqrt L$$

P=sqrt(L)
Here they're italicizing their variables, which is what I would expect. But this formula does not seem right. For example, if I plug in 1 meter for length, then my period becomes 1 m^1/2. It seems to me that a constant with units of time / distance² would be needed to make this formula dimentionally consistent. But since they're proportional, wouldn't it make more sense to say
$$P \propto \sqrt L$$
P propto L
?

The 3rd formula in question is:

Recall that the energy of a moving object is equal to its mass times the square of its velocity.
$${\rm{E = mC}}^{\rm{2}}$$
E=mC²

Again, nothing is italicized. It seems to me that everything here should be italicized. Again, C is used for velocity. Wouldn't it be more correct to say speed since no vector arrows are used. And should this formula have a 1/2 in front of m turning it into the kinetic energy formula? They're not talking about the mass converting into energy, as in Einstein's equation, but the energy of an asteroid striking Earth.

 

[Doc Al]

I suspect that the authors of that textbook are not physicists.

[FYI: The Latex problem is being looked into.]

 

[tony873004]

I suspect that the authors of that textbook are not physicists.

No, they're geologists. Maybe they have their own conventions?