Uses
'numexec' = 2 executables,
paraboloid1.exe and paraboloid2.exe, via 'manager'.
Computes the profile
and the volume of a generalized paraboloid of revolution,
around the horizontal axis, given by the (adimensionalized) function
r ⁄ R = (h ⁄ H)β ,
where 0 ≤ h ≤ H and 0 ≤ r ≤ R or,
equivalently, Y = Xβ,
with X = h / H and Y = r / R,
both in [0, 1]. The paraboloid, such as a (drinking) glass, corresponds to
β = 1⁄2 (a cylinder, for β = 0).
From the parameters V, H and R,
only two can, obviously, be given, as nonzero. If three are given,
the last one (R) is ignored (computed).
Draws the plots of r and v vs. h,
with v the running volume for a solid of revolution,
v(h) = π
∫0h [r(x)]² dx .
The functions are simply
r ⁄ R = (h ⁄ H)β
and
v ⁄ V = (h ⁄ H)2 β +
1 , with β > −1 ⁄ 2. |
