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TOWER WITH CONSTANT PRESSURE, OR FUNNEL SURFACE

Cylindrical equation:
(tower) or ,
i.e.
(funnel).
Cartesian parametrization: (tower). Cartesian parametrization the coordinate lines of which are the asymptotic lines: (view opposite). |

The tower with constant pressure is the surface
of revolution obtained by rotating a logarithmic
curve around its asymptote.

Its name comes from the fact that, if this surface is
filled with a homogeneous material, then the pressure applied on any horizontal
section by the upper part is constant.

Derivation of the equation:
The pressure at the altitude z is equal to ;
assuming P constant and differentiating, we get the differential
equation:
which immediately gives the result, with . Remark: if we take the variation of g due to the
altitude into account, ,
we get the surface ,
with ,
represented opposite.
Much as the first one has a |

See also Gabriel's
horn.

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© Robert FERRÉOL 2017