= Bridgman unsupported-area seal
{c}
{title2=$q=pA_p/A_{\rm seal}$}
= Unsupported-area seal
{synonym}
Consider an ideal pressure-driven closure plug with a large chamber-facing <projected area> $A_p$. Its opposite side seats against a smaller annular packing <surface area> $A_{\rm seal}$. The remaining projected part $A_u=A_p-A_{\rm seal}>0$ is the unsupported area: it has no opposing packing contact in that plane. Here $p$ is the chamber <pressure> relative to the exterior. Let $q$ denote the mean axial compressive contact <stress> on the packing, not the chamber's <hydrostatic stress>.
\Image[/bridgman-unsupported-area-force-balance.png]
{title=<Bridgman unsupported-area seal>: unequal <surface areas> make the packing load itself}
{description=Original functional section and <force> diagram, with no historical dimensions. Chamber <pressure> acts over $A_p$; the packing reaction acts over the smaller $A_{\rm seal}$. The central stem occupies the unsupported projected part $A_u$. Blue arrows show the chamber load on the closure; orange arrows show the opposing packing reaction. The drive <piston> that pressurizes the chamber is a separate experimental function.}
Neglect <friction>, the plug's <weight>, and other axial reactions. The plug's <Newton's second law> in static balance is
$$
pA_p-qA_{\rm seal}=0,\qquad
q=p\frac{A_p}{A_{\rm seal}}
=p\left(1+\frac{A_u}{A_{\rm seal}}\right)>p.
$$
The load is the same on both sides; its smaller supporting <surface area> raises the packing's mean contact <stress>. For a stipulated ratio $A_p/A_{\rm seal}=1.25$ and $p=1\,\mathrm{GPa}$, the ideal seating <stress> is $q=1.25\,\mathrm{GPa}$. Its excess over chamber <pressure> is $0.25\,\mathrm{GPa}$. Reducing $A_u$ to zero removes this amplification. This is the elementary <force> balance behind self-energizing seating, consistent with the lecture's Figure 1 caption.<General Survey of Certain Results in the Field of High-Pressure Physics by Percy Williams Bridgman>[p. 53, Figure 1 caption: packing compression maintained above liquid pressure; the formula here is an idealized derivation]{ref}
The relation is a model, not a universal sealing law. The mean axial contact <stress> need not equal the local contact <stress> along every possible leakage path. Confinement and <plasticity in continuum mechanics> determine whether the packing closes a gap or instead extrudes into it. <Friction> diverts load into other surfaces; material <plasticity in continuum mechanics> changes contact geometry; the vessel must carry its own <stress>. A finite initial seating load may also be needed before chamber <pressure> can develop. An arbitrarily small $A_{\rm seal}$ does not yield arbitrarily useful sealing: the assumptions fail when local deformation, extrusion or structural failure takes over.
Back to article page
