What we result in piston pump cylinder

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RESULT FROM PRESSURE–PISTON–CYLINDER MATHEMATICS (RESULT ONLY)
From piston–cylinder pressure analysis (force balance, work–energy relation, and stability), applied analogously to a propellant tank, we get:
Pressure creates force proportional to area
Force increases linearly with pressure, but stored energy increases faster
Equilibrium exists only when internal pressure force = resisting force
Tank wall acts like a constrained piston
As pressure rises, wall strain replaces piston motion
Once resisting stress limit is reached, motion becomes uncontrolled
No stable equilibrium exists beyond critical pressure
Small pressure increase past critical causes rapid volume change
Rapid expansion converts pressure energy into kinetic energy
Stored elastic energy in walls is released instantly
System jumps from static equilibrium to dynamic failure
This transition is discontinuous (sudden), not gradual
Explosion corresponds to runaway piston motion
Containment fails when work done by pressure exceeds material work capacity
Higher pressure means exponentially higher failure severity
Pressurized tanks behave like locked pistons
Unlocking (rupture) releases all work potential at once
Failure timing depends on pressure, not fuel chemistry
Pressure alone is sufficient to cause explosion
Chemical burning is secondary
One-Line Piston–Cylinder Result
Pressure–piston–cylinder mathematics shows that a propellant tank explodes when the work potential of internal pressure exceeds the mechanical work capacity of the tank walls, causing instantaneous uncontrolled expansion.
FINAL UNIVERSAL RESULT (ALL METHODS AGREE)
(Control Volume + Thermodynamics + Piston–Cylinder)
Explosion occurs when internal pressure energy required by flow and thermodynamic equilibrium exceeds the structural work and force limits of containment, causing irreversible loss of equilibrium and violent expansion.
If you want, I can now express this as one clean formula, or show how engineers calculate the exact failure pressure.

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