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Because of the pressure difference. The small amount of air trapped in the pen will expand when the pressure in the aircraft reduces. Commercial aircraft pressures are set to about the same as those at 10,000 feet. There will be a higher pressure inside the pen than in the fuselage, the pressures will try to equalise out and may force some of the ink out of the pen in the process.

--NOTE--

The pen should not overflow when you - board - the airplane. It should only happen some time after take off. The pressure when you board the plane is no different from the pressure in the departure lounge.

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Q: Why a fountain pen overflows when you board an airplane?
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There was a change in pressure within the cabin. The pen's ink compartment was at higher pressure pressure when you boarded, but the cabin pressure must have decreased enough at altitude to cause the pen to leak.


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