There is an old warning on mountain flying that wind flowing through a narrow valley will cause a venturi effect thus causing a drop in static pressure and making our little Cessna fly lower than indicated, possibly hitting some hidden mountain peak. I'm certain I know the answer to this one, but I'd like to hear someone explain it better, so here is my question:

You fly a Cessna 172 level at FL50 (pressure altitude) with a huge 40kts headwind. You need to traverse a narrow valley passing between two huge peaks on either side. Will your airplane fly at a constant true altitude in a straight line, or will the venturi effect caused by the wind and the valley cause our aircraft to sink while passing through the valley

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