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The tube perpendicular to the filler neck goes to the coolant overflow bottle.
As the coolant heats up, it expands, it needs somewhere to expand in to, this is the coolant overflow bottle. As it cools, it contracts and pulls a vacuum and draws the coolant back into the coolant system.
The radiator cap is spring loaded (I believe it's 1.3 bar) and that pressure is needed for the coolant to vent into the overflow bottle. You shouldn't be ditching this to the floor, it goes to the coolant overflow bottle.
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As seen in the picture above.