Water in straw, then cut straw

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When a straw filled with water is lifted with a finger covering the top, the water remains inside due to air pressure differences. Gravity causes a slight decrease in the water level as the air pressure above the straw lowers. If the straw is cut while submerged, the remaining water may rise higher in the shorter straw to balance the new air pressure with the reduced water weight. This occurs because the external atmospheric pressure pushes up on the lighter column of water, potentially raising it further. The discussion highlights the relationship between air pressure, gravity, and the behavior of liquids in confined spaces.
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A straw is in a glass of water. I then cover the top of the straw with my finger and lift the straw out of the water. The water stays in the straw.

Is this correct?...

The water in the straw falls ever so little because gravity pulls it down. The air pressure above the straw decreases as a result, until the combination of that lowered pressure and the pressure of the water in the straw equal the atmospheric pressure.

If I were to then cut the straw somewhere in the liquid region so now the straw was shorter, and so there was now less water than before...

Would the water that remained in the straw be pushed up higher into the remaining segment of straw...in order to increase the air pressure above the water? So that the combination of the new air pressure inside the straw and the pressure of the decreased amount of water equalled the atmospheric pressure?
 
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If I read this correctly, you are reducing the weight of water that has to be supported by the difference in pressure (and so force on the cross-section area of the straw). Since the outside air is pushing upward on a lower weight of water, it should push it farther up the straw until the pressure from the 'compressed' air in the upper part of the straw balances the upward pressure
 
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