What is the effect of applied pressure on a partially filled U-shaped tube?

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The discussion revolves around a U-shaped tube partially filled with water, where one end is capped and air is trapped at atmospheric pressure. When a gauge pressure of 1500 mmHg is applied to the open end, the task is to calculate the resulting height difference in the water columns on each side of the tube. Additionally, the discussion includes an explanation of how this system differs from a closed-ended manometer used for measuring absolute pressure. Participants are encouraged to attempt solving the problem before seeking help. The conversation emphasizes understanding the principles of fluid mechanics in relation to pressure changes in the tube.
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Homework Statement


A U-shaped tube is partially filled with water. One end of the tube is then capped
so that the air in that end is trapped (initially at atmospheric pressure). The tube has a bore
diameter of 10mm. The initial height of the entrapped air gap is 200mm.
A gauge pressure of 1500 mmHg is then applied to the other end of the tube.

a) Calculate the difference in the height of the water column on each side of the tube after
the pressure is applied.
b) Explain how the function of this system is different in principle to the function of a
closed ended manometer used to measure absolute pressure.
c) Make a plot of applied gauge pressure versus tube fluid height difference.

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