A closed container is partially filled with water. Initially, the air above the

Question

A closed container is partially filled with water. Initially, the air above the water is at atmospheric pressure (1.01×105Pa) and the gauge pressure at the bottom of the water is 2500Pa. Then additional air is pumped in, increasing the pressure of the air above the water by 1500Pa

What then is the gauge pressure at the bottom of the water?

By how much must the water level in the container be reduced, by drawing some water out through a valve at the bottom of the container, to return the gauge pressure at the bottom of the water to its original value of 2500Pa? The pressure of the air above the water is maintained at 1500Pa above atmospheric pressure.

Explanation / Answer

P1 = gh1 = 2500 Pa

=> h1 = 2500/g

After increasing the pressure of air above the water by 1500 Pa,

new gauge pressure, P2 = 1500 + gh1 = 1500 + 2500 = 4000 Pa

Let 'h' be the reduced water level.

Then,

1500 + gh = 2500

=> h = 1000/g

Reduction in water level, h = h1 - h = (2500 - 1000) / g = 1500 / (1000 * 9.81) = 15.29 cm

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