How Does Adding a Lighter Liquid Affect Water Displacement in a Modified U-Tube?

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In the modified U-tube setup, the right arm is shorter and open at a height of 10.0 cm, while water is poured into the left arm until it flows out of the right arm. When a lighter liquid with a density of 0.830 g/cm3 is added to the left arm, it reaches a height of 9.20 cm without mixing with the water. The key question is to determine the volume of water displaced in the right arm as the lighter liquid is added. The displacement can be calculated based on the height difference and the cross-sectional area of the tube. Understanding the principles of fluid mechanics and buoyancy is essential for solving this problem.
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Figure 14-32 shows a modified U-tube: the right arm is shorter than the left arm. The open end of the right arm is height d = 10.0 cm above the laboratory bench. The radius throughout the tube is 1.30 cm. Water is gradually poured into the open end of the left arm until the water begins to flow out the open end of the right arm. Then a liquid of density 0.830 g/cm3 is gradually added to the left arm until its height in that arm is 9.20 cm (it does not mix with the water). How much water (in cm3) flows out of the right arm?
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How much water will be displaced - as you add a specific volume?
 
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