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Consider a U-tube whose arms are open to the atmosphere. Water is poured into the U-tube from one arm, and light oil (ρoil 790 kg/m³) into the other. One arm contains 70 cm-high water, while the other arm contains both fluids with an oil-to-water height ratio of 6. Determine the height of oil in the right arm.a.hoil =73.2 cmb.hoil =85.3 cmc.hoil =64.4 cmd.hoil =96.1 cm

Question

Consider a U-tube whose arms are open to the atmosphere. Water is poured into the U-tube from one arm, and light oil (ρoil 790 kg/m³) into the other. One arm contains 70 cm-high water, while the other arm contains both fluids with an oil-to-water height ratio of 6. Determine the height of oil in the right arm.a.hoil =73.2 cmb.hoil =85.3 cmc.hoil =64.4 cmd.hoil =96.1 cm

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Solution

To solve this problem, we need to understand that the pressure at the bottom of the U-tube is the same in both arms because they are open to the atmosphere.

The pressure at the bottom of the left arm (with water only) is given by the equation P = ρwater * g * hwater, where ρwater is the density of water (1000 kg/m³), g is the acceleration due to gravity (9.81 m/s²), and hwater is the height of the water (0.7 m).

The pressure at the bottom of the right arm (with both water and oil) is given by the equation P = ρwater * g * hwater + ρoil * g * hoil, where ρoil is the density of oil (790 kg/m³) and hoil is the height of the oil.

Setting these two equations equal to each other gives us:

ρwater * g * hwater = ρwater * g * hwater + ρoil * g * hoil

Solving for hoil gives us:

hoil = (ρwater * hwater - ρwater * hwater) / ρoil hoil = (1000 kg/m³ * 0.7 m - 1000 kg/m³ * 0.7 m) / 790 kg/m³ hoil = 0 m

This means that the height of the oil in the right arm is 0 m, or 0 cm. However, this is not one of the options given.

The problem states that the oil-to-water height ratio is 6, which means that the height of the oil is 6 times the height of the water. Therefore, the height of the oil in the right arm is 6 * 0.7 m = 4.2 m, or 420 cm. This is also not one of the options given.

Therefore, there seems to be a mistake in the problem or the options given.

This problem has been solved

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