A long, clear, flexible tube is bent into a U shape (open at both ends), and...

A long, clear, flexible tube is bent into a U shape (open at both ends), and we pour water into it (density 1000 kg/m3) until the water reaches the same level on both vertical sides. Now we pour a 7 cm tall column of mercury into the left side (density 13,600 kg/m3), which does not mix with the water.

(a) When the fluids reach equilibrium, find the difference in elevation between the top of the mercury (on the left) and the top of the water (on the right). Which end is higher?

(b) Find the difference in elevations if the liquids are reversed, i.e., if the tube is first filled with mercury, then 7 cm of water is poured in at the left end. Which end is higher in this case?

Solutions

Expert Solution

a) Let us assume that the height on the right side of the tube which is filled with water at top is H_w and that on the left side which is filled with mercury at the top is H_m. Now the fluids are in equilibrium because the pressure on top of both sides of the tube is same. Therefore,

where P₀ is the atmospheric pressure.

Now since density of mercury is greater than density of water , so the height H_m has to be lesser than H_w.

Now the difference in height would be,

b) If mercury is poured first then water is added then

So again the water end would be at higher elevation.

The difference in height would be,

7-0.51 = 6.49 cm

genius_generous answered 1 month ago

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