A U-tube contains water. In one limb, a 20 cm high oil column of density 800 kg/m³ is poured over the water. Both limbs are open to the atmosphere. The difference between the two free-surface levels is N cm. Find N.
Physics · Fluid Mechanics · question based on variation of pressure
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Question

A U-tube contains water. In one limb, a 20 cm high oil column of density 800 kg/m³ is poured over the water. Both limbs are open to the atmosphere. The difference between the two free-surface levels is N cm. Find N.

Physics · Fluid Mechanics · question based on variation of pressure

G1 Physics · Accepted Answer

Let h be the height of water, measured upward from the oil-water interface to the water free surface in the other limb. At the level of the oil-water interface, pressures in the two limbs must be equal. Therefore, ρ(oil)g(20 cm) = ρ(water)gh. Hence, 800×20 = 1000×h. Therefore, h = 16 cm. The oil free surface is 20 cm above the interface, whereas the water free surface is 16 cm above the same level. Thus the free-surface difference is 20−16 = 4 cm. Hence, N = 4.