A U tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the relative density of spirit?

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The setup you described is a classic example of a U-tube manometer used to measure pressure differences. Here, we have water and methylated spirit separated by mercury.

To find the relative density of the spirit, we'll use the principle that the pressure at any point in a fluid at rest is the same throughout.

First, let's calculate the pressure difference between the two arms of the U-tube. We'll use the equation:

P=Patm+ρghP=Patm+ρgh

Where:

• PP is the pressure at a certain point,
• PatmPatm is the atmospheric pressure (which we'll assume cancels out in this scenario),
• ρρ is the density of the fluid,
• gg is the acceleration due to gravity, and
• hh is the height of the fluid column.

Since the pressure is the same in both arms, we can equate the pressure expressions for water and spirit:

ρwaterghwater=ρspiritghspiritρwaterghwater=ρspiritghspirit

Given that the height of water is 10.0 cm10.0cm and the height of spirit is 12.5 cm12.5cm, and knowing that the density of water is approximately 1000 kg/m31000kg/m3 (or 1.0 g/cm31.0g/cm3), we can find the relative density of spirit.

ρspiritρwater=hwaterhspiritρwaterρspirit=hspirithwater

ρspirit1000 kg/m3=10.0 cm12.5 cm1000kg/m3ρspirit=12.5cm10.0cm

ρspirit=10.012.5×1000 kg/m3ρspirit=12.510.0×1000kg/m3

ρspirit≈800 kg/m3ρspirit≈800kg/m3

So, the relative density of the spirit is approximately 0.80.8 times the density of water.

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