#7Q1) Mechanics and Properties of Matter

Determination of the relative density of a liquid using the U tube

DifficultyMedium

Est. Time45 mins

Required Apparatus

A U tube, two half-metre rulers, coconut oil, water, clamp stands, and a set square.

Scientific Theory

If $h_{w}$ is the height of the water column and $h_{l}$ the height of the liquid column from the common interface level, $\rho_{w}$ and $\rho_{l}$ the densities of water and liquid respectively and $p_{0}$ the atmospheric pressure, then,

p_{0}+h_{w}\rho_{w}g=p_{0}+h_{l}\rho_{l}g

h_{w}=(\frac{\rho_{l}}{\rho_{w}})h_{l}

Gradient of the graph $h_{w}$ against $h_{l} = \frac{\rho_{l}}{\rho_{w}} =$ Relative density of liquid.

Experimental Method

Attach the U tube vertically on to the stand. Fix close to this the vertical limbs the half-metre rulers on to the stand.
Pour a certain quantity of water (liquid of higher density) into one limb of the U tube and then pour into the other limb another quantity of coconut oil.
Using the set square obtain respective readings ( $x$ and $y$ ) for water meniscus and liquid meniscus and then the reading ( $z$ ) corresponding to the oil / water interface correctly.
Adding more of coconut oil (with lesser density) in small quantities into its limb, obtain about six sets of readings of $x$ , $y$ and $z$ .

Important Points1
The set square can be used for accurate determination of the reading relevant to the bottom of the liquid meniscus.
2
If the liquid of lower density (coconut oil) is poured first into the U tube then when water is poured coconut oil would creep on to the top of the water meniscus causing experimental errors. Hence the liquid of higher density (water) should be poured first into the U tube.
3
When pouring coconut oil care should be taken to prevent the common interface entering the curved portion of the U tube.