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  4. A U tube with both ends open to atmosphere is partially filled with water reaching a mark of 45 mm. An immiscible liquid is poured into one side until it stands at a distance of 5 mm above the water level on the other side. Meanwhile water level rises by 40 mm from its original level. Density of liquid is kg / m 3.

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Q. A $U$ tube with both ends open to atmosphere is partially filled with water reaching a mark of $45\, mm$. An immiscible liquid is poured into one side until it stands at a distance of $5\, mm$ above the water level on the other side. Meanwhile water level rises by $40\, mm$ from its original level. Density of liquid is________ $kg / m ^{3}$.

Mechanical Properties of Fluids

Solution:

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The system is in equilibrium and pressure on both sides is equal.
This means, $h _{ w } \rho_{ w } g = h _{0} \rho_{0} g$
$\therefore \rho_{0}=\frac{h_{w} \rho_{w}}{h_{0}}=\frac{85 \times 10^{-3} \times 10^{3}}{90 \times 10^{-3}}$
$=\frac{17}{18} \times 10^{3}$
$\therefore \rho_{0}=944.44\, kg / m ^{3}$ ....(Rounding off to $2$ decimal places)