First slide

Pressure in a fluid-mechanical properties of fluids

Question

If two liquids of same masses but densities $ρ_{1}$ and $ρ_{2}$ respectively are mixed, then density of mixture is given by

Moderate

A

$ρ = \frac{ρ_{1} + ρ_{2}}{2}$
B

$ρ = \frac{ρ_{1} + ρ_{2}}{2 ρ_{1} ρ_{2}}$
C

$ρ = \frac{2 ρ_{1} ρ_{2}}{ρ_{1} + ρ_{2}}$
D

$ρ = \frac{ρ_{1} ρ_{2}}{ρ_{1} + ρ_{2}}$

Solution

$\begin{array}{l} ρ = \frac{Total mass}{Total volu me} = \frac{2 m}{V_{1} + V_{2}} = \frac{2 m}{m (\frac{1}{ρ_{1}} + \frac{1}{ρ_{2}})} \\ ∴ ρ = \frac{2 ρ_{1} ρ_{2}}{ρ_{1} + ρ_{2}} \end{array}$

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