1.4 Density of a mixture of two or more liquid

  Fluid Mechanics

• If two liquid of densities ${\rho _1}$ and ${\rho _2}$ having volume $V_1$ and $V_2$ are mixed, then the density of the resulting mixture is given by, $${\text{Density = }}\frac{{{\text{Total mass}}}}{{{\text{Total volume}}}}$$ or $$\rho = \frac{{{m_1} + {m_2}}}{{{V_1} + {V_2}}}$$ As we know, $m = \rho V$, So, $$\rho = \frac{{{\rho _1}{V_1} + {\rho _2}{V_2}}}{{{V_1} + {V_2}}}$$ If ${V_1} = {V_2}$ then, $$\rho = \frac{{{\rho _1} + {\rho _2}}}{2}$$

• If two liquids of densities ${\rho _1}$ and ${\rho _2}$ having mass $m_1$ and $m_2$ are mixed, then the resulting density of the mixture is given by, $${\text{Density = }}\frac{{{\text{Total mass}}}}{{{\text{Total volume}}}}$$ or $$\begin{equation} \begin{aligned} \rho = \frac{{{m_1} + {m_2}}}{{{V_1} + {V_2}}} \\ \rho = \left[ {\frac{{{m_1} + {m_2}}}{{\left( {\frac{{{m_1}}}{{{\rho _1}}} + \frac{{{m_2}}}{{{\rho _2}}}} \right)}}} \right] \\\end{aligned} \end{equation} $$ If ${m_1} = {m_2}$ then, $$\rho = \frac{{2{\rho _1}{\rho _2}}}{{{\rho _1} + {\rho _2}}}$$