## The Density of a Mixture of Substances – Hydrostatics

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**Density of a Mixture of Two Liquids:**

1. When two liquids of masses m_{1} and m_{2} having densities ρ_{1} and ρ_{2} are mixed together, then density of mixture is

ρ = \(\frac{m_{1}+m_{2}}{\left(\frac{m_{1}}{\rho_{1}}\right)+\left(\frac{m_{2}}{\rho_{2}}\right)}=\frac{\rho_{1} \rho_{2}\left(m_{1}+m_{2}\right)}{\left(m_{1} \rho_{2}+m_{2} \rho_{1}\right)}\)

2. When two liquids of same mass m but of different densities ρ_{1} and ρ_{2} are mixed together, then density of mixture is

ρ = \(\frac{2 \rho_{1} \rho_{2}}{\rho_{1}+\rho_{2}}\)

3. When two liquids of same volume V but of different densities ρ_{1} and ρ_{2} are mixed together, then density of mixture is

ρ = \(\frac{\rho_{1}+\rho_{2}}{2}\).

Density of a liquid varies with pressure,

ρ = \(\rho_{0}\left[1+\frac{\Delta p}{K}\right]\)

where,

ρ_{0 }= initial density of the liquid,

K = bulk modulus of elasticity of the liquid

Δp = change in pressure.

4. With rise in temperature (ΔT) due to thermal expansion of a given body, volume will increase while mass will remains constant, so density will decrease.

ρ = \(\frac{\rho_{0}}{(1+\gamma \cdot \Delta T)}\) ≃ ρ_{0} (1 – γ . ΔT); where γ is volumetric expansion.

**Hydrostatics:
**Hydrostatics is a property of liquid or fluid in mechanics. A fluid is a material which flows at room temperature, because its upper molecule overlaps the inner molecule, which tends to flow the liquid in forward direction. In hydrostatics, we will learn about the condition of fluids when it is in rest or exerted by an external force. Here we will study the fluids in motion.

Properties of Fluids | Thrust |

Pressure | Pressure Exerted by Liquid |

Buoyant Force | Pascal’s Law |

Archimedes’ Principle | Law of Floatation |

Density | Relative Density |

Density of a Mixture |