# Density of a Mixture of Substances – Hydrostatics

## The Density of a Mixture of Substances – Hydrostatics

We are giving a detailed and clear sheet on all Physics Notes that are very useful to understand the Basic Physics Concepts.

Density of a Mixture of Two Liquids:
1. When two liquids of masses m1 and m2 having densities ρ1 and ρ2 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 ρ1 and ρ2 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 ρ1 and ρ2 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,
ρ0 = 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 = $$\frac{\rho_{0}}{(1+\gamma \cdot \Delta T)}$$ ≃ ρ0 (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.