Physics > Fluid Mechanics > 1.0 Introduction
Fluid Mechanics
1.0 Introduction
1.1 Ideal liquid
1.2 Density of a liquid $\left( \rho \right)$
1.3 Relative density of a liquid $(RD)$
1.4 Density of a mixture of two or more liquid
1.5 Density variation with temperature
1.6 Density variation with pressure
2.0 Fluid pressure
2.1 Atmospheric pressure
2.2 Pressure variation with depth
2.3 Measurement of pressure
2.4 Pressure difference in accelerating fluids
3.0 Pascal's law
4.0 Buoyant force
5.0 Flow of fluids
6.0 Viscosity
7.0 Stoke's law
8.0 Intermolecular forces
9.0 Angle of contact
1.6 Density variation with pressure
1.2 Density of a liquid $\left( \rho \right)$
1.3 Relative density of a liquid $(RD)$
1.4 Density of a mixture of two or more liquid
1.5 Density variation with temperature
1.6 Density variation with pressure
2.2 Pressure variation with depth
2.3 Measurement of pressure
2.4 Pressure difference in accelerating fluids
Mass of a liquid remains constant with change in pressure. So, $$\rho \propto \frac{1}{V}$$ or $$\begin{equation} \begin{aligned} \frac{{\rho '}}{\rho } = \frac{V}{{V'}} \\ \frac{{\rho '}}{\rho } = \frac{V}{{V + dV}}\quad \left( {As,\;V' = V + dV} \right) \\\end{aligned} \end{equation} $$ We know, $$B = - \left( {\frac{{dP}}{{dV}}} \right)V$$ or $$dV = - \left( {\frac{{dP}}{B}} \right)V$$ So, $$\begin{equation} \begin{aligned} \frac{{\rho '}}{\rho } = \frac{V}{{V - \left( {\frac{{dP}}{B}} \right)V}} \\ \rho ' = \frac{\rho }{{1 - \frac{{dP}}{B}}} \\\end{aligned} \end{equation} $$