Properties of fluid

Density or mass density

$$ \rho = \frac{Mass\ of\ fluid }{Volume\ of\ liquid}$$

The SI unit of density is kg/m³

Specific weight or weight density

$$w = \frac{Weight\ of\ fluid }{Volume\ of\ liquid} = \frac{(Mass\ of\ fluid) * Accelaration\ due\ to\ gravity}{Volume\ of\ fluid}$$

$$= \frac{Mass\ of\ fluid\ *\ g}{Volume\ of\ fluid} $$

$$ = \rho\ *\ g $$ $$ w = \rho $$

The SI unit of specific weight is N/m³

Specific volume

$$ specific\ volume = \frac{Volume\ of\ fluid }{Mass\ of\ liquid} = \frac{1}{\frac{Mass\ of\ fluid}{Volume\ of\ fluid}} = \frac{1}{\rho}$$

Specific gravity

$$ S(for\ liquids) = \frac{weight\ density\ (density)\ of\ liquid}{weight\ density\ (density)\ of\ water}$$

$$ density\ of\ liquid = S\ *\ density\ of\ water = S\ *\ 1000\ kg/m^3$$

Viscosity

$$ \mu = \frac{shear\ stress}{\frac{change\ of\ velocity}{change\ of\ distance}} = \frac{force/area}{\frac{length}{time} * \frac{1}{length}} $$ $$ = \frac{force/(length)^2}{\frac{1}{time}} = \frac{force * time}{(length)^2} $$

The SI unit of viscosity is Ns/m²

1 Ns/m² = 10 poise

1 centipoise = 1/100 poise

Kinematic viscosity

$$ \nu = \frac{viscosity}{density} = \frac{\mu}{\rho} $$

The SI unit of kinematic viscosity is m²/s

1 stoke = 10^-4 m²/s

1 centistoke = 1/100 stoke

Compressibility and Bulk Modulus

$$ Bulk\ modulus\ (K) = \frac{increase\ of\ pressure}{volumetric\ strain} $$

$$ = \frac{dp}{\frac{-d \forall}{\forall}} = \frac{-dp}{d \forall} \forall $$

$$ compressability = \frac{1}{K} $$

The SI unit of bulk modulud is N/m²

Volumetric strain

$$ volumetric\ strain = \frac{-d \forall}{\forall} $$