**1 Physical Properties of Fluids**

## Physical Properties of Fluids

### 1 Physical Properties of Fluids

Density (mass density): The mass per unit volume is defined as density. The unit used is kg/m3. The measurement is simple in the case of solids and liquids. In the case of gases and vapours it is rather involved. The symbol used is ρ. The characteristic equation for gases provides a means to estimate the density from the measurement of pressure, temperature and volume.

Specific Volume: The volume occupied by unit mass is called the specific volume of the material. The symbol used is v, the unit being m3/kg. Specific volume is the reciprocal of density. In the case of solids and liquids, the change in density or specific volume with changes in pressure and temperature is rather small, whereas in the case of gases and vapours, density will change significantly due to changes in pressure and/or temperature.

Weight Density or Specific Weight: The force due to gravity on the mass in unit volume is defined as Weight Density or Specific Weight. The unit used is N/m3. The symbol used is γ. At a location where g is the local acceleration due to gravity,

Specific weight, γ = g ρ

In the above equation direct substitution of dimensions will show apparent nonhomogeneity as the dimensions on the LHS and RHS will not be the same. On the LHS the dimension will be N/m3 but on the RHS it is kg/m2 s2. The use of go will clear this anomaly. As seen in section 1.1, go = 1 kg m/N s2. The RHS of the equation 1.3.1 when divided by go will lead to perfect dimensional homogeneity. The equation should preferably be written as,

Specific weight, γ = (g/go) ρ

Since newton (N) is defined as the force required to accelerate 1 kg of mass by 1/s2, it can also be expressed as kg.m/s2. Density can also be expressed as Ns2/m4 (as kg = Ns2/m). Beam balances compare the mass while spring balances compare the weights. The mass is the same (invariant) irrespective of location but the weight will vary according to the local gravitational constant. Density will be invariant while specific weight will vary with variations in gravitational acceleration.

Specific Gravity or Relative Density: The ratio of the density of the fluid to the density of water—usually 1000 kg/m3 at a standard condition—is defined as Specific Gravity or Relative Density δ of fluids. This is a ratio and hence no dimension or unit is involved.

Specific Volume: The volume occupied by unit mass is called the specific volume of the material. The symbol used is v, the unit being m3/kg. Specific volume is the reciprocal of density. In the case of solids and liquids, the change in density or specific volume with changes in pressure and temperature is rather small, whereas in the case of gases and vapours, density will change significantly due to changes in pressure and/or temperature.

Weight Density or Specific Weight: The force due to gravity on the mass in unit volume is defined as Weight Density or Specific Weight. The unit used is N/m3. The symbol used is γ. At a location where g is the local acceleration due to gravity,

Specific weight, γ = g ρ

In the above equation direct substitution of dimensions will show apparent nonhomogeneity as the dimensions on the LHS and RHS will not be the same. On the LHS the dimension will be N/m3 but on the RHS it is kg/m2 s2. The use of go will clear this anomaly. As seen in section 1.1, go = 1 kg m/N s2. The RHS of the equation 1.3.1 when divided by go will lead to perfect dimensional homogeneity. The equation should preferably be written as,

Specific weight, γ = (g/go) ρ

Since newton (N) is defined as the force required to accelerate 1 kg of mass by 1/s2, it can also be expressed as kg.m/s2. Density can also be expressed as Ns2/m4 (as kg = Ns2/m). Beam balances compare the mass while spring balances compare the weights. The mass is the same (invariant) irrespective of location but the weight will vary according to the local gravitational constant. Density will be invariant while specific weight will vary with variations in gravitational acceleration.

Specific Gravity or Relative Density: The ratio of the density of the fluid to the density of water—usually 1000 kg/m3 at a standard condition—is defined as Specific Gravity or Relative Density δ of fluids. This is a ratio and hence no dimension or unit is involved.