The physical properties of fluids are as follows:

**1.3.1 Mass Density or Density**

Mass density or simply density of a fluid is defined as the mass per unit volume. It is denoted as p (rho). If 6.m and Si are mass and volume respectively of a fluid element enclosing a point P, then p is mathematically written as

Fig. 1.1 shows a fluid element enclosing point P.

S.I. (Standard International) unit of p is given by

P _{water} = 1000 kg / m^{3}

**1.3.2 Specific Weight or Weight Density**

The specific weight or weight density of a fluid is defined as the weight of the fluid per unit volume. It is denoted as w. It is mathematically expressed as

w = gp or w = pg

where dW = weight of fluid element.

= gdm.

W _{water} = 9.81 x 1000 N/m^{3}

The volume of a fluid per unit mass is called specific volume. It is denoted as v. It is mathematically expressed as

u = 1 /p

In S.I unit it is m^{3 }/ kg. We encounter v frequently in case of gases only.

**1.3.4 Specific Gravity**

The specific gravity of a liquid is defined as the ratio of weight density or density of the liquid to the weight density or density of pure water at pressure 101 KN/m^{2} and temperature at 4°C. It is denoted as S. It is mathematically expressed as

S = w _{liquid} / w _{std.water} = w _{liduid} / 9.81 x 1000 N/m^{3}

or w_{ liquid }= S x 9.81 x 1000 N/m^{2}

S can also be expressed as

S = p _{liquid} / p _{std.water} = p _{liduid} / 1000 kg/m^{3}

or p_{ liquid }= S x 1000 kg/m^{2}