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**Properties of Fluid **

Any characteristic of a system is called *property *. It may either be *intensive * (mass independent) or *extensive * (that depends on size of system). The state of a system is described by its properties. The number of properties required to fix the state of the system is given by *state postulates*. Most common properties of the fluid are:

**1. Pressure **(p): It is the normal force exerted by a fluid per unit area. More details will be available in the subsequent section (Lecture 02). In SI system the unit and dimension of pressure can be written as, N/m^{2} and ML^{-1}T^{-2}, respectively.

**2. Density**: The density of a substance is the quantity of matter contained in unit volume of the substance. It is expressed in three different ways; mass density , specific weight (ρg) and relative density/specific gravity . The units and dimensions are given as,

For mass density; Dimension: ML^{-3} Unit: kg/m^{3}

For specific weight; Dimension: ML^{-2}T^{-2} Unit: N/m^{3}

The standard values for density of water and air are given as 1000kg/m^{3} and 1.2 kg/m^{3}, respectively. Many a times the reciprocal of mass density is called as specific volume .

**3. Temperature **(T): It is the measure of hotness and coldness of a system. In thermodynamic sense, it is the measure of internal energy of a system. Many a times, the temperature is expressed in centigrade scale (°C) where the freezing and boiling point of water is taken as 0°C and 100°C, respectively. In SI system, the temperature is expressed in terms of absolute value in Kelvin scale (K =°C+ 273).

**4. Viscosity **(u): When two solid bodies in contact, move relative to each other, a friction force develops at the contact surface in the direction opposite to motion. The situation is similar when a fluid moves relative to a solid or when two fluids move relative to each other. The property that represents the internal resistance of a fluid to motion (i.e. *fluidity *) is called as *viscosity *. The fluids for which the rate of deformation is proportional to the shear stress are called Newtonian fluids and the linear relationship for a one-dimensional system is shown in Fig. 1.1.2. The shear stress (τ) is then expressed as,

(1.1.2) |

where, is the shear strain rate and μ is the dynamic (or absolute) viscosity of the fluid.

The dynamic viscosity has the dimension ML^{-1}T^{-1} and the unit of kg/m.s (or, N.s/m^{2} or Pa.s). A common unit of dynamic viscosity is *poise * which is equivalent to 0.1 Pa.s. Many a times, the ratio of dynamic viscosity to density appears frequently and this ratio is given by the name kinematic viscosity . It has got the dimension of L^{2}T^{-1} and unit of *stoke * (1 stoke = 0.0001 m^{2}/s). Typical values of kinematic viscosity of air and water at atmospheric temperature are 1.46 x 10^{-5} m^{2}/s and 1.14 x 10^{-6} m^{2}/s, respectively.

Fig. 1.1.2: Variation of shear stress with rate of deformation.