**Important Fluid Properties GATE Notes**

**Fluid Definition**

**Real Fluid**

- A fluid is said to be real if it has a viscosity, finite compressibility, and surface tension.

**Ideal Fluid**

- A fluid is said to be ideal if it is assumed to be both incompressible and non-viscous.
- Its Bulk Modulus is infinite.
- Ideal fluids do not have surface tension. In fact, ideal fluids do not exist in nature and are imaginary.

**Read Also- Fluid Mechanics: Objective Questions**

**Definitions of Important Terms Related to Fluid**

**Density**

The density of a fluid is defined as the mass of the fluid over an infinitesimal volume or mass per unit volume. It’s

The unit in the SI system is- kg/m³.

ρ = m/V

where, ρ = density

m = mass

V = Volume

**Specific weight (ω) or weight density**

- It is a ratio of weight to volume.

ω = weight/volume

ω = mg / V = ρg

where ρ = Density

g = Acc. Due to gravity

*Remember- Specific weight of water is 9810 N/m³*

**Specific Volume**

It is a ratio of volume to the mass, i.e. Volume per unit mass.

Specific Volume = 1/ density = 1/ρ

**Specific Gravity (S) or Relative density**

It is the ratio of the density of the fluid to the density of standard fluid or Ratio of Specific weight of a fluid to the Specific weight of the standard fluid.

*Note-*

- The specific gravity of water at 4 °C is ‘1’.
- For Mercury Specific gravity is 13.6.
- Specific gravity varies with temperature, therefore, it must be determined at a specified temperature (4 °C or 27 degrees Celsius).

**Read Also- Dimensional Analysis and its Application Notes**

**Newton’s Law of Viscosity **

It says that the shear stress between adjacent fluid layers is proportional to the negative value of the velocity gradient between the two layers.

Mathematically, it is defined as-

τ = µ du/dy = µ dθ/dt

τ = Shear Stress

µ = Coefficient of Viscosity or Absolute Viscosity or Dynamic Viscosity

du/dy = Velocity gradient

dθ/dt = Rate of Angular deformation or Rate of Shear Strain

*Remember- For Newtonian Fluid, the Coefficient of Viscosity remains constant.*

**Viscosity/Kinematic Viscosity**

- It is Viscosity that offers resistance to the fluid flow.
- This is basically can be defined in two ways, namely- Dynamic Viscosity (µ) and Kinematic Viscosity (ν).

**Dynamic Viscosity (µ)**

- Its SI unit is pascal-second or N-sec/m²
- Its cgs unit, most commonly used, is Poise = Dyne-sec/cm²
- 1 Poise = 0.1 N-sec/m²

**Read Also- Vortex Motion Definition**

**Kinematic Viscosity (ν)**

ν = µ/ρ

- Its SI unit is m²/s
- Its cgs unit is stoke = cm²/s
- 1 stoke = 10
^{-4}m²/s

**Note:**

- The viscosity of liquids decreases with temperature whereas the viscosity of gases increases with an increase in temperature.
- The viscosity of liquids is due to cohesion and molecular momentum transfer.
- Liquids with increasing order of viscosity are gasoline, water, crude oil, castor oil.
- The viscosity of water at 1 degree Celsius is 1 centipoise.

**Read Also- Hydrostatics Definition and Laws**

**Read Also- Non-Newtonian Fluids**