Important Fluid Properties GATE Notes Definitions, Formula

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.

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).

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

GATE Short Notes: Basic Properties of Fluids