Introduction
A fluid is a substance which is capable of flowing or deforming under the action of shear force (however the small force maybe). Examples: liquids, gases, and vapors.
Density
The density of a fluid is the ratio of mass to its volume at a specified temperature and pressure. It is denoted by the symbol ‘ρ’.
It is defined as the ratio of the density (or specific weight) of any fluid to the density (or specific weight) of standard fluid. It is dimensionless.
Viscosity is defined as the property of the fluid by virtue of which it offers resistance to the movement of one layer of fluid over an adjacent layer of fluid.
Ideal Fluids: A hypothetical fluid that is incompressible and has zero viscosity ( μ = 0).
Real Fluids: A fluid, which possesses viscosity. All the fluids, in actual practice, are real.
Newtonian Fluid: A fluid is said to be Newtonian fluid if obeys Newton’s law of viscosity i.e. shear stress is directly proportional to the rate of shear strain or velocity.
Non- Newtonian Fluids: Fluids that do not obey Newton’s law of viscosity are known as Non-Newtonian fluids.
The general relationship between shear stress (τ) and velocity gradient is given by
A fluid is a substance which is capable of flowing or deforming under the action of shear force (however the small force maybe). Examples: liquids, gases, and vapors.
Density
The density of a fluid is the ratio of mass to its volume at a specified temperature and pressure. It is denoted by the symbol ‘ρ’.
- Unit : $Kg/m^3$
- Dimension : $ML^{-3}$.
- Maximum density of water is at 4°C and its value is 1000 kg/m3.
- Density of air at 20°C is 1.2 kg/m3.
- Density depends on temperature and pressure.
As the pressure increases, the density of fluid increases because there is a reduction in volume.
Specific weight / weight density (w)
It is defined as the ratio of the weight of the fluid to its volume at a specified temperature and pressure.
- Unit : $N/m^3$
- Dimension : $ML^{-2}T^{-2}$.
- Weight density of water is 1000 * 9.81 = 9810 N/m3.
- Specific weight depends on temperature, pressure and location.
- Density is absolute quantity but weight density varies from place to place it is not an absolute quantity.
Specific Gravity
It is defined as the ratio of the density (or specific weight) of any fluid to the density (or specific weight) of standard fluid. It is dimensionless.
- Specific gravity of water = 1
- Specific gravity of mercury = 13.6
Viscosity
Viscosity is defined as the property of the fluid by virtue of which it offers resistance to the movement of one layer of fluid over an adjacent layer of fluid.
Viscosity in a fluid is due to Cohesive forces between fluid molecules and Molecular momentum exchange.
Newton's law of viscosity:
It states that the shear stress τ on a fluid element layer is directly proportional to the rate of shear strain.
- Here ‘μ’ is the constant of proportionality and this is known as coefficient of viscosity or absolute viscosity or dynamic viscosity.
- Its SI unit is N-s/m2. The dimension of dynamic viscosity is $ML^{-1}T^{-1}$.
- C.G.S unit of viscosity is dyne-sec /cm2 or poise.
- 1 Poise = 0.1 N-s/m2
KINEMATIC VISCOSITY (v)
It is defined as the ratio of the dynamic viscosity and density of fluid.
- Its SI unit is m2/sec.
- In C.G.S, the unit of kinematic viscosity is stokes.
- 1 stokes = 10^-^4 m2/sec
Variation of Viscosity with temperature
In the case of liquids, cohesive forces (forces of attraction between same nature molecules) are large and dominate over molecular momentum exchange. With an increase in temperature, the cohesive forces decrease and hence the resistance to the flow also decreases. Therefore in case of liquids with increase in temperature, the viscosity of the liquids decreases.
In case of gases, intermolecular distance is very large and hence cohesive forces are negligible and molecular momentum exchange dominates over cohesive forces. With increase in temperature, molecular disturbance increases which in turn increases resistance to flow. Therefore, viscosity of gases increases with increase in temperature.
In the case of liquids, cohesive forces (forces of attraction between same nature molecules) are large and dominate over molecular momentum exchange. With an increase in temperature, the cohesive forces decrease and hence the resistance to the flow also decreases. Therefore in case of liquids with increase in temperature, the viscosity of the liquids decreases.
In case of gases, intermolecular distance is very large and hence cohesive forces are negligible and molecular momentum exchange dominates over cohesive forces. With increase in temperature, molecular disturbance increases which in turn increases resistance to flow. Therefore, viscosity of gases increases with increase in temperature.
Classification of fluids
Ideal Fluids: A hypothetical fluid that is incompressible and has zero viscosity ( μ = 0).
Real Fluids: A fluid, which possesses viscosity. All the fluids, in actual practice, are real.
Newtonian Fluid: A fluid is said to be Newtonian fluid if obeys Newton’s law of viscosity i.e. shear stress is directly proportional to the rate of shear strain or velocity.
Non- Newtonian Fluids: Fluids that do not obey Newton’s law of viscosity are known as Non-Newtonian fluids.
The general relationship between shear stress (τ) and velocity gradient is given by
τ = A(du/dy)^n + B
where A, B and n are constants.
Case I : Dilatant fluids (B = 0, n > 1)
where, μ_app is apparent viscosity.
For dilatant fluids, μ_app increases with the rate of deformation and hence these fluids are
also known as shear thickening fluids.
Examples : Rice starch, sugar in water.
Case II : Pseudo plastic fluids (B = 0, n < 1)
For pseudo-plastic fluids, n < 1 thus, the apparent viscosity (μ_app) decreases with the rate of
deformation and hence pseudo-plastic fluids are also called as shear-thinning fluids.
Examples : Blood, Milk, and colloidal solution.
Case III : Bingham plastic fluids (B = constant, n = 1)
IF the shear stress is less
than B, it acts like a solid and after B it behaves like a fluid.
example : toothpaste.
Time-dependent fluids
1. Thixotropic fluids: In these fluids, apparent viscosity decreases with time.
Examples : paints, lipstic.
2. Rheopectic fluids : In these fluids apparent viscosity increases with time.
Examples : Bentonite solution, gypsum solution in water.
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