Short Answer:
Newtonian fluids are those fluids that obey Newton’s law of viscosity, which states that the shear stress acting between adjacent fluid layers is directly proportional to the rate of change of velocity (velocity gradient) between them. In these fluids, viscosity remains constant at a given temperature and pressure, regardless of the applied shear rate.
In simple words, a Newtonian fluid has a constant viscosity that does not change with the speed of flow. Common examples of Newtonian fluids include water, air, alcohol, and light oils, where the relationship between shear stress and velocity gradient is linear.
Detailed Explanation :
Newtonian Fluids
Newtonian fluids are a special class of fluids that follow Newton’s law of viscosity, which defines the relationship between shear stress and velocity gradient in a flowing fluid. In these fluids, the shear stress (τ) is directly proportional to the rate of shear strain (du/dy), and the constant of proportionality is known as dynamic viscosity (μ).
Mathematically, the relationship is given by:
where,
- τ = Shear stress (N/m² or Pa)
- μ = Dynamic viscosity (N·s/m² or Pa·s)
- du/dy = Velocity gradient or rate of shear strain (s⁻¹)
This linear relationship is the fundamental behavior of Newtonian fluids. The viscosity (μ) of such fluids depends only on temperature and pressure, and not on the amount of shear or flow speed applied.
Characteristics of Newtonian Fluids
- Constant Viscosity:
The viscosity remains constant at a given temperature and pressure, irrespective of the rate of shear strain or deformation. - Linear Relationship:
The graph between shear stress (τ) and velocity gradient (du/dy) is a straight line passing through the origin, indicating a direct proportional relationship. - Obedience to Newton’s Law:
Newtonian fluids strictly follow the equation . - Temperature Dependence:
Although viscosity is independent of shear rate, it varies with temperature. For liquids, viscosity decreases with an increase in temperature, while for gases, it increases. - Predictable Flow Behavior:
The flow characteristics are simple and easy to predict, making them ideal for engineering calculations involving laminar and turbulent flows.
Examples of Newtonian Fluids
Common examples of Newtonian fluids include:
- Water – its viscosity remains constant during normal flow conditions.
- Air – a gas with constant viscosity under moderate pressures and temperatures.
- Alcohol and Kerosene – both exhibit a linear relationship between shear stress and velocity gradient.
- Light Oils – show nearly constant viscosity at normal operating temperatures.
These fluids are commonly used in hydraulic systems, lubrication, and flow experiments because of their predictable behavior.
Graphical Representation
When shear stress (τ) is plotted against the rate of shear strain (du/dy):
- For Newtonian fluids, the graph is a straight line passing through the origin, showing constant viscosity.
- The slope of this line represents the dynamic viscosity (μ).
This linear graph differentiates Newtonian fluids from non-Newtonian fluids, which show a curved or nonlinear relationship.
Mathematical Behavior
In Newtonian fluids, the relationship between shear stress and velocity gradient remains linear:
and hence,
This means that doubling the rate of shear will double the shear stress, as viscosity remains constant. Therefore, flow analysis becomes straightforward because the internal friction (resistance) between fluid layers is directly predictable from their velocity difference.
Factors Affecting Newtonian Fluid Behavior
- Temperature:
Temperature has the most significant effect on viscosity.- For liquids, viscosity decreases as temperature increases (molecules move faster and overcome internal friction).
- For gases, viscosity increases with temperature (faster-moving molecules transfer momentum more effectively).
- Pressure:
For most Newtonian fluids, viscosity increases slightly with pressure, though the effect is usually small for liquids. - Fluid Composition:
The type of molecules, their size, and intermolecular forces determine how the fluid responds to shear stress. - Flow Conditions:
The Newtonian behavior holds true under normal flow conditions but may change under extreme pressures or at very high shear rates.
Applications of Newtonian Fluids
Newtonian fluids are widely used in engineering and industrial applications because of their predictable flow characteristics. Some of the main areas include:
- Hydraulic Systems:
Fluids like water and light oils used in hydraulic machinery behave as Newtonian fluids, ensuring stable pressure transmission. - Aerodynamics:
Air, a Newtonian fluid, is used for designing airfoils and analyzing airflow over aircraft wings and vehicles. - Pipelines and Flow Systems:
Newtonian fluids simplify calculations for head loss, velocity distribution, and energy analysis in laminar and turbulent flows. - Lubrication:
Light lubricating oils that behave as Newtonian fluids provide smooth flow between machine parts under normal working conditions. - Research and Calibration:
Newtonian fluids are often used as standard fluids for testing viscometers and validating fluid dynamics experiments.
Difference Between Newtonian and Non-Newtonian Fluids
- Newtonian Fluids: Have constant viscosity and obey .
Example: Water, air, alcohol. - Non-Newtonian Fluids: Viscosity changes with shear rate, and the relationship between shear stress and velocity gradient is nonlinear.
Example: Blood, toothpaste, paint, mud.
This difference is crucial for selecting fluids for specific engineering applications such as lubrication, fluid transport, and chemical processing.
Graphical Comparison
If we plot shear stress (τ) versus velocity gradient (du/dy):
- The Newtonian fluid shows a straight line, indicating constant viscosity.
- Non-Newtonian fluids show curved lines, indicating that viscosity changes with the shear rate.
This simple distinction helps in identifying fluid behavior during experiments or practical applications.
Importance of Newtonian Fluids in Engineering
- Simplified Analysis:
The constant viscosity assumption simplifies calculations in pipe flow, boundary layer analysis, and laminar flow studies. - Predictable Energy Losses:
Engineers can easily predict pressure drop, head loss, and energy dissipation in systems involving Newtonian fluids. - Machine Design:
Equipment like pumps, turbines, and bearings are often designed assuming Newtonian fluid behavior to ensure accurate performance analysis. - Standard Reference Fluids:
Water and air, the most common Newtonian fluids, are used as reference fluids for measuring and comparing the flow characteristics of other materials.
Conclusion
In conclusion, Newtonian fluids are those fluids that obey Newton’s law of viscosity, where shear stress is directly proportional to the rate of shear strain, and viscosity remains constant at a given temperature and pressure. These fluids show a linear relationship between stress and strain rate, making them easy to analyze and predict. Common examples include water, air, alcohol, and light oils. The study of Newtonian fluids is fundamental in mechanical and fluid engineering because it forms the basis for understanding real-world fluid behavior and designing efficient fluid systems.