Short Answer:

Dynamic viscosity is defined as the property of a fluid that resists the relative motion between its layers when an external force or shear stress is applied. It represents the internal friction within a moving fluid. A fluid with high dynamic viscosity flows slowly, while one with low viscosity flows easily.

In simple terms, dynamic viscosity measures the resistance of a fluid to flow. It is denoted by the symbol μ (mu) and its SI unit is Pascal-second (Pa·s) or N·s/m². For example, the dynamic viscosity of water at 20°C is approximately 1.002 × 10⁻³ Pa·s.

Detailed Explanation :

Dynamic Viscosity

Dynamic viscosity, also called absolute viscosity, is an important property that defines how much resistance a fluid offers when one layer of the fluid moves over another. It is the measure of the internal friction between adjacent layers of a moving fluid. This property arises due to the cohesive forces and molecular interactions within the fluid.

When a fluid flows, its layers do not move at the same velocity. The layer close to a solid surface moves slower, and the layers farther away move faster. This variation in velocity between the layers creates a shearing effect. The resistance offered by the fluid to this relative motion is its dynamic viscosity.

Mathematically, the relationship between shear stress and velocity gradient for a Newtonian fluid is given by Newton’s law of viscosity:

where,

• τ = Shear stress between fluid layers (N/m² or Pa)
• μ = Dynamic viscosity of the fluid (N·s/m² or Pa·s)
• du/dy = Rate of change of velocity with respect to distance (s⁻¹)

This law shows that shear stress is directly proportional to the velocity gradient, and the constant of proportionality is the dynamic viscosity μ.

Concept of Dynamic Viscosity

The concept of dynamic viscosity helps us understand how easily a fluid flows when subjected to shear forces.

• A fluid with high dynamic viscosity (like honey or oil) has strong internal friction and resists motion.
• A fluid with low dynamic viscosity (like air or water) has weak internal friction and flows easily.

Dynamic viscosity is therefore a direct measure of a fluid’s internal resistance to flow. It plays an essential role in calculating energy losses, pressure drops, and flow rates in pipelines and mechanical systems.

Units of Dynamic Viscosity

In different systems of units, dynamic viscosity is expressed as:

• SI Unit: Pascal-second (Pa·s) or N·s/m²
• CGS Unit: Poise (P)
• Commonly used smaller unit: Centipoise (cP)

Example:
The dynamic viscosity of water at 20°C is 1.002 × 10⁻³ Pa·s = 1.002 cP.

Factors Affecting Dynamic Viscosity

Several factors affect the value of dynamic viscosity:

1. Temperature:
   • For liquids, dynamic viscosity decreases with an increase in temperature because molecular bonds weaken, allowing the fluid to flow more easily.
   • For gases, dynamic viscosity increases with temperature because of the greater momentum exchange between rapidly moving gas molecules.
2. Pressure:
   • The effect of pressure on liquids is small; a slight increase in pressure slightly increases viscosity.
   • For gases, viscosity is almost independent of pressure at moderate conditions.
3. Molecular Structure:
   • Fluids with larger or more complex molecules (like oils or polymers) have higher viscosity due to greater internal friction.
4. Impurities:
   • The presence of impurities can increase or decrease viscosity depending on their chemical nature.

Measurement of Dynamic Viscosity

Dynamic viscosity can be measured using several instruments, depending on the type of fluid and accuracy required. Some common methods include:

1. Capillary Tube Viscometer:
   The time taken for a fluid to flow through a narrow tube under gravity is measured. Using Poiseuille’s equation, viscosity is calculated.
2. Rotational (Torsion) Viscometer:
   One cylinder rotates inside another with fluid in between. The torque required to maintain motion gives the viscosity.
3. Falling Sphere Viscometer:
   A sphere falls through a stationary fluid. The terminal velocity of the sphere helps determine viscosity using Stokes’ law.

These instruments are used in laboratories and industries to measure viscosity of oils, lubricants, paints, and other fluids.

Importance of Dynamic Viscosity in Engineering

Dynamic viscosity plays a vital role in various engineering applications, especially in mechanical, civil, and chemical engineering. Some key uses are:

1. Design of Hydraulic Machines:
   Viscosity affects the energy loss and efficiency of pumps, turbines, and hydraulic systems. The correct selection of working fluid depends on its viscosity.
2. Lubrication:
   In machines, lubricating oils are selected based on their viscosity to reduce friction between moving parts and prevent wear.
3. Flow Through Pipes and Channels:
   Viscosity influences the flow behavior of fluids in pipes. High viscosity leads to greater resistance and pressure loss, while low viscosity allows smoother flow.
4. Heat Transfer Systems:
   In heat exchangers, the viscosity of fluids affects convection and heat transfer rates. Fluids with moderate viscosity allow better heat transfer.
5. Aerodynamics and Fluid Flow:
   The viscosity of air and gases determines the drag and lift forces acting on vehicles, airplanes, and other bodies moving through fluids.

Examples of Dynamic Viscosity Values

• Air (20°C): 1.81 × 10⁻⁵ Pa·s
• Water (20°C): 1.002 × 10⁻³ Pa·s
• Mercury (20°C): 1.55 × 10⁻³ Pa·s
• Engine Oil (40°C): 0.25 Pa·s
• Honey: 2 to 10 Pa·s

These examples show that thicker substances like honey have higher viscosity than lighter fluids like water or air.

Relation Between Dynamic and Kinematic Viscosity

Dynamic viscosity (μ) and kinematic viscosity (ν) are related by the fluid density (ρ):

This means kinematic viscosity is the dynamic viscosity divided by the density of the fluid. Hence, for two fluids with the same dynamic viscosity, the denser fluid will have a lower kinematic viscosity.

Conclusion

In conclusion, dynamic viscosity is the property of a fluid that resists motion between its layers under the action of shear stress. It measures the internal friction and determines how easily a fluid flows. Dynamic viscosity depends on temperature, pressure, and the molecular structure of the fluid. It plays a vital role in engineering applications like lubrication, fluid flow, and hydraulic design. Understanding dynamic viscosity helps engineers select the right fluids and design efficient and reliable systems.