Newton's law of viscosity
Introduction
Sir Isaac Newton is renowned for his significant contributions to the field of physics. Among his many discoveries, Newton's law of viscosity is a critical principle in fluid dynamics. This law, often referred to as Newton's second law, describes the relationship between the shear stress and shear rate of a fluid.
Definition
Newton's law of viscosity states that the shear stress between adjacent fluid layers is proportional to the negative gradient of their velocity in the direction perpendicular to their plane. Mathematically, this can be represented as:
τ = -η (du/dy)
Where:
- τ is the shear stress between the layers (force per unit area)
- η is the dynamic viscosity (a measure of a fluid's resistance to shear)
- du/dy is the velocity gradient perpendicular to the direction of shear.
Dynamic Viscosity
Dynamic viscosity (η) is a measure of a fluid's internal resistance to flow and shear. It is a property that depends on the nature and temperature of the fluid. For example, honey has a higher dynamic viscosity than water, meaning it resists flow and shear to a greater extent. The unit of dynamic viscosity in the International System of Units (SI) is the pascal-second (Pa·s).
Newtonian and Non-Newtonian Fluids
Based on Newton's law of viscosity, fluids can be classified into two main types: Newtonian and non-Newtonian fluids.
Newtonian fluids are those that follow Newton's law of viscosity. The shear stress in these fluids is directly proportional to the rate of strain, and the viscosity remains constant, regardless of the shear rate. Examples of Newtonian fluids include water, air, and honey.
Non-Newtonian fluids, on the other hand, do not follow Newton's law of viscosity. Their viscosity changes with the shear rate. There are several types of non-Newtonian fluids, including pseudoplastic, dilatant, plastic, and thixotropic fluids. Examples of non-Newtonian fluids include ketchup, blood, and certain types of mud and paint.
Applications of Newton's Law of Viscosity
Newton's law of viscosity has a wide range of applications in both science and engineering. It is used in the design and analysis of systems in which fluid flow is important. This includes the design of pipe systems, the analysis of blood flow in arteries, the design of aircraft and automobiles, and the prediction of weather patterns.
