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What does it mean by momentum transfer is not a vector (3 components) but rather a tensor (9 components)?
asdf1 said:What does it mean by momentum transfer is not a vector (3 components) but rather a tensor (9 components)?
Tensor analysis is the type of subject that can make even the best of students shudder. My own post-graduate instructor in the subject took away much of the fear by speaking of an implicit rhythm in the peculiar notation traditionally used, and helped us to see how this rhythm plays its way throughout the various formalisms. Prior to taking that class, I had spent many years “playing” on my own with tensors. I found the going to be tremendously difficult but was able, over time, to back out some physical and geometrical considerations that helped to make the subject a little more transparent. Today, it is sometimes hard not to think in terms of tensors and their associated concepts. This article, prompted and greatly enhanced by Marlos Jacob, whom I’ve met only by e-mail, is an attempt to record those early notions concerning tensors. It is intended to serve as a bridge from the point where most undergraduate students “leave off” in their studies of mathematics to the place where most texts on tensor analysis begin. A basic knowledge of vectors, matrices, and physics is assumed. A semi-intuitive approach to those notions underlying tensor analysis is given via scalars, vectors, dyads, triads, and higher vector products. The reader must be prepared to do some mathematics and to think. For those students who wish to go beyond this humble start, I can only recommend my professor’s wisdom: find the rhythm in the mathematics and you will fare pretty well.
Newton's Law of Viscosity, also known as Newton's Law of Fluid Flow, states that the shear stress of a fluid is directly proportional to the rate of shear strain, assuming a constant temperature and pressure. This law explains the relationship between the force required to move a fluid and the fluid's resistance to flow.
The equation for Newton's Law of Viscosity is τ = μ(dv/dy), where τ is the shear stress, μ is the dynamic viscosity, and (dv/dy) is the rate of shear strain. This equation is also known as the shear stress equation.
Newton's Law of Viscosity is applied in a variety of real-life situations, such as in the design of fluids for industrial processes, the study of blood flow in the human body, and the analysis of air resistance on objects moving through the air. It is also used in the development of lubricants and in the understanding of weather patterns.
The viscosity of a fluid can be affected by temperature, pressure, and the type of fluid. Generally, as temperature increases, the viscosity of a fluid decreases, and as pressure increases, the viscosity also increases. Additionally, different types of fluids, such as liquids and gases, have different inherent viscosities.
Newtons's Law of Viscosity was a significant contribution to the field of fluid mechanics because it provided a mathematical relationship between the force required to move a fluid and the fluid's resistance to flow. This law also led to the development of other equations and principles in fluid mechanics, such as Bernoulli's principle and the Navier-Stokes equations.