# Why is viscous stress tensor symmetric?

## Why is viscous stress tensor symmetric?

If the fluid particles have negligible angular momentum or if their angular momentum is not appreciably coupled to the external angular momentum, or if the equilibration time between the external and internal degrees of freedom is practically zero, the torque will be zero and the viscous stress tensor will be symmetric …

### What are the two viscosity coefficients involved in the relationship between stress tensor and strain rate of fluids?

6. What are the two viscosity coefficients involved in the relationship between stress tensor and strain rate of fluids? Explanation: The two viscosities involved in stress train relationship of fluids is dynamic viscosity coefficient and bulk viscosity coefficient.

#### How many independent variables are there in a 2d strain tensor?

Stress Tensor Six independent components of the strain tensor acting on a infinitesimal rectangular parallelepiped.

What is viscous shear stress?

The property of a fluid to resist the growth of shear deformation is called viscosity. The form of the relation between shear stress and rate of strain depends on a fluid, and most common fluids obey Newton’s law of viscosity, which states that the shear stress is proportional to the strain rate: τ = µ dγ dt .

Why viscous force is proportional to velocity gradient?

The viscous drag is directly proportional to the velocity gradient. The viscous force acts parallel to layers. Therefore, the direction of the viscous drag is along the direction of the flow of the liquid.

## What is velocity gradient and coefficient of viscosity?

The ratio of the shearing stress to the velocity gradient is a measure of the viscosity of the fluid and is called the coefficient of viscosity η, or η=Fx/Av. A striking result of the kinetic theory of gases is that the viscosity of a gas is independent of the density of a gas.

### What is the deviatoric part of a tensor?

Hydrostatic and deviatoric components The stress tensor can be separated into two components. One component is a hydrostatic or dilatational stress that acts to change the volume of the material only; the other is the deviatoric stress that acts to change the shape only.

#### What is the stress tensor in a cylindrical coordinate system?

direction. In a cylindrical coordinate system, the stress tensor would be comprised of thecomponents of the stresses acting inonthe the three surfaces having outward normals positiver,andz directions. Why are the “tensor

Is viscous stress scalar or vector?

Shear and bulk viscous stress. As with any symmetric tensor, the viscous stress tensor ε can be expressed as the sum of a traceless symmetric tensor εs, and a scalar multiple εv of the identity tensor. In coordinate form, This decomposition is independent of the coordinate system and is therefore physically significant.

Is viscous stress a symmetric tensor?

As with any symmetric tensor, the viscous stress tensor ε can be expressed as the sum of a traceless symmetric tensor εs, and a scalar multiple εv of the identity tensor. In coordinate form, This decomposition is independent of the coordinate system and is therefore physically significant.

## What is the viscosity tensor in fluid mechanics?

Viscous stress tensor. The tensor μ has four indices and consists of 3 × 3 × 3 × 3 real numbers (of which only 21 are independent). In a Newtonian fluid, by definition, the relation between ε and E is perfectly linear, and the viscosity tensor μ is independent of the state of motion or stress in the fluid.