# Transverse and Shear Stress in Turbulent Flow

### Key Takeaways

• The stress acting in a direction normal to the surface of a material is called normal stress or transverse stress.

• The three normal stresses to be considered in pipes are axial stress, hoop stress, and radial stress.

• In turbulent flow, shear stresses are much greater than in laminar flow due to eddy currents, which increase the momentum flux in all directions.

Understanding the stresses acting on a piping system is critical when designing pipes

Understanding the stresses acting on a piping system is critical when performing stress analysis on pipes. Depending on the application, piping system analysis codes vary; however, the physics of piping stress analysis remains unchanged regardless of the application. Here, we will discuss piping stress analysis and how transverse and shear stress impact fluid flow in a pipe.

## Piping Stress Analysis

Piping stress analysis is performed primarily for safety. Analyzing stresses acting on a piping system ensures the safety of personnel. The next objective of piping stress analysis is to increase the life of the pipes. Proper design and maintenance are essential for the long shelf life of the piping system. When pipes are subjected to stress, over time the stress causes wear and tear, resulting in breaks, temporary shutdowns, or even fatal accidents. Considering the value of human life and the capital invested in building a piping system, it is important to conduct piping stress analysis.

## Types of Stresses on a Piping System

Stresses have devastating effects on the life of pipes. The stress acting in a direction normal to the surface of the material is called normal stress or transverse stress. The three normal stresses that need to be considered in pipes are:

Axial stress or longitudinal stress - Normal stress that acts in parallel to the longitudinal axis in the pipe. The common reasons for this stress generation are internal design pressure, an axial force acting on the pipe, or a bending force.

Circumferential or hoop stress - Normal stress that acts perpendicular to the axial direction or circumferential direction of the pipe. Internal pressure is the primary cause of hoop stress in pipes.

Radial stress - Normal stress acting parallel to the pipe radius, primarily caused by internal pressure.

The piping system is subject to shear stress due to forces acting on its cross-section or torsional moments. The other stress to take into account is thermal stress, otherwise called expansion stress, which is generated when the free thermal movement of the pipe is restricted.

The flow inside a pipe can be either laminar or turbulent. Depending on the flow type, the forces and stresses acting on the fluid differ. The upcoming section describes the stresses in laminar and turbulent flows

## Transverse and Shear Stress in Turbulent Flows

Most of the flow in pipes is turbulent. The stress developed in a turbulent flow is different from laminar flow. In laminar flow, shear stress is generated due to molecular interchanges between adjacent fluid layers and cohesive forces between liquid molecules. In turbulent flow, the shear stress is much greater than in laminar flow due to the eddy currents, which increase the momentum flux in all directions. The turbulent flow total shear stress can be given by:

T is the total shear stress in turbulent flow, Tlam is the shear stress contributed by laminar flow, and T' is the turbulence shear stress generated due to velocity fluctuations and eddy motion in turbulent flow. The major part of the total stress in turbulent flow is formed by T'.

In a 3D fluid flow, different stresses are generated in the fluid depending on the momentum and momentum transfer. The stresses that act in the x-direction of the momentum in x-direction can be given by Txx. Similarly, the y-direction of the momentum in y-direction and the z-direction of the momentum in z-direction are given by Tyy and Tzz. The stresses  Txx,Tyy, and Tzz are called normal stresses or transverse stresses. The other stress acting on the fluid is called shear stress, namely Txy, Txz, Tyx, Tyz, Tzx, and Tzy, where the first subscript denotes the direction of the momentum and second subscript represents the direction in which it is transferred.

It is important to understand the transverse and shear stress acting on a fluid flow in order to design an appropriate piping system. The pipe material thickness and cross-section are determined by evaluating the stresses acting on the pipe in pipe stress analysis.

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