Wall Shear Stress of Flowing Fluids; Explanations and Equations

What is Wall Shear Stress?

Fluid mechanics is a very important area in engineering. Also and there are various kinds of physical phenomena about fluids. One of these phenomena is the wall shear stress of flowing fluids. So, we explain this and you will find information and calculations about this issue.

Direction of wall shear stress.
Image Source: Researchgate.com.

What is Wall Shear Stress?

Firstly, think about a fluid that flows over a surface. Because of this flow, there will be a frictional force over the surface. So, this force originated from the shear force on that surface. With the increasing viscosities of fluids, this shear force increases. We can calculate this wall shear stress with this formula;

Wall shear stress formula.

In this equation,

  • Cf: Friction coefficient between the surface and the fluid. They are determining this value with experiments. This value has no units, it’s dimensionless.
  • q: Viscosity of the fluid which has the unit of Pa.s or lbf·s/ft2 in English units. 
  • V: Velocity of the fluid over the surface which has the units of m/s or ft/s.

As you understand, with the increasing friction coefficient, the wall shear stress increases. Also with the increasing viscosity of the fluid, it increases. Furthermore, it increases exponentially with the increasing velocity of the fluid.

Maybe the most important factor to increase the wall shear stress of a flowing fluid is the velocity of the fluid.

Applications

There are different kinds of applications of this phenomenon in engineering. One of these applications is the aerodynamical drags on surfaces of planes or automobiles. The drag coefficient is very important in these applications where engineers are trying to decrease it. Also, they are not increasing or decreasing the other parameters that we stated above.

In addition, other applications of the lubrication of machinery, especially bearings. Also, for elastohydrodynamic lubrication of machine parts, it is very important to shear stress and force should not exceed the maximum strength of the material.

Conclusion

These are the general explanations of this phenomenon of flowing fluids. They are very important in such engineering applications.

In conclusion, do not forget to leave your comments and questions below about this topic.

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