Question

In many problems involving application of Newton's Second Law to the motion of solid objects, friction is neglected for the sake of making the solution easier. The counterpart of friction between solids is viscosity of liquids. Do problems involving fluid flow become simpler if viscosity is neglected? Explain.

Short answer

Answer: Neglecting viscosity can indeed simplify certain fluid flow problems, such as those involving ideal fluid flow. However, there are cases where considering viscosity is necessary, especially when dealing with boundary layers, turbulence, or other situations where viscous effects play a significant role. Therefore, the decision to neglect viscosity should be made on a case-by-case basis, depending on the problem conditions and the desired level of accuracy.

Step-by-step solution

Understanding Viscosity

Viscosity is a property of fluids that represents their resistance to deformation or flow. It is caused by the internal friction of molecules in the fluid, and it plays a critical role in determining the flow behavior of liquids.

Viscosity in Fluid Flow Problems

In problems involving fluid flow, viscosity is often an important factor that determines the behavior of the fluid. For example, in the case of fluid flow through a pipe or between surfaces, the viscous effects can cause the fluid to slow down and create a pressure drop. Additionally, in fluid dynamics problems, viscosity dictates the balance of forces, such as shear stress and pressure gradients.

Neglecting Viscosity

In some cases, neglecting viscosity can simplify the problem. For example, in the case of ideal fluid flow, where viscosity is considered negligible, the flow can be assumed to be inviscid and irrotational. This can make the problem easier to solve as it eliminates the need to account for viscous effects in the equations, such as the Navier-Stokes equations.

Limitations of Neglecting Viscosity

However, neglecting viscosity can also render some fluid flow problems unrealistic or impossible to solve accurately. For instance, many boundary layer flows and turbulence phenomena are highly influenced by viscous effects, and neglecting them would yield incorrect results. In such situations, considering viscosity is essential to accurately solve the problem.

Conclusion

In summary, neglecting viscosity can indeed simplify certain fluid flow problems, such as those involving ideal fluid flow. However, there are cases where considering viscosity is necessary, especially when dealing with boundary layers, turbulence, or other situations where viscous effects play a significant role. Therefore, the decision to neglect viscosity should be made on a case-by-case basis, depending on the problem conditions and the desired level of accuracy.