Frictional Resistance for Fluids in Motion and its Variation with Temperature

Fluid flow is characterized by the presence of frictional resistance, which is the resistance offered by the fluid to the motion of an object through it. This frictional resistance is influenced by various factors, including the temperature of the fluid. The given question asks about the variation of frictional resistance with temperature for both laminar and turbulent flows.

The Effect of Temperature on Frictional Resistance
- It is well-known that temperature affects the viscosity of fluids. Viscosity is a measure of a fluid's resistance to flow and is directly related to the frictional resistance experienced by the fluid.
- As the temperature of a fluid increases, its viscosity generally decreases. This is because higher temperatures increase the kinetic energy of the fluid molecules, causing them to move more freely and reducing the internal friction within the fluid.
- Conversely, as the temperature of a fluid decreases, its viscosity generally increases. Lower temperatures reduce the kinetic energy of the fluid molecules, causing them to move slower and increasing the internal friction within the fluid.

Frictional Resistance and its Variation with Temperature for Laminar Flow
- Laminar flow occurs when a fluid flows in smooth layers with little to no mixing between them. In laminar flow, the fluid molecules move in an orderly manner along parallel paths.
- For laminar flow, the frictional resistance is primarily influenced by the viscosity of the fluid. As mentioned earlier, the viscosity of a fluid decreases with increasing temperature and increases with decreasing temperature.
- Therefore, the frictional resistance for laminar flow is expected to vary slightly with temperature. This is because the change in viscosity due to temperature variations is not significant enough to cause a substantial change in the frictional resistance experienced by the fluid.

Frictional Resistance and its Variation with Temperature for Turbulent Flow
- Turbulent flow occurs when a fluid flows in an irregular and chaotic manner, with significant mixing and eddying of fluid particles.
- In turbulent flow, the frictional resistance is influenced by various factors, including the viscosity of the fluid. However, unlike laminar flow, the frictional resistance in turbulent flow is also affected by other factors such as the fluid's density and velocity.
- While the viscosity of a fluid still plays a role in determining the frictional resistance in turbulent flow, the effect of temperature on viscosity is not the sole determinant.
- Therefore, the frictional resistance for turbulent flow is expected to vary considerably with temperature. This is because the change in viscosity due to temperature variations can interact with other factors affecting turbulent flow and lead to significant changes in the overall frictional resistance experienced by the fluid.

Conclusion
In summary, the given question correctly states that the frictional resistance for fluids in motion varies considerably with temperature for laminar flow and slightly with temperature for turbulent flow. This is because the effects of temperature on viscosity and other factors influencing flow behavior differ between laminar and turbulent flows.