To understand what happens to the frictional head loss in a water pipe with increasing roughness, we need to explore the concepts of fluid flow and frictional resistance within pipes.

Understanding Frictional Head Loss

The frictional head loss in a pipe is related to the resistance that the fluid encounters as it moves through the pipe. This resistance is influenced by several factors, including the pipe's surface roughness. The Darcy-Weisbach equation gives us insight into how these factors are interrelated:

h_f = \frac{f \cdot L \cdot V^2}{2 \cdot g \cdot D}

• h_f is the head loss due to friction (m).
• f is the Darcy-Weisbach friction factor (dimensionless).
• L is the length of the pipe (m).
• V is the velocity of the fluid (m/s).
• g is the acceleration due to gravity (m/s²).
• D is the diameter of the pipe (m).

Effect of Roughness on Frictional Head Loss

The key factor here is the friction factor f, which is influenced by the roughness of the pipe's interior surface. When scaling occurs, the interior surface of the pipe becomes rougher. The relationship between pipe roughness and the friction factor is described by the Colebrook-White equation, which is more complex but shows that as roughness increases, so does the friction factor.

For a given flow rate (constant V), if the roughness increases, f also increases, leading to a greater head loss h_f.

Conclusion

Based on the above analysis, as the scaling increases the roughness of the pipe, the frictional head loss increases. Therefore, the correct answer to the question is:

Correct Answer: Increases