ANS:A - increase.

For a hydraulically smooth pipe, the friction factor fff at a Reynolds number Re=2100\text{Re} = 2100Re=2100 is denoted as f1f_1f1​. This friction factor f1f_1f1​ corresponds to a certain level of surface roughness. When the pipe is further smoothened (i.e., the roughness is reduced):

• Friction Factor fff: The friction factor fff for flow in a pipe is influenced by the relative roughness ( ϵ/D\epsilon / Dϵ/D, where ϵ\epsilonϵ is the absolute roughness and DDD is the pipe diameter) and the Reynolds number Re\text{Re}Re.
• Impact of Smoothening:
  • If the pipe surface is made smoother (reducing ϵ\epsilonϵ), the relative roughness ϵ/D\epsilon / Dϵ/D decreases.
  • A decrease in relative roughness typically leads to a reduction in the friction factor fff for a given Reynolds number Re\text{Re}Re.
  • This reduction occurs because smoother surfaces induce less resistance to flow, resulting in lower frictional losses.

Therefore, when the pipe is further smoothened, the friction factor fff at the same Reynolds number Re=2100\text{Re} = 2100Re=2100 will decrease. This decrease reflects the improved flow conditions due to reduced surface roughness, leading to more efficient fluid transport with lower frictional losses.