ANS:D - none of these.

Let's analyze each statement regarding the friction factor:

1. Friction factor is always inversely proportional to the Reynolds number.
   • This statement is not accurate. The friction factor (fff) varies with the Reynolds number (ReReRe) and depends on whether the flow is laminar or turbulent:
     • For laminar flow, the friction factor fff is inversely proportional to ReReRe: f=16Ref = \frac{16}{Re}f=Re16​.
     • For turbulent flow, the friction factor fff depends on the relative roughness (ε/D) of the pipe and the Reynolds number, and it is not simply inversely proportional.
2. Friction factor is not dimensionless.
   • This statement is incorrect. The friction factor (fff) is indeed dimensionless. It represents the ratio of the shear stress at the wall to the dynamic pressure of the fluid.
3. Friction factor is not dependent on the roughness of the pipe.
   • This statement is incorrect. The friction factor (fff) for turbulent flow depends significantly on the relative roughness (ε/D) of the pipe. Rougher surfaces lead to higher friction factors due to increased surface roughness causing greater turbulent flow resistance.

• The friction factor is not always inversely proportional to the Reynolds number.
• The friction factor is indeed dimensionless.
• The friction factor depends on the roughness of the pipe, especially in turbulent flow.