In the expression 1/√f = 4 log(3.7 D / e), the parameter e is defined as surface roughness.

In the expression 1/√f = 4 log(3.7 D / e), the parameter e is defined as surface roughness.

• A. True
• B. False
• C. Only for rough seas
• D. Dependent on wind direction

Answer: (A)

The main idea here is that this form comes from turbulent flow in a conduit where the roughness of the inner surface controls the friction factor. When the flow is in the fully rough regime, the friction factor f depends mainly on the relative roughness e/D, and the relationship can be written as 1/√f ≈ 4 ln(3.7D/e). The symbol e represents the roughness height of the surface—i.e., the size of the roughness elements on the conduit’s interior. So the statement that e is defined as surface roughness is correct. This isn’t about sea state or wind direction. It’s not about atmospheric surface roughness in open air; it’s about the roughness of the surface in contact with the flowing fluid, which sets the friction factor in this regime. If the surface were smooth, the relation would look different and depend on Reynolds number; the fully rough form highlights the role of roughness height rather than wind or sea conditions.

The main idea here is that this form comes from turbulent flow in a conduit where the roughness of the inner surface controls the friction factor. When the flow is in the fully rough regime, the friction factor f depends mainly on the relative roughness e/D, and the relationship can be written as 1/√f ≈ 4 ln(3.7D/e). The symbol e represents the roughness height of the surface—i.e., the size of the roughness elements on the conduit’s interior. So the statement that e is defined as surface roughness is correct.

This isn’t about sea state or wind direction. It’s not about atmospheric surface roughness in open air; it’s about the roughness of the surface in contact with the flowing fluid, which sets the friction factor in this regime. If the surface were smooth, the relation would look different and depend on Reynolds number; the fully rough form highlights the role of roughness height rather than wind or sea conditions.