Compute the relative roughness ε/D for a pipe with ε = 0.045 mm and D = 100 mm.

• A. 4.50×10^-4
• B. 4.50×10^-3
• C. 4.50×10^-5
• D. 4.05×10^-4

Answer: (A)

Relative roughness is the dimensionless ratio of the pipe’s roughness height to its diameter, ε/D. Use consistent units. Here both measurements are in millimeters, so ε/D = 0.045 / 100 = 0.00045. In scientific notation, that’s 4.5×10^-4. This is the correct value. The other numbers would come from dividing by a different diameter or from placing the decimal differently (for example, 0.045/10 would give 4.5×10^-3, while 0.045/111 is about 4.05×10^-4).