Which statement defines relative roughness?

Which statement defines relative roughness?

• A. The ratio of the pipe diameter to the absolute roughness.
• B. The ratio of the roughness to the diameter.
• C. The ratio of absolute roughness to the pipe diameter.
• D. The product of roughness and diameter.

Answer: (C)

Relative roughness is the dimensionless quantity that describes how rough the pipe wall appears to the flowing fluid, defined as the absolute roughness divided by the inside diameter. The absolute roughness is the actual height of the surface irregularities on the pipe’s interior, a fixed property of the material and its condition, while the diameter scales how large the wall irregularities look to the flow. When this ratio is larger (rougher surface or smaller diameter), the flow experiences more friction losses, especially in turbulent flow, which is why this ratio is used in friction-factor correlations like the Moody chart and the Colebrook-White equation. That’s why expressing relative roughness as the ratio of absolute roughness to the pipe diameter is the correct definition. The other options either invert the relationship, use the wrong quantity, or combine them in a way that doesn’t yield a dimensionless measure of wall roughness.

Relative roughness is the dimensionless quantity that describes how rough the pipe wall appears to the flowing fluid, defined as the absolute roughness divided by the inside diameter. The absolute roughness is the actual height of the surface irregularities on the pipe’s interior, a fixed property of the material and its condition, while the diameter scales how large the wall irregularities look to the flow. When this ratio is larger (rougher surface or smaller diameter), the flow experiences more friction losses, especially in turbulent flow, which is why this ratio is used in friction-factor correlations like the Moody chart and the Colebrook-White equation. That’s why expressing relative roughness as the ratio of absolute roughness to the pipe diameter is the correct definition. The other options either invert the relationship, use the wrong quantity, or combine them in a way that doesn’t yield a dimensionless measure of wall roughness.