--- title: "Nikuradse's experiment on roughened pipes" subject: "Hydraulics" chapter: 1 key: "semester_4/hydraulics:nikuradse-experiment-roughened-pipes" source: https://www.bctengineer.com/q/semester_4/hydraulics/nikuradse-experiment-roughened-pipes site: BCT Engineering --- # Nikuradse's experiment on roughened pipes Hydraulics · Chapter 1: Pipe flow - Asked in: 2068 Magh, 3+5 marks - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/hydraulics/nikuradse-experiment-roughened-pipes - Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-1 ## Question Explain the experiment made by Nikuradse on resistance to artificially roughened pipes. Discuss the characteristic features of the result obtained. ## Short answer Nikuradse glued uniform sand grains inside pipes to create known k/D, measured head loss over a wide Re range, and plotted f vs Re. Results: laminar f=64/Re independent of roughness; smooth turbulent f follows Blasius curve; transition region where f depends on both Re and k/D; fully rough regime where f becomes constant for a given k/D, given by 1/√f = 2 log₁₀(D/k) + 1.14. Higher roughness leaves the smooth curve earlier. ## Answer #### The experiment Nikuradse (1933) coated the inside of pipes with uniform sand grains of known size $k$ glued with varnish, giving relative roughness $k/D$ = 1/30, 1/61, 1/120, 1/252, 1/504 and 1/1014. Water was passed through each pipe at a wide range of discharges (Reynolds number from about $5\times10^2$ to $10^6$). He measured the discharge and the pressure drop over a length of pipe, calculated the friction factor $f$ from $h_f = \dfrac{fLV^2}{2gD}$, and plotted $\log f$ against $\log Re$ for each $k/D$. He also measured velocity profiles to get the log laws. #### Results (characteristic features) ```text log f | \ laminar rough: f flat for each k/D | \ f=64/Re ____________________ k/D = 1/30 | \ / ___________________ 1/61 | \ crit/ _/ ________________ 1/504 | \ / _/ __/ | `-._/ _/ / smooth (Blasius) curve | `-----' +--------------------------------- log Re ``` | Region | Reynolds number | Behaviour of $f$ | |---|---|---| | Laminar | $Re < 2000$ | $f = 64/Re$ for all roughnesses (a single straight line) | | Critical | 2000 to 4000 | $f$ rises sharply; unstable | | Smooth turbulent | above 4000 up to a limit depending on $k/D$ | All pipes follow the smooth curve, $f = f(Re)$, e.g. Blasius $0.316/Re^{0.25}$. The roughness is within the laminar sub-layer | | Transition | intermediate | Pipe leaves the smooth curve; $f$ depends on both $Re$ and $k/D$. The larger the $k/D$, the earlier it departs | | Fully rough | high $Re$ | Curve is horizontal: $f$ depends only on $k/D$, $\dfrac{1}{\sqrt f} = 2\log_{10}\dfrac{D}{k} + 1.14$ | Other features: - Roughness has no effect on laminar flow. - Pipes with higher $k/D$ leave the smooth curve at lower $Re$ and reach higher constant $f$ values. - The classification by the roughness Reynolds number $\dfrac{u_*k}{\nu}$: smooth below about 4, transition 4 to 100, fully rough above about 100 (some texts use 70). - Some curves show a slight dip below the smooth line before rising (in the transition for uniform roughness), a feature not seen in commercial pipes. The results formed the basis of the Moody chart and the Colebrook-White equation. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How did Nikuradse create known roughness? A. By corroding steel pipes B. By gluing uniform sand grains of known size k inside pipes C. By using wavy pipe walls D. By varying fluid viscosity Answer: B. Pipes were coated with uniform sand grains, giving relative roughness k/D from 1/30 to 1/1014. (Key point: Experimental method) 2. How does roughness affect f in laminar flow in his results? A. Larger k/D gives larger f B. Larger k/D gives smaller f C. It has no effect; all pipes follow f = 64/Re D. f is constant Answer: C. In laminar flow all curves lie on the single line f = 64/Re. (Key point: Laminar results) 3. Which describes the fully rough region? A. f falls with Re B. f depends on Re only C. f depends on both Re and k/D D. f is constant with Re and depends only on k/D Answer: D. The curves become horizontal, with 1/sqrt f = 2 log(D/k) + 1.14. (Key point: Fully rough region) 4. How do pipes with larger k/D behave as Re increases? A. They leave the smooth curve at lower Re and reach higher constant f B. They leave the smooth curve at higher Re and reach lower f C. They never leave the smooth curve D. They follow the laminar line longer Answer: A. Rougher pipes depart earlier from the smooth curve and level off at higher f. 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