How did Nikuradse create known roughness?

By gluing uniform sand grains of known size k inside pipes

How does roughness affect f in laminar flow in his results?

It has no effect; all pipes follow f = 64/Re

Which describes the fully rough region?

f is constant with Re and depends only on k/D

How do pipes with larger k/D behave as Re increases?

They leave the smooth curve at lower Re and reach higher constant f

They leave the smooth curve at higher Re and reach lower f

They never leave the smooth curve

They follow the laminar line longer

2068 Magh · 3+5 marks

Nikuradse's experiment on roughened pipes

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.

Explain the experiment made by Nikuradse on resistance to artificially roughened pipes. Discuss the characteristic features of the result obtained.

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)

 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.

✓ Answer checked by Claude Sonnet 5.5

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Nikuradse's experiment on roughened pipes

The experiment

Results (characteristic features)

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