Question

Flow takes place at Reynolds Number of 1500 in two different pipes with relative roughness of 0.001 and 0.002. The friction factor
1. Will be higher for the pope with relative roughness of 0.001
2. Will be higher for the pipe having relative roughness of 0.002
3. Will be the same in both the pipes
4. In the two pipe cannot be compared on the basis of data given

Answer 1

Correct Answer - Option 3 : Will be the same in both the pipes

Concept:

Friction factor (For laminar) \( = \frac{{64}}{{Re}}\)

As the Reynolds number is the same for both pipe flow.

∴ The friction factor will be the same for both pipes.

Relative roughness \( = \frac{K}{{\delta '}}\)

where k is the average height of the irregularities and δ’ is the thickness of laminar sub-layer

\(\frac{{\rm{k}}}{{{\rm{\delta '}}}} < 0.25 \Rightarrow {\rm{Smooth\;boundary}}\)

\(\frac{{\rm{k}}}{{{\rm{\delta '}}}} > 6 \Rightarrow {\rm{Rough\;boundary}}\)

\(0.25 < \frac{k}{{\delta '}} < 6.0 \Rightarrow Transition\;\)