Question

Consider the following statements:

1. In flow through hydro-dynamically smooth pipes, the friction factor f is always a constant.

2. In flow through hydro-dynamically smooth pipes, the friction factor f is always a function of the flow Reynolds number.

3. In a fully developed rough turbulent pipe flow, the friction factor f is a function of relative roughness only.

4. In a fully developed rough turbulent pipe flow, the friction factor f is a function of the flow Reynolds number and relative roughness.

Which of the above statements are correct?
1. 1 and 3
2. 2 and 3
3. 2 and 4
4. 1 and 4

Answer 1

Correct Answer - Option 2 : 2 and 3

Explanation:

If K/δ < 0.25 ⇒ Pipe is said to be Hydro-dynamically smooth

and

if K/δ > 6 ⇒ Pipe is said to be Hydro-dynamically rough

Where, K = Surface roughness and δ is laminar sub-layer thickness.

For rough pipe, the relation between friction factor and surface roughness of pipe is based on Nikursade’s experiment and it is given by:

\(\frac{1}{{\sqrt f }} = 2{\log _{10}}\left( {\frac{D}{{2K}}} \right) + \;1.74\) ;

Relative Roughness = K/D

It is clear from above that friction factor is the non-linear function of relative roughness (K/D).

For Smooth pipe, the relation between friction factor and Reynolds No. of pipe is based on Nikursade’s experiment and it is given by:

\(\frac{1}{{\sqrt f }} = 2{\log _{10}}\left( {Re\sqrt f } \right) - 0.8\) ;

It is clear from above that friction factor is the non-linear function of Reynolds Number for smooth pipe.