The Moody chart, a logarithmic chart between frction factor and _________ for a variety of relative roughness in a pipe flow.

Explanation

Moody’s diagram is used to calculate the friction factor of commercial pipes.

It is drawn between friction factor and Reynolds number for various relative roughness.

It is derived for the circular pipe but applicable to other cross-sections as well provided that the diameter is replaced by 4 times the hydraulic radius.

Thus the moody’s chart is a graphical representation between the friction factor, relative roughness, and Reynolds number

Hence the correct answer is option 2.

Note: Relative roughness is the ratio of pipe roughness and the pipe diameter.

Relative roughness \( = {\rm{\;}}\frac{{{{\rm{K}}_{\rm{s}}}}}{{\rm{D}}}\)

Important Points:-

Friction factor for laminar flow is dependent only on Reynold’s number.

It is given as:-

\({\rm{f\;}} = {\rm{\;}}\frac{{64}}{{{{\rm{R}}_{\rm{e}}}}}\)

For Turbulent flow, the friction factor is given as:-

Friction factor for Turbulent flow:

1) Smooth Pipe:

\({\rm{f}} = \frac{{0.316}}{{{{\left( {{{\rm{R}}_{\rm{e}}}} \right)}^{1/4}}}};4000 \le {{\rm{R}}_{\rm{e}}} \le {10^5}\)

\({\rm{f}} = 0.0032 + \frac{{0.221}}{{{{\left( {{{\rm{R}}_{\rm{e}}}} \right)}^{0.237}}}};{10^5} \le {{\rm{R}}_{\rm{e}}} \le 4 \times {10^7}\)

2) Rough Pipe:

\(\frac{1}{{\sqrt {\rm{f}} }} = 2{\log _{10}}\left( {\frac{{\rm{R}}}{{{{\rm{K}}_{\rm{s}}}}}} \right) + 1.74\)

Note: For smooth pipe friction factor is a function of Reynolds no duty.

f = g(Re) → for smooth pipe

f = h(Ks/D) → for rough pipe

f = K(Re, Ks/D) → Transition