OR Draw rough nature of Moody Chart showing different regimes of fluid flow and explain its significance

The Moody chart or Moody diagram is a graph in non-dimensional plot that relates the Darcy Weisbach friction factor (f), Reynolds number(Re) and Relative Roughness parameter(ϵ/d) for fullydeveloped flows in a circular pipe.

It can be used to calculatethe Head loss $(h_f)$ through pipes for a given flow rate or the flow rate through a pipe for a given head loss.

Head loss can be calculated using the Darcy Weisbach equation,

$h_f= \frac{flV^2}{2gd}$

where,

ρ →Density of the fluid

f→ Friction factor from the Moody chart

l → Length of the pipe

V → Average fluid velocity in the pipe

d → Pipe diameter

It can be seen from the figure that the graph consists of 3 fluid flow regimes:

Laminar Flow(Re≤2300)

Transition Flow (2300$ \lt Re\lt4000$)and

Turbulent Flow(Re≥4000)

It can be seen that the friction factor for laminar flow is a function of Reynolds number alone and is independent of relative roughness of the pipe.

While the friction factor for turbulent flow is a function of both Reynolds number and relative roughness of the pipe.

The friction factor for transition flow can usually be interpolated between the laminar value at Re = 2300 and the turbulent value at Re = 4000.

The Relative Roughness parameter is the ratio of the mean height of roughness of the pipe to the pipe diameter (ϵ/d).

It can also be seen that in the highly turbulent region (i.e. at high Re) for rough pipes the fiction factor becomes independent of the Reynolds number and depends only on the relative roughness this happens since the thickness of the laminar sub layer reduces, completely exposing the surface roughness.