I am not totally convinced of this. Perhaps smooth is not always better than corrugated. But I wouldn't be surprised if there were some gains by switching to smooth intake tubing.

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Explanation of the empirical results may be explained in the following manner:

Head Loss in a Pipe

Overall head loss in a pipe is affected by a number of factors which include the viscosity of the fluid, the size of the internal pipe diameter, the internal roughness of the inner surface of the pipe, the change in elevation between the ends of the pipe and the length of the pipe along which the fluid travels.

Valves and fittings on a pipe also contribute to the overall head loss that occurs, however these must be calculated separately to the pipe wall friction loss, using a method of

modeling pipe fitting losses with k factors.

Darcy Weisbach Formula

The Darcy formula or the Darcy-Weisbach equation as it tends to be referred to, is now accepted as the most accurate pipe friction loss formula, and although more difficult to calculate and use than other friction loss formula, with the introduction of computers, it has now become the standard equation for hydraulic engineers.

Weisbach first proposed the relationship that we now know as the Darcy-Weisbach equation for calculating friction loss in a pipe.

**Darcy-Weisbach equation:**
hf = f (L/D) x (v^2/2g)

where:

hf = head loss (m)

f = friction factor

L = length of pipe work (m)

d = inner diameter of pipe work (m)

v = velocity of fluid (m/s)

g = acceleration due to gravity (m/s²)

or:

hf = head loss (ft)

f = friction factor

L = length of pipe work (ft)

d = inner diameter of pipe work (ft)

v = velocity of fluid (ft/s)

g = acceleration due to gravity (ft/s²)

The establishment of the friction factors was however still unresolved, and indeed was an issue that needed further work to develop a solution such as that produced by the

Colebrook-White formula and the data presented in the Moody chart.

The Moody Chart

The Moody Chart finally provided a method of finding an accurate friction factor and this encouraged use of the Darcy-Weisbach equation, which quickly became the method of choice for hydraulic engineers.

Friction Factor Chart / Moody Chart

The friction factor or Moody chart is the plot of the relative roughness (e/D) of a pipe against the

Reynold's number. The blue lines plot the friction factor for flow in the wholly turbulent region of the chart, while the straight black line plots the friction factor for flow in the wholly laminar region of the chart.

In 1944, LF Moody plotted the data from the Colebrook equation and the resulting chart became known as

**The Moody Chart** or sometimes the Friction Factor Chart. It was this chart which first enabled the user to obtain a reasonably accurate friction factor for turbulent flow conditions, based on the Reynolds number and the Relative Roughness of the pipe.

Friction Factor for Laminar Flow

The friction factor for laminar flow is calculated by dividing 64 by the

Reynold's number.

Friction factor (for laminar flow) = 64 / Re

MANNING'S ROUGHNESS COEFFICIENT

Manning's Formula for Gravity Flow
Polyethylene PE - Corrugated with corrugated inner walls 0.018 - 0.025

Polyvinyl Chloride PVC - with smooth inner walls 0.009 - 0.011

CONCLUSIONS:

e/D of the corrugated surface > e/D of the smooth surface

Corrugated duct creates larger layer of the turbulent flow close to the wall effectively reducing the laminar (fast) flow cross section area. Any bends make conditions worse.

**Therefore, replacing corrugated hoses with smooth bore ducting improves the turbo compressor efficiency.**