Rough duct correlations

Friction factors

Laminar Flow: Re < 2300

In the case of purely laminar flow, the roughness has no influence on the friction factor, which is given by:

Re is the Reynolds number, given by

Turbulent Flow: Re ≥ 4000

It is noted that the experiments of Nikuradse [30] are often cited as having identified three different friction factor regimes during turbulent flow in rough pipes. These experiments, however, were performed using smooth pipes with grains of sand of “uniform” size glued to them. His results are not typical for the roughness typically found in commercial rough pipes. Therefore, the results of Colebrook [31], on which the Moody diagram is based, are used over those of Nikuradse.

For smooth circular pipes, the friction factor is of the form. The most suitable correlation in this regime is that given by Colebrook,

For rough pipes, the friction factor correlation is of the form.

The correlation by Jain is the most accurate explicit formula that approximates the original implicit correlation by Colebrook.

Transition to Turbulent Flow: 2300 < Re < 4000

There is little accurate data for this region. We would like a function which creates a continuous transition from laminar to turbulent conditions. We use a linear joining function between the laminar and turbulent friction factors, given by:

f₄₀₀₀ depends on the roughness.

Nusselt numbers

The Nusselt number in rough ducts is only significantly different from smooth ducts in non-laminar flow conditions.

The following correlation is used for Re > 2300.

where

• n = 68Pr^0.215 for Pr ⩽6
• n = 0 for Pr > 6