Vapor/steam is a single phase fluid, and should be treated as such. This means that single phase correlations are applicable for this case. If your correlations overestimate the pressure gradient, it is most likely the friction factor that is inadequate. Select a valid correlation, and be aware that the literature operates with different definitions of the friction factor (f_Darcy and f_Fanning: f_Darcy=4*f_Fanning). dp/dx=f_Darcy*0.5*rho*v^2/D

When calculating the friction factor for superheated vapor in pipes, you can use the Haaland equation or the Chen equation, as these are well-suited for both laminar and turbulent flow regimes and are commonly used for gases and vapors.

Raja Saviour: A word of caution: The Haaland and the Chen correlations are valid for (fully) turbulent flow only (and not laminar flow). However, they both include the effect of surface roughnness.

Thank you for pointing that out. You’re correct that the Haaland and Chen correlations are indeed applicable only for fully turbulent flow. These correlations are particularly useful because they account for the effects of surface roughness, which is crucial in many practical applications.

For laminar flow situations, the friction factor can be determined using simpler correlations such as:

f=64Ref = \frac{64}{\text{Re}}f=Re64​

where Re\text{Re}Re is the Reynolds number. This formula is valid for laminar flow (Re < 2000) and does not account for surface roughness, as it assumes smooth pipe conditions.

When dealing with superheated steam or other gases in laminar flow, you should also ensure that the flow regime is accurately determined before selecting the appropriate friction factor correlation. For turbulent flows where surface roughness becomes significant, using the Haaland or Chen correlations can provide a more accurate estimation.

Always consider the flow regime and the characteristics of the fluid when choosing a friction factor correlation to ensure the accuracy of your calculations.

I have used the Churchill equation for friction factor for many years. It is as accurate as the more difficult (iterative) Colebrook equation. It covers both the laminar and turbulent range of Re, and allows well for surface roughness.

You make an excellent point about the Churchill equation. It is indeed a robust and versatile correlation for calculating the friction factor across both laminar and turbulent flow regimes. One of its major advantages is that it handles the entire range of Reynolds numbers and accounts for surface roughness effectively.

The Churchill equation provides accurate results similar to the more complex and iterative Colebrook equation but without the need for iterative solving. This makes it a practical choice for many applications where simplicity and reliability are key.

In summary, if you've had success with the Churchill equation and find it meets your accuracy requirements, it's a solid option. Its comprehensive approach to both flow regimes and roughness makes it a valuable tool in engineering practice.

I am grateful for your answers, they have all helped me with my problem. In this regard, I would like to comment that I have found significant problems in calculating the pressure drop (dP) in superheated vapor transport pipes, (10 kg/s, 10 bar, close to saturation). The correlations of Churchill or Fang et al (2011) in Nuclear engineering and design give me the impression that there is still a problem to be solved in predicting dP in superheated steam flow.

Dario Colorado-Garrido There is little real difficulty in calculating the pressure drop for steam in any pipe, provided the diameter is accurate and roughness known: it is much more difficult in the superheater itself as temperature changes can be large and flow distribution difficult.

There are even graphical methods that are accurate for pipework. Would be good to know what problem you foresee.