Stephen Hall offers practical tips on calculating pressure loss due to friction
THE Darcy-Weisbach equation is widely used to calculate pressure loss due to friction for liquids in pipelines. It is also sufficiently accurate for gases for most applications if the pressure drop is less than about 10% of the inlet pressure; the expansion of the gas as it loses pressure isn’t enough to throw the calculation out of its range of accuracy.
The equation depends on the Darcy (or Moody) friction factor, an empirically-derived value that was read from a chart that was originally published in 1944. This necessitates a multi-step procedure to apply Darcy-Weisbach:
The beauty of Darcy-Weisbach is that it applies to any Newtonian fluid, pipes with smooth or rough internal surfaces, and any flow rate. By restricting its use to water or natural gas, the equation can be simplified by incorporating the density and viscosity of the specified fluid into a parameter in the simplified equation. For example the Hazen-Williams equation is used to design water pipelines; the Weymouth and Panhandle equations are for natural gas.
Here is a handy simplified formula that is applicable to any Newtonian fluid, but is restricted to turbulent flow (Reynolds number >4,000) and commercial steel pipes (roughness = 0.045 mm). For smooth tubes such as glass or polished stainless steel, use coefficient 0.014 instead of 0.016.
Before embracing a simplified approach, test it by comparing its results to a validated standard. The results for the simplified formula are within 10% of the Darcy-Weisbach equation in the range of 0.3–3 m/s flow velocity (Reynolds number 2,700–340,000). Repeating the comparison with Therminol at a viscosity of 0.050 Pa-s again gives excellent agreement in the turbulent range from Reynolds number above 3,000. But the velocity must exceed 1.5 m/s to be in that range. As seen in the third chart the simplified formula is applicable over a range of Reynolds numbers, not specific pressure drop or velocity.
You need to be logged in to read the rest of this article
Chief Process Engineer at Genesis AEC, a US design and construction service provider in the life science industry
He authored Rules of Thumb for Chemical Engineers, 6th Edition (Elsevier, 2018).
This article has been featured in:
Rules of Thumb: Tanks and Vessels
Rules of Thumb: Control Valve Lift
Rules of Thumb: Chromatography Systems
Rules of Thumb: Pump and System Curves
Rules of Thumb: Flow Parameters
Postgraduate research degrees in membranes
Insurance Risk Engineer – Refinery/Hydrocarbon Business Interruption
Mark Stracey Recruitment, United Arab Emirates, £65,000 - £110,000 yearly
Insurance Risk Engineer – Refining and Petrochemicals
Mark Stracey Recruitment, United Arab Emirates, £65,000 - £135,000 yearly
Oil and Chemicals Risk Engineer
Mark Stracey Recruitment, Abu Dhabi, United Arab Emirates
A conversation with the experts: watch the recordings of our previous webinars and sign-up to attend future online webcasts.
You do not have to be a chemical engineer to join IChemE. Our global membership community includes people from a range of disciplines who have an interest in and/or relevant experience in chemical engineering and our membership rates range from a low single fee for students to annual subscriptions for professional Members.
Catch up on the latest news, views and jobs from The Chemical Engineer. Below are the four latest issues. View a wider selection of the archive from within the Magazine section of this site.
We offer readers a flexible range of subscription options and you are certain to find one that suits your needs.
Postgraduate research degrees in membranes
Insurance Risk Engineer – Refinery/Hydrocarbon Business Interruption
Mark Stracey Recruitment, United Arab Emirates, £65,000 - £110,000 yearly
Insurance Risk Engineer – Refining and Petrochemicals
Mark Stracey Recruitment, United Arab Emirates, £65,000 - £135,000 yearly
Oil and Chemicals Risk Engineer
Mark Stracey Recruitment, Abu Dhabi, United Arab Emirates,
AWE, Berkshire, United Kingdom, £26,500 - £39,750 yearly
Associate Professor / Professor in Chemical Process Engineering
University of Technology Sydney, New South Wales, Australia,
Oil and Chemicals Risk Engineer
Mark Stracey Recruitment, Abu Dhabi, United Arab Emirates,
2022 Graduate Engineer (Process / Waste Engineering)
© 2022 Institution of Chemical Engineers