Bernoulli’s Equation Reimagined Through the Thermodynamics of Fluid Flow

A fluid dynamics researcher has proposed a fundamentally reinterpreted and generalized version of Bernoulli’s equation, arguing that the classic formulation should be rebuilt on thermodynamic grounds rather than on the conventional local pressure accounting that has dominated pipe-flow analysis for generations. The work, published in Discover Fluid Mechanics, derives the new equation using the total chemical potential, a quantity drawn directly from thermodynamics.

The study, authored by Dag Chun Standnes, presents a version of Bernoulli’s equation that the author reports gives consistent results for entire pipe flow systems with varying geometry and design, in line with empirical data and fundamental principles and laws of physics. The reinterpretation hinges on a crucial change in the role played by the internal water pressure, while the generalization comes from the inclusion of viscous pressure, a term absent from the conventional equation.

In the conventional treatment, the equation is typically applied to local subsections of a flow system, comparing conditions at one point in a pipe with conditions at another. The new framework argues that this local approach is precisely where the traditional interpretation falls short.

Because the framework is built on chemical potential, the author concludes that Bernoulli’s equation should instead be formulated as a pressure balance between external supply and internal demands. The external supply is delivered, for example, by a pump, whereas the internal demands are represented by changes in dynamic pressure, hydrostatic pressure and viscous pressure. This external-internal distinction, the paper argues, changes the way the equation should be interpreted and applied.

A central requirement of the new approach is that entire systems must be considered rather than isolated segments. The reason, according to the study, is that the external pressure supplied depends on the internal flow resistance terms, and those resistance terms in turn depend on the whole system. An analysis confined to a local subsection therefore cannot, in this view, correctly capture the pressure balance that governs the flow.

The framework also demands that individual pressure terms be applied according to their respective physical content. One striking consequence concerns a long-standing assumption in fluid mechanics: the study states that a high dynamic pressure value, corresponding to high flow speed, is not the cause of a decrease in internal water pressure as conventionally assumed. This reinterpretation directly challenges a textbook-level reading of the relationship between speed and static pressure in pipe flow.

The author reports that the generalized equation will be especially useful for design and engineering purposes, where pipe systems of varying geometry and layout must be analyzed and specified. Beyond engineering applications, the paper suggests the framework could also impact how the Euler and Navier-Stokes equations, the foundational equations of fluid motion, should be interpreted and applied.

The paper is published as an open access article in Volume 2 of Discover Fluid Mechanics, dated 28 August 2026, and the author states that all data generated or analysed during the study are included in the published article. The work positions itself as both a theoretical reinterpretation of a classical equation and a practical tool, aiming to bring the analysis of pipe flow into closer alignment with thermodynamics, empirical observations and the fundamental laws of physics.

Subject of Research: A thermodynamic reinterpretation and generalization of Bernoulli's equation for entire pipe flow systems using the total chemical potential.

Article Title: Derivation of a reinterpreted and generalized Bernoulli’s equation using the total chemical potential

Article References: Standnes, D. C. (2026). Derivation of a reinterpreted and generalized Bernoulli’s equation using the total chemical potential. Discover Fluid Mechanics, 2(1), Article 11. https://doi.org/10.1007/s44369-026-00016-4

Image Credits: AI Generated

DOI: 10.1007/s44369-026-00016-4

Keywords: Bernoulli's equation, fluid mechanics, chemical potential, thermodynamics, pipe flow, viscous pressure, hydrostatic pressure, dynamic pressure, cavitation, Navier-Stokes equations, Euler equations, pressure balance