How to Calculate Dimensionless Numbers in Fluid Mechanics and Their Applications in Chemical Engineering Processes: Reynolds, Mach, Froude, Euler, Power, Stokes, Weber, Capillary, and Cavitation Numbers

Asep Bayu Dani Nandiyanto (Universitas Pendidikan Indonesia)
Obie Farobie (IPB University)
Belkheir Hammouti (Euromed University of Fes)

ASEAN Journal for Science and Engineering in Materials
Vol 5, No 3 (2026): AJSEM: Volume 5, Issue 3, December 2026

This paper explains how to calculate and interpret dimensionless numbers in fluid mechanics for chemical engineering applications, focusing on the Reynolds, Mach, Froude, Euler, Power, Stokes, Weber, Capillary, and Cavitation numbers. The first part presents each dimensionless number individually based on its definition, formula, required variables, threshold values, physical meaning, calculation example, interpretation, and handling strategy. The second part presents integrated case examples to show how several dimensionless numbers can be used together to analyze more complex chemical engineering systems. The examples include pipe flow, gas flow, heat exchangers, slurry pipelines, pumps, valves, nozzles, mixing vessels, wastewater aeration basins, aerated fermentation bioreactors, spray drying systems, cyclones, and particle-laden flows. Through these examples, this paper aims to help readers connect dimensionless-number calculations with process behavior, engineering interpretation, and practical decision-making in chemical engineering.