Derivation of Navier–Stokes equation in rotational frame for engineering flow analysis

Abstract

One of the most frequently used governing equations underpinning engineering flow analysis is the renowned Navier–Stokes (NS) equation. Several references regarding the derivation of equation of motion in Cartesian coordinates are available in standard textbooks. However, derivation of above equation in rotational frame is missing in literatures. Flow analysis using NS equation in rotational frame is a prerequisite for analysis of various engineering problems like rotational flow dynamics in chemical reactors, lubricating oil behavior in various rotating machines, electrolyte flow behavior in electrochemical reactors with rotating electrodes, etc. Systematic understanding of each terms in the equation is essential to develop a suitable governing mathematical model of any physical flow problem with various level of complexities. This is possible only if same can be derived from fundamentals, detailing terms behind the equation. A systematic approach is made here to derive NS equation in rotational frame from basic Cartesian form.

Keywords

• Navier–Stokes equation
• Rotational frame
• Coriolis force