Special Cases of the Navier-Stokes Equations

• Published in: Fundamentals of Ship Hydrodynamics p. 1
• Main Author: Birk Lothar
• Format: Book Chapter
• Language: English
• Published: Chichester, UK John Wiley & Sons 2019; John Wiley & Sons, Ltd
• Subjects: boundary layer equations; constant density; continuity equation; dynamic viscosity; Marine Engineering & Naval Architecture; Navier‐Stokes equations; numerical solutions methods; ship propulsion problem; ship resistance; Ships & Vessels
• ISBN: 1118855485; 9781118855485
• DOI: 10.1002/9781119191575.ch7

The Navier‐Stokes equations (NSE) contain the fluid properties density and dynamic viscosity. The density is also part of the continuity equation. This chapter simplifies both the continuity equation and the NSE for the ship resistance and propulsion problem by making reasonable assumptions about density and viscosity. Additional insight into the NSE can be gained by rewriting them in a dimensionless form. This is general practice for implementation of numerical solutions methods. Froude number and Reynolds number are arguably the most important qualifiers of flow conditions in ship hydrodynamics. The chapter presents an example to teach us something about the terms in the NSE. It employs the numbers to calculate the four dimensionless constants of the NSE. Prandtl's ideas allow a simplification of the NSE into the boundary layer equations. The boundary layer equations form the basis of skin friction computations and provide important insights into the flow around ship hulls.