Continuity Equation

• 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: conservation of mass principle; continuity equation; Eulerian fluid mechanics; finite control volumes; Marine Engineering & Naval Architecture; moving control volumes; Ships & Vessels
• ISBN: 1118855485; 9781118855485
• DOI: 10.1002/9781119191575.ch5

In Eulerian fluid mechanics, conservation laws may be set up for four different types of control volumes. A control volume may be infinitesimally small or finite in size. Independent of size, a control volume may be fixed in space or moving along with the flow. This chapter shows which combination of fixed or moving and finite or infinitesimal control volume yields which form of the conservation law. Finite control volumes lead to integral forms, whereas infinitesimally small control volumes result in differential forms of the conservation laws. Moving control volumes always contain the same fluid mass but may change their shape. The chapter discusses the application of all four types of control volumes to the conservation of mass principle. As a result, it obtains four equivalent mathematical models for the conservation of mass principle known as the continuity equation.