O'Reilly logo

Handbook of Compressible Aerodynamics by Jean Délery

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 5

First Applications of the Conservation Equations

5.1. Theorem of the dynalpy

In what follows, we restrict ourselves to flows where body forces are neglected (neither a heavy fluid nor an electrical conductor). If the motion is steady and (S) is a closed surface enclosing a finite volume (ϑ) that does not contain a body, then we write the equation of motion of section 4.4 as:

Image

where Image is the tension vector representing the contact forces exerted by the fluid contained in (S) on the external medium (hence the minus sign to the right-hand side). This relation can also be written as:

Image

The dynalpy vector is given by:

Image

The relation above shows the following result:

Image

which is read as:

In a steady flow, and in the absence of body forces, the flux of the dynalpy vector through a closed surface not containing any body is zero.

Let us consider an impermeable body (no mass exchange between the body and the external medium) placed in a flow and apply the above result to the fluid contained ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required