Page 34 - Fluid Power Engineering

12 Chapter Tw o

450
400
350
300
Power in KW 250

200
150
100
50
0
0 5 10 15 20
Radius of a HAWT in meters
FIGURE 2-3 Quadratic relationship between power and rotor size. Wind speed
is 8 m/s.

Basic Concepts/Equations
Three basic principles of physics are often used in this and subse-
quent chapters: Conservation of mass, conservation of energy, and
conservation of momentum. Before these equations can be described,
there is an important concept of control volume. The above princi-
ples must be applied in a defined control volume. The right and left
side of the equation must be referring to the same control volume;
in a derivation as one moves from one equation to another, all the
equations must refer to the same control volume. This initial control
volume may be of any shape; the most useful shapes are constant-
radius cylinder and variable-radius streamlined cylinder, as shown in
Fig. 2-4.
Streamlines can be conceptualized as infinitesimal tubes. Fluid
flows in these tubes axially and not perpendicular to the tubes, so
there is no exchange of matter across streamlines. This implies that in
the control volume above, there is no mass gain or loss except from
A 0 and A 2 .

Conservation of Mass
Assumptions:
All air that enters at A 0 leaves from A 2 . Fluid flow is stream-

lined and so there is no loss of mass from the surface of the
control volume.
Fluid is incompressible, that is, there is no change in density.