fluid_mechanics

5Finite Control
Volume Analysis
CHAPTER OPENING PHOTO: Wind turbine farms (this is the Middelgrunden Offshore Wind Farm in Denmark)
are becoming more common. Finite control volume analysis can be used to estimate the amount of energy
transferred between the moving air and each turbine rotor. (Photograph courtesy of Siemens Wind Power.)
Learning Objectives
After completing this chapter, you should be able to:
■ select an appropriate finite control volume to solve a fluid mechanics problem.
■ apply conservation of mass and energy and Newton’s second law of motion to
the contents of a finite control volume to get important answers.
■ know how velocity changes and energy transfers in fluid flows are related to
forces and torques.
■ understand why designing for minimum loss of energy in fluid flows is so
important.
Many fluid mechanics
problems
can be solved by using
control volume
analysis.
To solve many practical problems in fluid mechanics, questions about the behavior of the contents
of a finite region in space 1a finite control volume2 are answered. For example, we may be asked
to estimate the maximum anchoring force required to hold a turbojet engine stationary during a
test. Or we may be called on to design a propeller to move a boat both forward and backward. Or
we may need to determine how much power it would take to move natural gas from one location
to another many miles away.
The bases of finite control volume analysis are some fundamental laws of physics, namely,
conservation of mass, Newton’s second law of motion, and the first and second laws of thermodynamics.
While some simplifying approximations are made for practicality, the engineering answers
possible with the estimates of this powerful analysis method have proven valuable in numerous instances.
Conservation of mass is the key to tracking flowing fluid. How much enters and leaves a
control volume can be ascertained.
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