Conservation Laws - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 46

CHAPTER
3

Conservation Law s

LEARNING OUTCOMES

1. Develop equations that govern pressure

variation within a static fluid

conservation of mass, conservation of
momentum, and conservation of energy

2. Determine the buoyancy forces that act on

objects immersed within a fluid

5. Describe the conservation of momentum

principle with acceleration

3. Develop a general relationship for the time

rate of change of any fluid system property

6. Derive the Navier-Stokes equations

7. Explain the Bernoulli principle and the

assumptions inherent in this principle 4. Apply the generalized formula for the time

rate of change of a system property to the

3.1 FLUID STATICS EQUATIONS

Fluid statics problems deal with fluids that either are at rest or are only undergoing
constant velocity rigid body motions. This implies that the fluid is only subjected to nor-
mal stresses because by definition a fluid will continually deform under the application
of a shear stress. Shear stress would induce angular deformations within the fluid (see
Figure 2.15) and therefore acceleration in particular directions. Another way to think
about these types of problems is that the relative position of all fluid elements remains
the same after loading. Therefore, the fluid elements would only experience pure trans-
lation or pure rotation. These types of problems fall under the class of hydrostatics and
the analysis methods for these problems are typically simpler than fluid dynamics pro-
blems. Newton's second law of motion, simplified to the sum of the forces acting on the
fluid is equal to zero ( P - 0), is the primary relationship used to solve these

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problems.
Although fluid statics problems make the assumption that the fluid elements are not
undergoing deformation, it is still possible to gain important data and insight from this