Fundamentals of Fluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 11

angular). Since a fluid element deforms continually under a shear force and there are no
deformations in static fluid mechanics, the implication is that no shear stresses are acting
on the fluid. In general, the salient aspect of static fluid mechanics is the pressure distribu-
tion throughout the fluid. For dynamic fluid mechanics, the fluid may have an acceleration
term (i.e., non-constant velocity) and can undergo deformations. In these cases, Newton's
second law of motion can be used to evaluate the forces acting on the fluid. Generally, for
this type of analysis, the pressure distribution and the velocity distribution throughout the
fluid are of interest. From these calculated fluid parameters, any other parameter of inter-
est, such as acceleration, wall shear stress or shear rate can be obtained.

2.2 FUNDAMENTAL FLUID MECHANICS EQUATIONS

Determining the solution of any engineering problem should begin by writing down
the known quantities (also termed “the givens”), including the equations that govern the
system being addressed. In general, there are five fundamental relationships ( Table 2.1 )of
interest in fluid mechanics. In no way, do these relationships limit a person to five solution
methods or five problem types. Instead, they provide a foundation for solving a variety of
complex problems. These possible solution routes also use a variety of different computa-
tional analysis methods. For instance, if one were interested in the velocity profile of the
fluid, then one would probably focus on kinematic relationships throughout the fluid. Yet,
conservation laws may be necessary to help with the calculations. However, if the stress
distribution were of interest, one might start with kinetic relationships and use kinematics/
conservation laws to help solve the problem. Algebra, trigonometry, and calculus tech-
niques are some computational methods that may be needed to solve biofluid mechanics
problems. Known variables in most fluid mechanics problems typically include, geometric
constraints, fluid material properties (density/viscosity), and temperature of the system,
among other inflow and outflow boundary conditions (i.e., the inflow velocity profile and
the outflow pressure).
The laws that govern fluid flow are common among other engineering disciplines and
they should not be encountered for the first time in this textbook. These laws are described
in detail in the chapters that follow, and the derivation of common fluid mechanics para-
meters and equations of state will be detailed in those chapters. Here we will briefly sum-
marize the laws that fluid flow must obey.

TABLE 2.1 Relationships That Are Useful in Fluid Mechanics Problems

KINEMATIC Velocities, Accelerations, Shear Rates - Fluid Properties

STRESSES Force Intensities Acting over Particular Area - Flow Properties

CONSERVATION Mass, Momentum and Energy - Physical Properties

REGULATING Initial and/or Boundary Conditions - Geometric and/or Limiting Properties

CONSTITUTIVE Mathematically Describes the Fluid - Laws to Describe Flow