Fundamentals of Fluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 40

END OF CHAPTER SUMMARY
2.1 Fluid mechanics is the study of fluids at rest and at motion. A fluid is defined as a material
that continuously deforms under a constant load.
2.2 Five relationships are most useful in fluid mechanics problems: kinematic, stresses, conser-
vation, regulating and constitutive. Five laws also govern most fluid flows

d ðρ V Þ

Conservation of Mass: m system 5 m in 2 m out 2

dt

m - Þ
dt

d ð

Conservation of Linear Momentum: -

5

The First Law of Thermodynamics: δ U 5δ Q 2δ w

The Second Law of Thermodynamics: dS

dt $

0

Conservation of Angular Momentum: - - 3 - 5

2.3 The analysis of fluid mechanics problems can be significantly altered depending on the
choice of the system of interest and the volume of interest. Mass that is not originally within
the system of interest cannot enter the volume of interest during problem solution.
2.4 By assuming a fluid is a continuum, we can suppose that there are no inhomogeneities
within the smallest division of fluid that are made. Properties such as viscosity, density and
temperature, among others., must be constant throughout the entire fluid.

2
4

3
5 ;

σ xx τ xy τ xz

2.5 It is useful to use the stress tensor σ 5 τ yx σ yy τ yz to define the various stresses on

τ zx τ zy σ zz

F - δ

fluid elements. Normal stresses are defined as σ n 5 lim

A - , whereas shear stresses are δ

A - δ 0

-

F - δ

A - . Only six of these stresses are independent of each other, to con-
serve momentum throughout the fluid element. A useful relationship for the hydrostatic
pressure as a function of the normal stresses is p hydrostatic 5 2 3 ðσ xx 1σ yy 1σ zz Þ:
2.6 A fluid can undergo four general motions. These are useful in defining the position of fluid
packets, the velocity and the acceleration of the fluid.

defined as τ n 5 lim

δ

A - δ 0

-

Þ i - Þ j - Þ -

- ð

t Þ 5 u x ð t 1 u y ð t 1 u z ð t

d - ð du y ð

Þ

t Þ du x ð t Þ t du z ð t Þ

i - j - - Þ i - Þ j - Þ - - ð t Þ 5 5 1 1 5 v x ð t 1 v y ð t 1 v z ð t

dt dt dt dt

d - ð d 2 - ð d 2 u x ð d 2 u y ð d 2 u z ð t Þ t Þ dv x ð t Þ dv y ð t Þ dv z ð t Þ t Þ t Þ t Þ

i - j - - i - j - - - ð t Þ 5 5 5 1 1 5 1 1

dt 2 dt 2 dt 2 dt 2

dt dt dt dt

Þ i - Þ j - Þ - or

5

a x ð

1

a y ð

1

a z ð

t t t