Fundamentals of Fluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 12

1. Conservation of Mass: Stated simply, whatever mass flows into a system must flow out
of the system or be accounted for by an increase in the mass of the system or via a
change in density (

ρ

) of the fluid ( Figure 2.3 ). (Remember that density is defined as mass
divided by volume, [V].) This law is similar to Kirchhoff's current law, which is
common in circuit analysis.

d ðρ V Þ

m system 5 m in 2 m out 2 ð 2 : 1 Þ

dt

2. Conservation of Linear Momentum: The time rate of change of momentum (mass
multiplied by velocity) of a body is proportional to the net force acting on that body. If
the mass of the body remains constant with time, then the force is equal to the mass
multiplied by the acceleration of the body (Newton's second law of motion, in
simplified form, Figure 2.4 ). Also, the acceleration of the body will proceed in the same
direction as the direction of the net force. This is a common equation used in solid
mechanics, engineering statics, and engineering dynamics.

m - Þ
dt

d ð

- 5 ð 2 : 2 Þ

3. The First Law of Thermodynamics: The change of the internal energy ( U) of a system is

equal to the change of the amount of energy added to a system (through heat,

δ

δ Q),

FIGURE 2.3 Flow direction Pictorial

representation of the conser-
vation of mass principle.
At time 1, the density of
the fluid within the square
chamber is represented with
approximately three shape
elements within the square
chamber. At some time later,
the density of the fluid can
either remain the same (“con-
stant density” case) because
the same quantity of elements
is present or increase because
one of the shape elements
did not leave the volume of
interest (“increase in density”
case).

Flow direction

Time 2 - “Constant density”

OR

Flow direction

Time 1

Time 2 - “Increase in
density”

FIGURE 2.4

When a force is applied to a
mass, the mass will move with a velocity
that is proportional to the applied force and
in the same direction as the net force. In
this simple representation, we are not depict-
ing all of the forces (such as friction or drag).

Net force
applied
to mass

F Mass moves

with some
acceleration

a

Mass