A2.4.3 Conservation of Mass and Motion Quantity
Fluid motion, or fluid dynamics, is a complex process that can be simplified by
assuming the incompressibility of the fluid and the stationarity of the flow.
Two key forms of fluid movement are laminar and turbulent flow. Under laminar
flow, the fluid layers slide smoothly over each other, the fluid particles move along
streamlines, in an orderly manner, without overlapping. Under such flow, there is
some energy dissipation due to the internal friction arising from viscosity.
Turbulent flow, common in natural environments, is characterized by erratic,
random, and circular motion in the form of swirls or turbulent vortices. These
vortices dissipate energy in a far greater amounts than viscous dissipation in laminar
regime.
A key principle in fluid dynamics calculations is that of mass conservation,
according to which the rate of temporal accumulation of fluid mass within a control
volume is given by the difference between the mass entering and leaving from that
volume per time unit.
When the incompressible laminar flow is stationary through a tube of variable
size (characteristic dimension = Dl 1 ), the mass flow rate Dm 1 /Dt, in the larger input
section A 1 , is:
Dm 1
Dt
¼
qDV 1
Dt
¼
qA 1 Dl 1
Dt
¼ qA 1 v 1
ðA2:33Þ
where the volume DV 1 ¼ A 1 Dl 1 is the volume of the mass Dm 1 , q is the density of
the fluid and v 1 is the velocity of the fluid in the section A 1 . As there is no lateral
loss of fluid and the flow occurs at constant density (incompressible flow), the mass
flow rate in the outlet A 2 , is equal to the outlet mass flow rate:
A 1 v 1 ¼ A 2 v 2
ðA2:34Þ
This equation shows that when the sectional area is large, the velocity is small
and when the sectional area is small the velocity of the fluid is greater.
Since:
Av ¼ ADl=Dt ¼ DV=Dt
ðA2:35Þ
where Av represents the volumetric flow rate (expressed in m
3 /s).
The principle of mass conservation can be formulated generically by
differentiation:
dM
dt
sistema
¼ 0
ðA2:36Þ
where M system ¼
R
massa
ðsystemÞ
dm ¼
R
volume
ðsystemÞ
qdV
Annex A2: Basic Topics on Laws of Motion and Evaporation
349
Fluid motion, or fluid dynamics, is a complex process that can be simplified by
assuming the incompressibility of the fluid and the stationarity of the flow.
Two key forms of fluid movement are laminar and turbulent flow. Under laminar
flow, the fluid layers slide smoothly over each other, the fluid particles move along
streamlines, in an orderly manner, without overlapping. Under such flow, there is
some energy dissipation due to the internal friction arising from viscosity.
Turbulent flow, common in natural environments, is characterized by erratic,
random, and circular motion in the form of swirls or turbulent vortices. These
vortices dissipate energy in a far greater amounts than viscous dissipation in laminar
regime.
A key principle in fluid dynamics calculations is that of mass conservation,
according to which the rate of temporal accumulation of fluid mass within a control
volume is given by the difference between the mass entering and leaving from that
volume per time unit.
When the incompressible laminar flow is stationary through a tube of variable
size (characteristic dimension = Dl 1 ), the mass flow rate Dm 1 /Dt, in the larger input
section A 1 , is:
Dm 1
Dt
¼
qDV 1
Dt
¼
qA 1 Dl 1
Dt
¼ qA 1 v 1
ðA2:33Þ
where the volume DV 1 ¼ A 1 Dl 1 is the volume of the mass Dm 1 , q is the density of
the fluid and v 1 is the velocity of the fluid in the section A 1 . As there is no lateral
loss of fluid and the flow occurs at constant density (incompressible flow), the mass
flow rate in the outlet A 2 , is equal to the outlet mass flow rate:
A 1 v 1 ¼ A 2 v 2
ðA2:34Þ
This equation shows that when the sectional area is large, the velocity is small
and when the sectional area is small the velocity of the fluid is greater.
Since:
Av ¼ ADl=Dt ¼ DV=Dt
ðA2:35Þ
where Av represents the volumetric flow rate (expressed in m
3 /s).
The principle of mass conservation can be formulated generically by
differentiation:
dM
dt
sistema
¼ 0
ðA2:36Þ
where M system ¼
R
massa
ðsystemÞ
dm ¼
R
volume
ðsystemÞ
qdV
Annex A2: Basic Topics on Laws of Motion and Evaporation
349