1.3 Fluid Dynamics
17
Re =
Inertial forces
Viscous forces
=
m a
μ
v
L
A
=
ρ L
3 v
t
μ
v
L
L 2 =
ρ L
3 1
t
μ
1
L
L 2 =
ρ L
2 1
t
μ
Or (Eq. 1.18):
Re =
ρvL
μ
(1.18)
where
• m: Mass (kg),
• a: Acceleration (m s
−1 ),
• A: Area (m
2 ),
• ρ: Fluid density (kg m
−3 ),
• v: Maximum fluid velocity (m s
−1 ),
• μ: Dynamic viscosity of the fluid (Pa s, N s m
−2 , or kg m
−1 s
−1 ), and
• L: Characteristic length of the system or diameter (D) of the pipe through which the
fluid flows (m). This parameter will often be replaced by the hydraulic diameter
7
(Eq. 1.19):
D h =
4 A
O
(1.19)
– A: Cross-sectional area (m
2 ) of the duct, and
– O: Perimeter (m).
Making use of Eq. 1.17, the Reynolds number can be defined as (Eq. 1.20):
Re =
v D h
ν
(1.20)
For air, which has a kinematic viscosity between 1.42 × 10
−5 m
2 s
−1 (10 °C) and
1.60 × 10
−5 m
2 s
−1 (30 °C), it can be written that:
Re = 67,280 D h v
The Reynolds number delimits the change between flow regimes. The limits vary
depending on closed-conduit flows or open flows. Thus, for a circular pipe, if Re >
10
3 the regime will be turbulent, whereas for fluid flowing over a flat plate this same
regime is reached at Re > 3.5 × 10
5 to 1 × 10
6 . In mine galleries, it is frequent to
7 The hydraulic diameter is the quotient between the cross-sectional area and its perimeter. This
parameter can be used to characterize an irregular surface using a single parameter. For this reason,
its use is extensible to other fields that have nothing to do with fluid mechanics, such as, for
example, in dimensioning the pillars in room and pillars mining when the pillar cross section has
to be characterized.
17
Re =
Inertial forces
Viscous forces
=
m a
μ
v
L
A
=
ρ L
3 v
t
μ
v
L
L 2 =
ρ L
3 1
t
μ
1
L
L 2 =
ρ L
2 1
t
μ
Or (Eq. 1.18):
Re =
ρvL
μ
(1.18)
where
• m: Mass (kg),
• a: Acceleration (m s
−1 ),
• A: Area (m
2 ),
• ρ: Fluid density (kg m
−3 ),
• v: Maximum fluid velocity (m s
−1 ),
• μ: Dynamic viscosity of the fluid (Pa s, N s m
−2 , or kg m
−1 s
−1 ), and
• L: Characteristic length of the system or diameter (D) of the pipe through which the
fluid flows (m). This parameter will often be replaced by the hydraulic diameter
7
(Eq. 1.19):
D h =
4 A
O
(1.19)
– A: Cross-sectional area (m
2 ) of the duct, and
– O: Perimeter (m).
Making use of Eq. 1.17, the Reynolds number can be defined as (Eq. 1.20):
Re =
v D h
ν
(1.20)
For air, which has a kinematic viscosity between 1.42 × 10
−5 m
2 s
−1 (10 °C) and
1.60 × 10
−5 m
2 s
−1 (30 °C), it can be written that:
Re = 67,280 D h v
The Reynolds number delimits the change between flow regimes. The limits vary
depending on closed-conduit flows or open flows. Thus, for a circular pipe, if Re >
10
3 the regime will be turbulent, whereas for fluid flowing over a flat plate this same
regime is reached at Re > 3.5 × 10
5 to 1 × 10
6 . In mine galleries, it is frequent to
7 The hydraulic diameter is the quotient between the cross-sectional area and its perimeter. This
parameter can be used to characterize an irregular surface using a single parameter. For this reason,
its use is extensible to other fields that have nothing to do with fluid mechanics, such as, for
example, in dimensioning the pillars in room and pillars mining when the pillar cross section has
to be characterized.