Environmental Engineering Reference
In-Depth Information
Outlet
Inlet
Outlet cone
Inlet cone
Throat
Downstream pressure tap
Upstream pressure tap
Fig. 1
Venturi tube: diagram and characteristics
From this equation, the volumetric flow
Q
that relates the volumetric flux with
the pressure loss in the system considering an incompressible fluid is given by
2
g(
−
P
)/ρ
Q
=
CA
0
1
,
(2)
4
(
D
0
/
D
1
)
−
where
v
is the velocity of the fluid,
the density,
P
the pressure,
g
the gravity acceler-
ation,
z
the height of the fluid,
D
1
the diameter of the straight section,
D
0
the diameter
of the throat,
A
0
the transversal area at the throat, and
C
a discharge coefficient.
ρ
2 The SPH Method
Nowadays the Smoothed ParticleHydrodynamics (SPH)method has become increas-
ingly popular to study fluid dynamics. This method uses particles to represent the
domain which could contain fluid and boundaries. The particles are interpolation
points where properties of the fluid such as velocity, density, pressure and others are
calculated. In SPH we can easily implement complicated physics and model systems
with a complex and irregular geometries.
The main characteristics of the SPH method has been described by Monaghan
(
1982
,
1992
,
2005
) and Liu (
2003
). The fundamental principle of the SPH method
consists in calculating an approximation of any function by means of an integral
interpolator
r
)
r
,
dr
,
A
(
r
)
=
A
(
W
(
r
−
h
)
(3)
where
W
is a weight function or kernel, and
h
is the smoothing length of the
weight function. Then Eq. (
3
) is approximated for any point with the sum
(
r
,
h
)
b
m
b
A
b
ρ
b
A
(
r
)
=
W
(
r
−
r
b
,
h
),
(4)
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