346
P. Liu
Eu is the Euler number, i.e.
Eu =
p 0
ρV 2
0
Re is the Reynolds number, i.e.
Re =
V 0 L
ν
Obviously, if two flows are similar, they must be described by the same
dimensionless physical equations. For a similar phenomenon between prototype and model, the similarity scale of basic physical quantities is
λ L =
L p
L m
, λ T =
T p
T m
, λ M =
M p
M m
In the equations, the subscript p represents the prototype, and the
subscript m represents the model, where λ L is the length scale, λ T is the time
scale, and λ M is the mass scale. According to the dimensionless equations, the
similarity criteria between the prototype and the model are as follows:
The Strohal number similarity criterion is
Sh p = Sh m ,
L p
V p T p
=
L m
V m T m
,
λ L
λ V λ T
= 1
Froude number similarity criterion is
Fr p = Fr m ,
V p
g p L p
=
V m
√
g m L m
,
λ V
λ g λ L
= 1
Euler number similarity criterion is
Eu p = Eu m ,
p p
ρ p V 2
p
=
p m
ρ m V 2
m
,
λ p
λ ρ λ 2
V
= 1
Reynolds number similarity criterion is
Re p = Re m ,
V p L p
ν p
=
V m L m
ν m
,
λ V λ L
λ ν
= 1