5 Experimental Fluid Mechanics
343
force, the ratio of inertial force to elastic force, the ratio of inertial force to
surface tension, the ratio of convective inertial force to non-stationary inertial
force, and the following six dimensionless numbers are introduced:
(1) Euler number (Eu) represents the pressure coefficient of the surface pressure distribution of the object, as well as the lift coefficient and drag
coefficient. Physically, the Euler number represents the ratio of inertial
force to differential pressure force.
(2) Froude number (Fr) represents the ratio of the flow inertial force to
the gravity and represents the ratio of the water flow velocity to the
microwave velocity of gravity wave.
(3) Reynolds number (Re) represents the ratio of flow inertial force to viscous
force.
(4) Mach number (Ma) represents the ratio of inertial force to elastic force,
which is a measure of compressibility of gas. It is usually used to express
the ratio of flight speed to acoustic speed of aircraft.
(5) Weber number (We) represents the ratio of inertial force to surface
tension.
(6) Strouhal number (St) represents the ratio of convective inertial force to
unsteady inertial force.
On the premise of geometric similarity, the decisive criterion of flow
phenomenon similarity is only the Reynolds number criterion, so the
dynamic similarity of the model experiment must obey the Reynolds number
similarity criterion.
Similarity First Theorem: Two similar systems have the same single-valued
condition and the same value of similarity criterion.
Similarity Second Theorem: if any physical phenomenon is expressed by
the functional relation of n physical quantities, and these physical quantities
contain m basic dimensions, then (n-m) similarity criteria can be obtained.
Similarity Third Theorem: for any phenomenon with the same characteristics, when the single-value conditions (geometric properties of the system,
physical properties of the medium, initial conditions and boundary conditions, etc.) are similar to each other, and the similarity criteria composed of
physical quantities of the single-value conditions are equal in numerical value,
then these phenomena must be similar.
These three theorems form the core of similarity theory. The third similarity theorem defines what conditions a model satisfies to make physical
phenomena similar. It is the law that the model test must follow.
343
force, the ratio of inertial force to elastic force, the ratio of inertial force to
surface tension, the ratio of convective inertial force to non-stationary inertial
force, and the following six dimensionless numbers are introduced:
(1) Euler number (Eu) represents the pressure coefficient of the surface pressure distribution of the object, as well as the lift coefficient and drag
coefficient. Physically, the Euler number represents the ratio of inertial
force to differential pressure force.
(2) Froude number (Fr) represents the ratio of the flow inertial force to
the gravity and represents the ratio of the water flow velocity to the
microwave velocity of gravity wave.
(3) Reynolds number (Re) represents the ratio of flow inertial force to viscous
force.
(4) Mach number (Ma) represents the ratio of inertial force to elastic force,
which is a measure of compressibility of gas. It is usually used to express
the ratio of flight speed to acoustic speed of aircraft.
(5) Weber number (We) represents the ratio of inertial force to surface
tension.
(6) Strouhal number (St) represents the ratio of convective inertial force to
unsteady inertial force.
On the premise of geometric similarity, the decisive criterion of flow
phenomenon similarity is only the Reynolds number criterion, so the
dynamic similarity of the model experiment must obey the Reynolds number
similarity criterion.
Similarity First Theorem: Two similar systems have the same single-valued
condition and the same value of similarity criterion.
Similarity Second Theorem: if any physical phenomenon is expressed by
the functional relation of n physical quantities, and these physical quantities
contain m basic dimensions, then (n-m) similarity criteria can be obtained.
Similarity Third Theorem: for any phenomenon with the same characteristics, when the single-value conditions (geometric properties of the system,
physical properties of the medium, initial conditions and boundary conditions, etc.) are similar to each other, and the similarity criteria composed of
physical quantities of the single-value conditions are equal in numerical value,
then these phenomena must be similar.
These three theorems form the core of similarity theory. The third similarity theorem defines what conditions a model satisfies to make physical
phenomena similar. It is the law that the model test must follow.