6
P. Liu
The relationship between mathematics and physics in fluid mechanics can
be summarized in the following four sentences:
Mathematics is beautiful.
Physics is wonderful.
If we combine mathematics with physics,
Beauty will never end.
1.2 Methods of Describing Fluid Motion
By definition, a particle is a mass space point (material point) that is sufficiently large (composed of many molecules) at the microlevel and small
enough to ignore its volume at the macro level. Take the air as an example. At
sea level, the pressure is 101325 Pa, the temperature is 288.15 K, the space
contains 2.7 × 10 19 air molecules per cubic centimeter, and the average free
path of molecules is 10 −8 m. Under what conditions, the molecular flow
satisfies the definition of particle continuous flow rather than discrete flow,
which involves the relationship between the average free path of molecules
and the characteristic scale of objects. The Denmark physicist M. Knudsen
(1871–1949, as shown in Fig. 1.7) studied the theory of molecular motion
and the phenomenon of low pressure in airflow. Knudsen number was
proposed to judge the relative dispersion of molecules. Kn number was
Fig. 1.7 M. Knudsen (1871–1949, Denmark physicist)
P. Liu
The relationship between mathematics and physics in fluid mechanics can
be summarized in the following four sentences:
Mathematics is beautiful.
Physics is wonderful.
If we combine mathematics with physics,
Beauty will never end.
1.2 Methods of Describing Fluid Motion
By definition, a particle is a mass space point (material point) that is sufficiently large (composed of many molecules) at the microlevel and small
enough to ignore its volume at the macro level. Take the air as an example. At
sea level, the pressure is 101325 Pa, the temperature is 288.15 K, the space
contains 2.7 × 10 19 air molecules per cubic centimeter, and the average free
path of molecules is 10 −8 m. Under what conditions, the molecular flow
satisfies the definition of particle continuous flow rather than discrete flow,
which involves the relationship between the average free path of molecules
and the characteristic scale of objects. The Denmark physicist M. Knudsen
(1871–1949, as shown in Fig. 1.7) studied the theory of molecular motion
and the phenomenon of low pressure in airflow. Knudsen number was
proposed to judge the relative dispersion of molecules. Kn number was
Fig. 1.7 M. Knudsen (1871–1949, Denmark physicist)