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P. Liu
8.21 Stokes (1819–1903)
George Gabriel Stokes (1819–1903) was a British dynamicist and mathematician, whose main contribution was to study the motion law of viscous fluid.
Navier extended L. Euler’s equation of motion for fluids from the molecular
hypothesis, and obtained the equation of motion with a viscosity constant in
1821. In 1845, Stokes employed the mechanical model of continuous system
and Newton’s physical law of viscous fluid, gave the basic equations of viscous
fluid motion with two viscosity constants in On the Theory of Internal Friction of Fluid in motion and the Theory of Balance and Motion of Elastomer.
This group of equations is called Navier–Stokes equation later and is the
most basic equations in fluid mechanics. In 1851, Stokes put forward the
resistance calculation formula when the ball moves slowly in the viscous fluid
in The Research Report of the Effect of Friction on the Pendulum Motion in
the Fluid , indicating that the resistance is proportional to the flow velocity
and viscosity coefficient, which is the Stokes formula of the resistance of the
ball in the flow. Stokes found the nonlinear characteristics of fluid surface
waves, whose velocity depends on wave amplitude, and for the first time
dealt with the nonlinear wave problem by perturbation method in 1847.
Stokes also studied elastic mechanics and he pointed out that there are two
basic resistances in isotropic elastic bodies, namely, the resistance to volume
compression and the resistance to shear. He explicitly introduced the shear
stiffness and compression stiffness (1845), proving that the elastic P-wave is
an irrotational expansion wave and the elastic transverse wave is an isochoric
distortion wave (1849). In mathematics, Stokes is famous for a conversion
formula (Stokes formula) between line integral and area integral in field
theory (Fig. 8.21).
8.22 Helmholtz (1821–1894)
Hermann Ludwig Ferdinand von Helmholtz (1821–1894), German
biophysicist and mathematician, was the founder of the law of conservation
of energy. He has made great contributions in physiology, optics, electrodynamics, mathematics, thermodynamics, and other fields. After studying
the optical structure of the eye, he developed the Younger-Helmholtz theory.
His research on muscle activity enriched the earlier theories of Julius Meyer
and James Jour, and helped him establish the theory of energy conservation.
In terms of electromagnetic theory, he measured the propagation speed of
P. Liu
8.21 Stokes (1819–1903)
George Gabriel Stokes (1819–1903) was a British dynamicist and mathematician, whose main contribution was to study the motion law of viscous fluid.
Navier extended L. Euler’s equation of motion for fluids from the molecular
hypothesis, and obtained the equation of motion with a viscosity constant in
1821. In 1845, Stokes employed the mechanical model of continuous system
and Newton’s physical law of viscous fluid, gave the basic equations of viscous
fluid motion with two viscosity constants in On the Theory of Internal Friction of Fluid in motion and the Theory of Balance and Motion of Elastomer.
This group of equations is called Navier–Stokes equation later and is the
most basic equations in fluid mechanics. In 1851, Stokes put forward the
resistance calculation formula when the ball moves slowly in the viscous fluid
in The Research Report of the Effect of Friction on the Pendulum Motion in
the Fluid , indicating that the resistance is proportional to the flow velocity
and viscosity coefficient, which is the Stokes formula of the resistance of the
ball in the flow. Stokes found the nonlinear characteristics of fluid surface
waves, whose velocity depends on wave amplitude, and for the first time
dealt with the nonlinear wave problem by perturbation method in 1847.
Stokes also studied elastic mechanics and he pointed out that there are two
basic resistances in isotropic elastic bodies, namely, the resistance to volume
compression and the resistance to shear. He explicitly introduced the shear
stiffness and compression stiffness (1845), proving that the elastic P-wave is
an irrotational expansion wave and the elastic transverse wave is an isochoric
distortion wave (1849). In mathematics, Stokes is famous for a conversion
formula (Stokes formula) between line integral and area integral in field
theory (Fig. 8.21).
8.22 Helmholtz (1821–1894)
Hermann Ludwig Ferdinand von Helmholtz (1821–1894), German
biophysicist and mathematician, was the founder of the law of conservation
of energy. He has made great contributions in physiology, optics, electrodynamics, mathematics, thermodynamics, and other fields. After studying
the optical structure of the eye, he developed the Younger-Helmholtz theory.
His research on muscle activity enriched the earlier theories of Julius Meyer
and James Jour, and helped him establish the theory of energy conservation.
In terms of electromagnetic theory, he measured the propagation speed of