3 Hydrodynamics
179
Fig. 3.5 William Froude (1810–1879, British scholar)
on this basis, people developed the theory of steady nonuniform gradual
flow in open channel and proposed the calculation method of water surface
profile. Jean-Charles de Borda (1733–1799, as shown in Fig. 3.7) the French
mathematician and physicist, put forward the calculation formula of local
energy loss caused by the sudden expansion of pipeline based on experimental research. Saint Venant (1797–1886, as shown in Fig. 1.31) the
French hydrologist, established Saint Venant equations (differential equations of conservation of mass and momentum) to describe the unsteady
one-dimensional gradual flow in open channels. Later, people gave equations of the unsteady two-dimensional gradual flow based on the average
of water depth. Saint Venant equations belong to the first-order hyperbolic quasilinear partial differential equations. The unknown function can
be obtained by solving the equations with initial and boundary conditions.
In practice, approximate calculation methods are often used, such as characteristic method, direct difference method, transient method, and finite
element method. With rapid development of numerical solution, the theory
of unsteady flow in open channel is widely used in flood control, irrigation, shipping, power generation, coastal reclamation, and environmental
protection. Its research objects include natural rivers, artificial channels, river
networks, reservoirs, lakes, tidal estuaries, harbors, and urban sewer systems.
179
Fig. 3.5 William Froude (1810–1879, British scholar)
on this basis, people developed the theory of steady nonuniform gradual
flow in open channel and proposed the calculation method of water surface
profile. Jean-Charles de Borda (1733–1799, as shown in Fig. 3.7) the French
mathematician and physicist, put forward the calculation formula of local
energy loss caused by the sudden expansion of pipeline based on experimental research. Saint Venant (1797–1886, as shown in Fig. 1.31) the
French hydrologist, established Saint Venant equations (differential equations of conservation of mass and momentum) to describe the unsteady
one-dimensional gradual flow in open channels. Later, people gave equations of the unsteady two-dimensional gradual flow based on the average
of water depth. Saint Venant equations belong to the first-order hyperbolic quasilinear partial differential equations. The unknown function can
be obtained by solving the equations with initial and boundary conditions.
In practice, approximate calculation methods are often used, such as characteristic method, direct difference method, transient method, and finite
element method. With rapid development of numerical solution, the theory
of unsteady flow in open channel is widely used in flood control, irrigation, shipping, power generation, coastal reclamation, and environmental
protection. Its research objects include natural rivers, artificial channels, river
networks, reservoirs, lakes, tidal estuaries, harbors, and urban sewer systems.