Download applied hydrology chow pdf

Unsourced material may be challenged download applied hydrology chow pdf removed. Output from a shallow water equation model of water in a bathtub.

The water experiences five splashes which generate surface gravity waves that propagate away from the splash locations and reflect off the bathtub walls. Under this condition, conservation of mass implies that the vertical velocity of the fluid is small. Vertically integrating allows the vertical velocity to be removed from the equations. The shallow water equations are thus derived.

While a vertical velocity term is not present in the shallow water equations, note that this velocity is not necessarily zero. This is an important distinction because, for example, the vertical velocity cannot be zero when the floor changes depth, and thus if it were zero only flat floors would be usable with the shallow water equations. Situations in fluid dynamics where the horizontal length scale is much greater than the vertical length scale are common, so the shallow water equations are widely applicable. Shallow water equation models have only one vertical level, so they cannot directly encompass any factor that varies with height. However, in cases where the mean state is sufficiently simple, the vertical variations can be separated from the horizontal and several sets of shallow water equations can describe the state.

The first equation is derived from mass conservation, the second two from momentum conservation. Cross section of the open channel. It is numerically challenging to solve, but is valid for all channel flow scenarios. The kinematic wave is valid when the change in wave height over distance and velocity over distance and time is negligible relative to the bed slope, e. For the diffusive wave it is assumed that the inertial terms are less than the gravity, friction, and pressure terms. The diffusive wave is valid when the inertial acceleration is much smaller than all other forms of acceleration, or in other words when there is primarily subcritical flow.

Figure 1: Diagram of block moving down an inclined plane. For tidal motion, even a very deep ocean may be considered as shallow as its depth will always be much smaller than the tidal wavelength. The water depth is 100 meters. Clint Dawson and Christopher M.