The buildup and decay of a laminar or turbulent flow over a sloping plane is treated by the kinematic-wave method, neglecting the slope of the water surface relative to the slope of the plane. The relationships developed show certain distinct differences from those postulated in the unit hydrograph method. liowever, a comparison of the results of calculations with published experimental measurements shows quite good agreement. The problem is extended to include the case of groundwater flow through a porous medium overlying a sloping impermeable stratum, where water is supplied by infiltration from the ground surface above. liere the depth of water may be appreciable, so that the actual slope of the water surface influences the gravity flow significantly, leading to a nonlinear diffusion problem. Solutions of this problem for the buildup and decay phases are compared with those obtained by the kinematic-wave method, and significant differences are noted for the latter phase. Further, the physical boundary condition at the upper edge of the slope changes at a critical precipitation rate, the depth of water being either finite or zero there depending upon whether the rate is greater than or less than the critical value. Figure 1) which is of length L, slope S ------sin O, and of unit width perpendicular to the plane of the diagram. We take the origin at A with the x axis along AB. Rain begins to fall at a rate Vo per unit area, where Vo is a constant. We shall examine the buildup of a two-dimensionM flow over the surface until a steady state is reached and the subsidence of the flow after the rain ceases. Flow over an impermeable surface. Consider an impermeable surface ( The continuity equation takes the form O__q.+ Oh Ox •-= Vo(1) where t is the time, q is the flow or discharge rate, and h denotes the depth of water. A relationship between q and h can be found from the dynamical equations. Following Keulegan [1944], we shall neglect the impact of raindrops on the surface and the acceleration terms x This paper is based upon an earlier version prepared while the second author was at Applied
A new computational capability is described for calculating the sound-pressure field radiated or scattered by a harmonically excited, submerged, arbitrary, three-dimensional elastic structure. This approach, called nashua, couples a nastran finite element model of the structure with a boundary element model of the surrounding fluid. The surface fluid pressures and normal velocities are first calculated by coupling the finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior fluid. After generation of the fluid matrices, most of the required matrix operations are performed using the general matrix manipulation package available in nastran. Farfield radiated pressures are then calculated from the surface solution using the Helmholtz exterior integral equation. The overall capability is very general, highly automated, and requires no independent specification of the fluid mesh. An efficient, new, out-of-core block equation solver was written so that very large problems could be solved. The use of nastran as the structural analyzer permits a variety of graphical displays of results, including computer animation of the dynamic response. The overall approach is illustrated and validated using known analytic solutions for submerged spherical shells subjected to both incident pressure and uniform and nonuniform applied mechanical loads.
The instantaneous unit hydrograph and the properties connecting it with the unit hydrograph for a rainfall excess of any finite duration are used to explore the relationship between the peak flow of a unit hydrograph and the duration of rainfall excess from which it arises. This relationship is found to be substantially independent of the skew or any other shape factor of the instantaneous unit hydrograph and dependent only in its base width, provided that this base width is properly defined. It is, however, found to be strongly dependent on the distribution of rainfall excess intensity over the duration of the storm. Some comments are made on the significance of these results for the designer seeking an estimate of the peak discharge; in particular it is suggested that a one‐parameter description of the instantaneous unit hydrograph may be sufficient for his purposes.
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