Consider the flow of water along a horizontal channel of constant width after a dam breaks. Sometime after the initial transients have died away⁶ the flow may be described by the nonlinear, unidirectional, shallow-waterwave equations (16.23a) and (16.23b):

Here h is the height of the flow, v is the horizontal speed of the flow, and x is distance along the channel measured from the location of the dam. Solve for the flow, assuming that initially (at t = 0) h = h_o for x 0 (no water). Your solution should have the form shown in Fig. 16.8.What is the speed of the front of the water?

Figure 16.8

Transcribed Image Text:

əh Ət + a(hv) ax = 0, = дv дv əh +u-+8= = 0. ax at ax (16.37)