Consider gradually varied flow over a bump in a wide channel, as shown in Fig. P13–89. 

FIGURE P13–89

The initial flow velocity is 0.75 m/s, the initial flow depth is 1 m, the Manning parameter is 0.02, and the elevation of the channel bottom is prescribed to be

where the maximum bump height Δz_b is equal to 0.15 m and the crest of the bump is located at x = 100 m. 

(a) Calculate and plot the critical depth of the flow and (where it exists) the normal depth of the flow. 

(b) Integrate the GVF equation over the range 0 ≤ x ≤ 200 m, and comment on the observed behavior of the free surface in light of the classification scheme presented in Table 13–3.

y = 1 m x = 0 100 m