Consider the occurrence of a surge at the water surface of a wide rectangular channel flow, as in the figure. where the one-dimensionally considered velocities are v1, and v2 and the depths are d1and d2, with the surge height h, whereby d2 - d1 = h, moving at a speed of VW. over depth d1. Joint application of continuity and momentum principles will indicate the surge front speed VW, to be

• A. \({{\rm{V}}_w} = \sqrt {g{d_1}} \;{\left( {1\frac{3}{2}\frac{h}{{{d_1}}}} \right)^{1/2}}\)
• B. \({{\rm{V}}_w} = \sqrt {g{d_1}} \;{\left( {1 + \frac{3}{2}\frac{h}{{{d_1}}} + \frac{1}{2}{{\left( {\frac{h}{{{d_1}}}} \right)}^2}} \right)^{1/2}}\)
• C. \({{\rm{V}}_w} = \sqrt {g{d_1}} \;{\left( {1 + \frac{h}{{{d_1}}}} \right)^{1/2}}\)
• D. \({{\rm{V}}_w} = \sqrt {g{d_1}} \;{(1 + \frac{h}{{{d_1}}})^2}^{1/2}\)