Springer Online Journal Archives 1860-2000
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Summary A theoretical study is made, of an irrotational, inviscid incompressible and steady flow over a two-dimensional trapezoidal obstacle; with disturbing height ε, lying on the bottom of the running stream, in terms of a linearised theory. Particular attention is given to two cases of the flow, the supercritical and the subcritical. The bottom is represented in integral form using Fourier's double-integral theorem. Following the method suggested by Thomson (1886) and Lamb (1932), we obtain a linearised free-surface profile in series form for the two cases of flow. The linearised solution obtained is based on the assumption that the height of the trapezoidal bump, ε, is small compared to the channel depth,h. The nature of the free-surface formed depends on whether the flow is subcritical or supercritical. The results are plotted for the two cases of the flow for different shapes of the bottom and different values of Froude number,F. The effect of the Froude number, the bottom height and the shape of the bottom are discussed.
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