Semicylindrical trough

A variation of the left-hand side theme and the issues of geometry is that of the semicylindrical trough lying on its side. The physical situation is quite similar to that of the triangular trough, except that the walls follow a circular curve. The physical system is shown in Figure 6. 

This is similar to the equation that we encountered in the last problem for the semicylindrical trough ... 

Instead of being concave, the water surface extending between adjacent soil particles may assume a semicylindrical shape, i.e., like a trough or channel. One of the radii of curvature then becomes infinite for example, r2 may be infinite (= °°) in such a case, the pressure is —alri by Equation 9.6. If the air-liquid surface is convex when viewed from the air side, the radii are negative we would then have a positive hydrostatic pressure in the water (see Eq. 9.6). In the intermediate case —one radius positive and one radius negative (a so-called saddle-shaped surface)—whether the pressure is positive or negative depends on the relative sizes of the two radii of curvature. 

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