Stable Channels

The form and size of a channel in cohesionless material stable against erosion for a definite discharge are studied. The angle of internal friction and the limiting tractive force 'tmax are taken as known. Distribution of shearing stresses is assumed to be such that they are proportional to the distance between bottom and water surface, measured at right angles to the bottom. In addition to the action of gravity and shearing stress the grains are acted upon by a hydrodynamic lift force. proving to be proportional to the shearing forces. The differential equation of the bottom form is established and integrated numerically; the form depends on internal friction. Based on the logarithmic law of velocity distribution and the assumed distribution of shearing str-essea, the velocities in all parts of the cross section can be found, and the total discharge is found by numerical integration. A profile consisting of thé curved "bank-part"of the above mentioned cross section and a "middle-part" of indefinite width and of constant depth y would be stable for the same tractive force. On the assumption however that nature will produce that cross section which has a minimum of area, only one definite solution, viz. the equilibrium profile, is found. The dimensions depend not on internal friction alone but also on the relative roughness of the bottom. Provided that the hydraulic roughness is assumed Ymax to be in conformity with that of natural watercourses, it is found that the area of the equilibrium profile varies slowly with