Regarding the hydraulic calculation of flow under an ice cover

Abstract

Stream flow under an ice cover is markedly complex and is determined by the difference in the frictional force exerted by the channel bottom and the ice surface on the water. In hydraulic calculations it is important to determine the position in the vertical of the maximum velocity.In the quadratic drag range, in determining the position of the maximum velocity it is desirable to obtain a simple equation for calculation, and for a small difference in roughness of the walls the equation of N. N. Pavlovskii can be used. Dividing the flow at the line of maximum velocity into two independent parts (see diagram) and utilizing the condition of balance of forces for equal motion there can be derived the equationin which C t is the Chezy coefficient, characterizing the complex relation with the velocity v t of the frictional force of dze current on the ice cover, C t = f (nb hi); C 2 is the Chezy coefficient characterizing the complex relation with the velocity v z of the frictional force of the current on the bottom, Cz= f(nz, h~).The relation between the average velocities of the flow in the upper and lower sections can be determined also by a logarithmic equation of the distribution of the velocity in the vertical. Taking %t =0.4, we have v,_._= 1 + 2.5 (C~lC,)