Fundamental differential equation of flow of a fluid with a variable mass in the case of bilateral water diversion

Conclusions

1.The relationships (26) and (27) obtained indicate that at the site of division of the flow there occurs a change in the depths h_o and h_cr related to the law of variation of discharge. Hence the line of the normal and the line of the critical depths will have a curvilinear outline. 2.For bilateral symmetric diversion of water the specific energy of the basic flow in section I-I is greater than the half-sum of the specific energies of the dividing flows.

If we assume that E _l.d = E_r.d = E_d, then E_b1>E_d.

Actually, the piezometric head in section I-I in the case of passage of part of the discharge into the diversions is partially expended on overcoming the losses and is partially transformed into kinetic energy of the diverted flows. 3.The fundamental differential equation of steady fluid flow obtained in the case of bilateral water diversion in open channels can be used only in the case when the distance between axes of the diversions is taken within limits from 0 tol.

If the diversions are spaced at a distance greater thanl or symmetric pairs of diversions are located at a distance at which the interaction of these symmetric pairs of diversions with each other is not observed, then a system of fundamental differential equations of steady flow of a fluid with a variable mass obtained for each pair of diversions separately is set up. 4.Design engineers should bear in mind that the schemes of flow division shown in Figs. 3–6 are possible only for the case when part of the discharge is throughgoing along the main channel. It is necessary to calculate the main channel with consideration that there is enough water for all diversion channels.