A BASIC SYSTEM OF EQUATIONS FOR THE MOTION OF A FLUID WITH VARIABLE FLOW RATE IN THE BILATERAL FLOW OFFTAKE

摘要

All theoretical studies conducted in modern hydrodynamics are based on a system of Eulerian equations, a continuity equation, and a characteristic equation. In the area of hydraulics that is concerned with a one-dimensional motion, the basis for all theoretical investigations is a system of three equations: (ⅰ) a Bernoulli equation, which is a particular solution of the Eulerian system, (ⅱ) a flow equation, which is an analog of the continuity equation, and (ⅲ) a characteristic equation. These equations are used to study the motion of a fluid at a constant flow rate. For the case of motion of a fluid at a variable flow rate, these equations must be modified and augmented with new equations to make the system complete. Most studies were mainly concerned with formulating a "basic equation" for the motion of a fluid at a variable flow rate. For the first time, the problem of constructing a general complete system of equations for the motion of a fluid at a variable flow rate for unilateral division of the flow was brought to a logical conclusion by Kiselev. To follow suit, it was our goal in this study to set up a general complete system of equations for the motion of a fluid at a variable flow rate for bilateral division of the flow.