Đang chuẩn bị liên kết để tải về tài liệu:
Open channel hydraulics for engineers. Chapter 7 unsteady flow

This chapter introduces issues concerning unsteady flow, i.e. flow situations in which hydraulic conditions change with time. Many flow phenomena of great importance to the engineer are unsteady in character, and cannot be reduced to steady flow by changing the viewpoint of the observer. The equations of motion are formulated and the method of characteristics is introduced as main part of this chapter. The concept of positive and negative waves and formation of surges are described. Finally, some solutions to unsteady flow equations are introduced in their mathematical concepts. | OPEN CHANNEL HYDRAULICS FOR ENGINEERS ----------------------------------------------------------------------------------------------------------------------------------- Chapter UNSTEADY FLOW _ 7.1. Introduction 7.2. The equations of motion 7.3. Solutions to the unsteady-flow equations 7.4. Positive and negative waves; Surge formation _ Summary This chapter introduces issues concerning unsteady flow, i.e. flow situations in which hydraulic conditions change with time. Many flow phenomena of great importance to the engineer are unsteady in character, and cannot be reduced to steady flow by changing the viewpoint of the observer. The equations of motion are formulated and the method of characteristics is introduced as main part of this chapter. The concept of positive and negative waves and formation of surges are described. Finally, some solutions to unsteady flow equations are introduced in their mathematical concepts. Key words Unsteady flow; method of characteristics; positive and negative waves; surge; numerical solution. _ 7.1. INTRODUCTION In unsteady flow in an open channel, velocities and depths change with time at any fixed spatial position. Open channel flow in a natural channel almost always is unsteady, although it often is analyzed in a quasi-steady state, e.g. for channel design or floodplain mapping. Unsteady flow in open channels by nature is non-uniform as well as unsteady because of the free surface. Mathematically, this means that the two dependent flow variables (e.g. velocity and depth or discharge and depth) are functions of both distance along the channel and time for one-dimensional applications. Problem formulation requires two partial differential equations representing the continuity and the momentum principle in the two .