Introduction to Transient Flow

To this point we have emphasized steady flows, flows that do not change with time at any location in the pipeline system. In this brief chapter we will introduce two general categories of unsteady flow that we call transient flow. All transient flows are transitions, of long or short duration, from one steady flow state to another. Either of these end states may be the rest state. Each transient flow is a response of the fluid to some change in the hydraulic facilities that control and convey the fluid, or in the surrounding environment, that influences the flow. The first type of transient, which we will refer to as quasi-steady flow, is characterized by the absence of inertial or elastic effects on the flow behavior. In such a flow the variation of discharges and pressures with time is gradual, and over short time intervals the flow appears to be steady. Typical examples are the drawdown of a reservoir, the draining of a large tank, or the variation in demand in a water distribution system over a 24-hour period. This type of transient was considered briefly in Chapter 6 and will be examined in more detail in Section 7.2. The second kind of transient is known as true transient flow, in which the effect of the fluid inertia and/or the elasticity of the fluid and pipe is an essential factor in the flow behavior and must be considered. If inertial effects are significant but pipe and fluid compressibility effects are relatively minor or negligible, then we have a true transient flow which we will refer to as a rigid-column flow. If in addition we must retain the elastic effects of the fluid and pipe in order to obtain an accurate characterization of the transient, we will call this a water hammer condition. The distinction between rigidcolumn flow and water hammer is not easily categorized and depends, in a general way, on how rapidly events change in a system. For example, the oscillation of the water level in the surge chamber of a hydroelectric facility can be analyzed accurately as a rigid-column flow. In this case inertial effects must be considered, but elastic or compressibility effects clearly are minor. On the other hand, the sudden closure of a valve in a pipeline is a water hammer situation; to simulate accurately the resulting behavior would require the inclusion of the elasticity of both the pipe and the liquid in the analysis. When the valve is closed more slowly, however, uncertainty arises. If the closure time is sufficiently long, then a rigid-column flow analysis may represent the physics of the problem well and produce good results. If the analyst is in doubt, then a water hammer analysis should be used because it is a more complete and general characterization of the flow. The groundwork for the study of true transients will be laid in Section 7.3 where both rigidcolumn flow and water hammer will receive attention. The study of water hammer problems will build on this foundation with extensive coverage in Chapters 8 through 13. Chapter 12 will treat both rigid-column flow and water hammer analyses in pipe networks.