Unsteady Flow

In the previous chapters, we discussed steady flow in open channels. However, the flow conditions in the real-life systems usually vary with time and thus the flows are unsteady. The unsteadiness may be due to natural processes, due to human actions, or due to accidents and incidents. The analysis of unsteady flows is usually more complex than that of steady flows because unsteady-flow conditions may vary with respect to both space and time, i.e., they are function of both space and time. Therefore, partial differential equations describe unsteady flows since the dependent variables (flow depth and flow velocity) are functions of more than one independent variables (space and time). A closed-form solution of these equations is not available except in very simplified cases and thus numerical methods are employed for their solution.

Unsteady flow is discussed in Chapters 11 through 16. A brief introduction is presented in this chapter; governing equations are dervied in the next chapter, and numerical methods for their solution are presented in Chapters 13 and 14. Two-dimensional unsteady flow is discussed in Chapter 15, and a number of special topics related to unsteady flow are described in Chapter 16.

In this chapter, a number of commonly used terms are first defined. The causes of unsteady flow are then discussed and equations for the velocity of a gravity wave are derived.