ABSTRACT
The flow of fluid in both pipes (pressure/closed conduit flow) and open channels (gravity/open conduit flow) are contained in a conduit and thus are referred to as internal flows, whereas the flow of fluid over a body that is immersed in the fluid is referred to as external flow (see Chapter 10). In pipe flow, the conduit is completely filled with fluid and the flow is mainly a result of invoking a pressure difference (pressure drop, Δp), which was addressed in Chapter 8, “Pipe Flow.” However, open channel flow—where the conduit is only partially filled with fluid and the top of the surface is open to the atmosphere—is addressed in Chapter 9. Open channel flow is a result of invoking gravity and occurs in natural rivers, streams, channels and in artificial channels, canals, and waterways. Furthermore, the results sought in a given flow analysis will depend upon whether the flow is internal or external. In an internal flow, energy or work is used to move/force the fluid through a conduit. Thus, one is interested in determination of the forces (reaction forces, pressure drops, flow depths), energy or head losses, and cavitation where energy is dissipated. The governing equations (continuity, energy, and momentum) and the results of dimensional analysis are applied to internal flows. Depending upon the flow problem, one may use either the Eulerian (integral) approach or the Lagrangian (differential) approach or both in the application of the three governing equations (Section 9.2). It is important to note that while the continuity and the momentum equations may be applied using either the integral or the differential approach, application of the energy equation is useful only using the integral approach, as energy is work, which is defined over a distance, L. Furthermore, as noted in previous chapters, for an internal fluid flow, while the application of the continuity equation will always be necessary, the energy equation and the momentum equation play complementary roles in the analysis of a given flow situation; when one of the two equations of motion breaks down, the other may be used to find the additional unknown quantity.
