Physically based approaches to hydraulic geometry relations for width, depth, velocity, and slope require equations of continuity of water, roughness, and sediment transport. Different methods have been employed for different expressions of roughness and sediment transport. Without delving into their underlying theories, this chapter briefly outlines these expressions as they will be invoked in subsequent chapters. Also, unit stream power, stream power as well as entropy have been employed, which are also briefly discussed.

It is hypothesized that river morphology is governed by the dominant discharge, saturation of sediment discharge, and maximization of Froude number leading to the minimum amount of energy dissipation. The minimum energy dissipation rate may be achieved by the adjustment of sediment transport rate, friction factor, or Froude number of the flow under some special conditions. This chapter discusses the derivation of river geometry based on the minimization of energy dissipation rate or the aforementioned factors.

A pipe is a closed conduit, and when it runs full its hydraulics is different from the hydraulics of open channels in which the upper surface of flow is exposed to the atmosphere. Pipes or closed conduits are used in sprinkler and drip irrigation systems to carry water from the source of water supply to the individual sprinkler or emitter. Water may be conveyed from a reservoir through a pipeline. These systems are also called pressurized irrigation systems. This chapter reviews the principles of pipeline hydraulics.