This chapter derives the at-a-station as well as the downstream hydraulic geometry using the tractive force theory. Here the threshold discharge does not necessarily correspond to the bankfull discharge for at-a-station hydraulic geometry. At a given section, there can be a threshold discharge where the channel is flowing partially. .

The concept of minimum variance is a statistical concept, and its premise is that a river tends to minimize the variability of factors that govern its hydraulic geometry. This concept has been applied in different ways and this chapter discusses the theory of minimum variance from different viewpoints.

A regime channel geometry can be computed using the second law of thermodynamics and the Gibbs equation which constitute the foundation of the thermodynamic method. With the use of a regime width relation, the need for a sediment transport rate relation can be obviated. This chapter discusses the thermodynamic methdology for deriving the hydraulic geometry of regime channels.

The stability of river channel adjustment toward equilibrium is controlled by a set of factors governed by the Froude number. When the channel is subjected to water discharge, sediment load, and sediment particle size, it tends to attain stability which corresponds to the minimum Froude number and minimum bed material motion. Field observations and computer simulations for sand-bed rivers show that a river in equilibrium tends to acquire a stable geometry with minimum Froude number. This leads to the hypothesis of minimum Froude number, which is presented in this chapter.

Relationships relating channel width, depth, and cross-section as well as discharge to drainage basin area are regional relationships, because they are developed at the basin scale. These relationships constitute regional hydraulic geometry, which is utilized in stream assessments, evaluating channel characteristics, identifying field indicators of bankfull discharge, and delineation of regional boundaries, hydrologic regions, and ecoregions. This chapter presents these regional relationships.

The similarity principle is based on the acknowledgment that a river, if left alone for a sufficiently long time with fixed values of water and sediment discharge loads, will adjust its width, depth, slope, and meandering pattern in a certain manner. If the values of water and sediment discharge loads imposed on the river change are different, the adjustment will be made similarly. This chapter derives the hydraulic geometry using this principle of similarity.

The average river-channel system tends toward an approximate equilibrium between the channel and water and sediment it transports. Both discharge and sediment load principally depend on the drainage basin. Under equilibrium, the stream channel depth, width, velocity, and suspended sediment load at a given cross-section can be expressed as power functions of discharge and these functions constitute the at-a-station hydraulic geometry (AHG). In a similar vein, stream channel depth, width, flow velocity, and suspended load along the river vary with discharge as simple power functions under the condition that the frequency of discharge at all cross-sections is equal. These functions are similar even for rivers having very different physiography and constitute the theory of downstream hydraulic geometry (DHG). The power functions for both types of hydraulic geometry-at-a-station and downstream-form the Leopold and Maddock (LM) (1953) theory which is discussed in this chapter. The discussion is divided according to the type of geometry. For the same discharge frequency along the river, depth, width, and velocity of flow increase with discharge downstream.

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.

Alluvial channels are continuously modified by sediment movement and exist in comparative equilibrium. The longitudinal profiles and cross-sections of these channels depend on hydraulic and sediment factors and boundary conditions which govern channel morphology. This chapter discusses the theory of channel mobility leading to stable hydraulic geometry.

Hydraulic geometry is a quantitative description of the variation of river characteristics with variation in discharge and sediment load. It is impacted by climate, geology, and human interference. Hydraulic geometry relations have been expressed in power form and have been derived using a multitude of hypotheses. These relations play a fundamental role in the design of alluvial canals, river training works, and watershed management. The objective of this chapter is to introduce preliminary concepts that are deemed important for understanding different aspects of hydraulic geometry.

Crops that can be grown in a particular area depend on climate and soil. Not all crops can be grown in all areas as different areas have different types of climate and soils. Further, water requirements of crops are influenced by climate. This chapter discusses those aspects of climate that are fundamental to agricultural farming and consequent irrigation.

Irrigation planning begins with an assessment of water resources availability and irrigation potential. Then, planning of an irrigation system depends on the size of the system. Small systems may be owned by individual farmers, and farmers plan these systems on their own, with limited outside help. On the other hand, large systems are owned by governments or groups of farmers, and their planning is quite technical. This chapter discusses the rudimentary aspects of irrigation planning.

Sources of water are either surface or subsurface. Surface water is stored in reservoirs and is conveyed to the farm for irrigation or is derived from rivers either directly or through canals. Subsurface water is extracted from aquifers by wells and then conveyed to the farm. This chapter provides a snapshot of these sources and availability of water therein.

For large irrigation systems there is usually an organizational structure that is tasked with managing water, structures and equipment, and people. It engages in decision-making, resource mobilization, communication, and conflict resolution. This chapter provides a snapshot of elements of irrigation management.

The quality of irrigation water has a significant impact on crop yield, degradation of soil, pollution of groundwater, and operation and life of irrigation systems. It also interacts with soil and its chemical and physical constituents. In irrigation engineering, water quality is evaluated by considering physical and chemical characteristics of water, but biological characteristics may also be important if wastewater is used for irrigation. This chapter discusses water quality from an agricultural irrigation viewpoint.