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2 . gradually varied flow where analogies with uniform flow may be used. Where flow can not be considered to be gradually varied (acceleration effects can not be neglected), other methods of calculating the water surface elevations are needed. Many non-uniform channels formed in natural material and containing steep chutes will not maintain gradually varied flow for any significant distance. To understand why this is so, steep channels will be defined and their characteris- tics considered. Steep channels are defined as waterways whose energy slope is steeper than the critical slope for the discharges considered. Critical slope is defined as that slope just sufficient to maintain critical flow. Critical flow is characterized by the fQllowing condi- tions: (1) specific energy is a minimum for the given discharge; or (2) discharge is a maximum for given specific energy; (3) specific force is a minimum for a given discharge; (4) the Froude number is equal to unity; or (5) the velocity of flow is equal to the celerity of small gravity waves in shallow water caused by local disturbances. Flow whose slope is flatter than critical is called tranquil and flow whose slope is steeper than critical is called rapid. In the establishment of an equilibrium flow condition for the size of bed material, slope, discharge, and sediment load, channels whose average slope is steep may traverse bedrock or may have relatively large boulders in the stream bed. The channel cross-sectional shapes created by these materials are usually sufficiently non-uniform as to inhibit the establishment of gradually varied rapid flow. In streams with channel slope near critical, the resulting flow usually alternates between tranquil and rapid; that is, very slight changes in energy can , . . . .