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What are the differences between stream capacity and stream competency? How does it relate to "suspended load"?

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Gravity is the influence that drives the water channeled downhill in streams. A stream is defined as all channelized movement of water, including large movements of water in rivers, such as the Yangtze River and the Mississippi River. Channel, channelized and channelizing are defined as the eroded pathway that the stream of water follows and the fact of these waters following eroded pathways. 

Stream capacity is the total quantity of sediment that a stream can carry, move, transport. Streams of water carry sediment. Each stream has a capacity for what can be carried by the volume and velocity (force) of water being channelized.

Stream competence is the size of sedimentary particle that can be carried, moved, transported in a channelized stream of water. Each stream has a competency for what size of sedimentary particle it can move by its force (volume and velocity). This competency may change as stream volume and flow of velocity change due to seasonal flooding and other factors of topography.

The difference between stream capacity and stream competence is that capacity measures quantity of sediment while competence measures size of particles comprising sediment. Some sedimentary particle sizes from large to small (or coarse to fine) are boulder, rock, pebble, sand, silt, clay.

Under normal circumstances, since channelized streams are influenced by the force of gravity, the major factor affecting stream capacity (quantity of sediment) and stream competence (sediment particle size) is channel slope. Channel slope derives the measurement of stream gradient. While each stream has its own slope, various streams may share the same gradient. Channel slope is the measure of the angle, from a horizontal zero degree slope, of the degree of slope of a given stream of water. The channel slope is measured using two points some distance from each other. The difference in the elevation at the two points divided by the linear distance between the points equals the channel slope and yields the stream gradient: e.g., (1) points A and B are at elevations of 300 feet and 100 feet, with a distance between of 20 yards, so the stream gradient is a 10 degree angle; (2) points C and D are at elevations of 360 ft and 140 ft, with a distance between of 20 yards, so the stream gradient is a 10 degree angle; the gradients are the same though the slopes of elevation of the channels are different.

The stream flow velocity (i.e., speed of a quantity of material past a given point during a specific time interval) of a stream of water is directly related to the channel slope of the stream. The greater the slope, the higher the flow velocity; the lesser the slope, the lower the flow velocity. Examples are the greater slope of the Colorado River flowing through the Grand Canyon and the lesser, almost flat, slope of the Mississippi River delta flowing into the Gulf of Mexico. The greater Colorado River slope results in high velocity and concordantly high stream capacity and competence. The lesser, nearly flat, Mississippi delta slope results in low velocity and concordantly low stream capacity and competence [stream capacity: quantity of sediment; stream competence: size of sediment particle].

Since water streams flow in channels under the influence of gravity, channelization is also a critical component affecting stream capacity (quantity) and stream competence (size), which are both directly related to stream flow velocity. Conversely, channelization and capacity/competence/velocity are indirectly related. As channelization increases, the others decrease: a broad channel has low velocity, lower capacity and lessened competence. Conversely, a narrow channel has high velocity, higher capacity and greater competence. Channelization also affects the stream load, which is related to stream discharge. Stream load is carried on stream discharge and is defined as "the sum of the mass that can be transported by a stream" (Gale Cengage and DiVenere). Stream load is directly related to both stream velocity and stream gradient...

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