USGS1955
This study of the channel of Brandy wine Creek, Pennsylvania, consists of three parts. The first is an analysis of the changes which take place in the width, depth, velocity, slope of the water surface, suspended load, and roughness factor with changing discharge below the bankfull stage at each of several widely separated cross sections of the channel. Expressed as functions of the discharge, it is found that the variables behave systematically. In every section studied, as the discharge increases, the velocity increases to about the 0.6 power, depth to the 0.4, and load to the 2.0 power of the discharge. The roughness decreases to the 0.2 power of the discharge. The relative magnitudes and the direction of these variations are similar to those which have been observed in other rivers in the United States, primarily in the West. Some modifications of the hypotheses applicable to the western rivers are probably required because on Brandywine Creek the difference between the materials on the bed and in the banks is considerably greater than it is on most of the western rivers studied. In the second part of the paper the progressive changes of the same variables in the downstream direction with increasing discharge at a given frequency are described. Despite the disorderly appearance of the stream, it is found that the variables display a progressive, orderly change in the downstream direction when traced from the headwater tributaries through the trunk stream of Brandywine Creek. At a given frequency of flow, width increases with discharge to about the 0.5 power. Depth increases downstream somewhat less rapidly, while the slope and roughness both decrease in the downstream direction. Despite a decrease in the size of the material on the bed, both the mean velocity and the mean bed velocity increase downstream. The rates of change of these variables are in close accord with the changes observed on rivers flowing in alluvium and in stable irrigation canals. These relationships hold for all flows up to the bankfull stage. Analysis of the streamflow records indicates that the annual maximum discharge equals or exceeds the bankfull stage roughly once every 2 years. The regularity in the behavior of the variables with changing discharges both at-a-station and in the downstream direction and the similar rates of change of the variables on Brandywine Creek and in stable irrigation canals suggest the existence of a quasi-equilibrium in the channel of the creek. Part three of this study is concerned with this concept of equilibrium in streams. By analogy with canals and with several rivers in diverse regions of the United States it may be concluded that this quasi-equilibrium is closely related to the discharge, and to the concentration of the suspended load. The shape and longitudinal profile of the channel are determined by these two independent factors which operate within the limits set by the local geology. The latter determines the initial size, shape, and resistance of the material provided to the channel. The existence of a quasi-equilibrium among the variables studied suggests that most reaches on Brandywine Creek are at grade. This is true if the term "grade," when applied to natural rivers, is synonymous with quasi-equilibrium. The adjustability of the variables in the channel rather than the stability of any particular shape or longitudinal profile of the channel is emphasized when t