Abstract
For flow over a square-edged broad-crested weir the ratio of the measured discharge to the discharge predicted by simple one-dimensional theory may be expressed as an empirical coefficient. This coefficient has been found to have an almost constant value for a certain range of heads on any such weir. The thesis describes the development and verification of an analytical approach to account for the flow pattern in this range and, hence, for the factors limiting the range and for the value of the coefficient under these conditions. The hypothesis has as its basis the fact that a separation zone or roller is formed at the upstream edge, where the main flow is unable to follow the sharp right-angle corner but follows instead a curved path of finite radius. A control for the flow over the weir is thus established at a cross-section over this roller. To permit mathematical development, the simplifying assumption is made that within the roller the static head is constant while the main flow outside the roller is irrotational and hence amenable to treatment by potential flow theory. It is then possible to select tentative lines for the surface and for the outline of the roller and, by a relaxation technique, to obtain the distribution of values of the stream function. Velocities at the boundaries are then calculated; if these do not satisfy Bernoulli's equation, the boundaries are modified and the calculation is repeated. The digital computer facilitates the calculation and the plotting of streamlines. Downstream the surface profile rises and, with increasing crest length, waves and a hydraulic jump may be formed establishing a second control at the downstream end. These facts are related to accepted friction and wave theory. Experimental work confirming the analytical treatment is described. With weirs set in a laboratory flume, the flow pattern near the upstream edge was established using a pitot cylinder. In addition, surface profiles were observed as were velocity and pressure distributions along the crest, which permitted an assessment of energy degradation. Flow-head relationships were recorded and they are compared with the findings of earlier workers.