Title:

The flow of water over trapezoidal weirs

One of the principal reasons for undertaking this research was that an apparatus was wanted, the flow from which would vary directly as the head. It is shown in the thesis that an equation of the type [equation] can be made to approximate very closely indeed to a straight line for a given range of head H by suitably choosing the values of p, q and r. The first term can be supplied by an orifice, or its equivalent, discharging under the same head as the weir and the next two terms can be provided by a suitably chosen weir. The thesis describes the general method of conducting the experiments and the special gauges used. To determine the values of q and r in the basic formula [equation] where Q = the flow in cusecs and H = the head in feet, experiments were made with various values of 0, the angle of slope of each weir side to the vertical. The value of r can be expressed as a simple function of 0 but q was found to be a much more complicated function and is best read off from a graph. The formulae are claimed to give results accurate within at least 2% over rest of the range of heads. Messrs. Gourley and Crimp conducted experiments with trapezoidal weirs but with only positive values of 0 (i.e. when the sides slope outwards). They evolved the formula Q = 3. 10b1. 02H1. 47+2. 48 tan 0 H2. 47 (where b = the width of the sill) and tables and graphs are given comparing this formula with the results of the present research. The final deduction was that a weir having b = 0. 329 feet and 0 = 1514 combined with a circular orifice, or its equivalent, so that [equation] would give a discharge very closely proportional to H, up to a value of H = 6 inches.
