END DEPTHS FOR CHANNELS OF DIFFERENT SHAPES

Abstract

End depth or brink depth of free overfall is another method of measurement of flow in open channel. Momentum eguation is used to derive general equation for end depth for horizontal channel and sloping channels of different shape. In 1936, Hunter Rouse- had obtained classical result by his experiment that the ratio of end depth to corresponding critical depth for horizontal rectangular free over fall is 0.715. In 1954, Charles Grant Edison10 reviewed this result by velocity distribution, by using energy coefficient ,< (or Coriolis Coefficient) calculated to be 0.718 which is closed to Hunter Rous6161 result. In the same year Pathi and Sharrawi 3 attempted to measure the pressure distribution of free over fall directly. In 1956, Delleur, Dooge and Gent4 show that the end depth ratio depends on relative slope of channel whether smooth or rough. In 1961 Di skins developed equations for end depth for exponential and trapezoidal channels at zero pressure distribution for mild and horizontal channels and prepared tables for relation between discharges and and depths.: N. Rajaratnam and D, Muralidhar had made extensive study of end depth problem for triangle, parabola and trapezoidal channel. In 1962, Advani 11 calculated the end depth for circular channel of mild slope with zero pressure distribution at the end section, Smith °12 also give a solution for the above with experimental datas. In 1964, Rajaratnam and D. Muralidhar9 had made extensive investigation of end depth problem for circular channels with zero and non zero pressure distribution of mild, Horizontal and steepslope. N. Rajaratnam & D. Muralidhar9 found that for horizontal bed slope Ye = 0.725 for circular channel c N. Rajaratnam c° D. Nuralidha6 found by experiments that ye = 0.795 for triangular channel yc ye y = 0.772 for parabolic channel c y and e = 0.705 for rectangular channel, which is 1.4 less yc than the classical value by H. Rousel, For steep sloping channels of any geometrical shape, the end depth ratio had been found to be a function of relative slope, Also variation of pressure coefficient for end section with relative slope are also presented. The direct relationship between end depth and discharge for different geometrical shape of trapezoidal mild sloped channels are press ted in the form of tables and nomographs by the author. The established curves can be conveniently used in predicting discharge with known end depth or vice—versa. The range of the values used in these curves cover the most common practical engineering problems.