Abstract: According to the definition of frictional head loss, the theoretical relations of frictional head loss with coefficient of bed resistance, conjugate depth ratio of hydraulic jump, ratio of width to height of initial section, and initial depth are deduced. The theoretical calculation equations of frictional head loss coefficient and the local head loss coefficient of free hydraulic jump in rectangular open channel are given, and the simple fitting formulas of frictional, local, and total head loss coefficients are put forward. It is shown that frictional head loss grows with the rise of the initial depth of hydraulic jump and the coefficient of bed resistance; but declines with the increase of the conjugate depth ratio and the ratio of width to height of initial section. Local head loss coefficient augments with the increasing of the Froude number of initial section. The proportion of local head loss in the total head loss becomes larger with the increase of Froude number. When Froude number is 3, the proportion of local head loss is 90%, and when Froude number is 6, the proportion of local head loss is over 95%. The research results could improve and enrich the theoretical system of hydraulic jump.

Key words: rectangular open channel, stilling pool, hydraulic jump, frictional head loss, local head loss, total head loss