Abstract:
Hydraulic jump is a phenomenon well known to hydraulic engineers as a useful
means of dissipating excess energy and prevent scour below overflow spillways,
chutes and sluices. In situations where the downstream depth is larger than the
sequent depth for a normal jump, a drop in the channel floor may be used to ensure a
jump. If this type of jump occurs in a sloping condition the analysis of the
phenomenon becomes very complex due to the inclusion of so many parameters
related to sudden drop and channel slope. A hydraulic model investigation is
conducted to evaluate the characteristics of hydraulic jump in a sloping channel with
abrupt drop in this present study.
The basic equation is based on the application of the one dimensional momentum
equation and continuity equation. The results of the experimental study were used to
evaluate a developed prediction equation for computing sequent depth ratio in a
sloping channel with abrupt drop whose format is similar to the well-known
Belanger equation for classical jump with modification of Froude number. The
modified Froude number term contains three additional parameters, two of them
incorporate the effect of Froude number and the third one represents for describing
the effect of drop height. A 12.19 m (40 ft) long tilting flume has been used to carry
out the investigations. Several contraction geometries were inserted in the channel to
reduce the height of the supercritical flow upstream of the drop section. Three drop
heights of 2 cm, 4.5 cm, and 6 cm were maintained together with three different
channel slopes (0.0042, 0.0083 and 0.0125). The initial depth, sequent depth,
velocity etc. were measured with different combinations of drop height and channel
slope. From the entire test runs three desired parameters k1, k2 and k3 were calculated
and then these three were calibrated with the experimental data to relate these factors
with some known variables like drop height, channel slope and inflow Froude
number. With the aid of these factors, modified inflow Froude number will be
calculated to get the desired form of Belanger’s format prediction model.
