Among hydraulic jumps on sloping bed, the one which begins on sloping bed and ends on the horizontal bed at downstream-case 2 of C. E. Kindsvater's classification-was experimentally studied.
1) Conjugate depth
The conjugate depth can be calculated by using the momentum equation for the jump when the pressure distribution along the sloping bed is known. Therefore, pressure distribution was experimentally obtained for various states of jump.
According to the test results, the pressure distribution was affected largely by the bed height of the entering jump from the toe of slope,
z, and was expressed as a function of
q/z√
gz.(
q: the discharge per unit width,
g the acceleration of gravity)
The conjugate depth which was calculated by using the experimental expression for pressure distribution at each of the slopes 1:1, 1:3 and 1:5 agreed with test results.
And then, the conjugate relation ξ=
h1/
h2 (
h1 the depth of entering jump,
h2: the tailwater. depth) may be presented as functions of the Froude number of entering jump
Fr1,
z/h1 and the bed slope, and the relation between ξ and
Fr1 which was illustrated with slope and
z/h1 as parameters agreed with Rindlaub's test results.
Because the variation of ξ lies within 5% for the change of tan a by the unity (
a: the angle between sloping bed and horizontal bed), the effect of slope can be disregarded in the approximation of ξ. The calculated results which were obtained by using the experimental equation and disregarding slope effect agreed with Bradley-Peterka's test data.
2) Jump length
The jump length, which was defined as the distance from the entering jump to the end of surface eddy, was shown as a function of
q/z√
gz without any relation with bed slope.
3) Head loss
The velocity distribution in the jump was found by using the pitot sphere and the energy coefficient was known. And then the dissipating process of energy head was found. According to this process, it was found that most energy to be lost is dissipated before the end of surface eddy.
The relation among the head loss, bed slope,
z/h1 and Froude number of entering jump is given.
抄録全体を表示