On the hydraulic jump, mainly for the jump in sloping bed, the distributions of velocities and its standard deviations were measured using the micro-current meter and micro-program calculator. The following were found.
1. On the jump in flat bed, the relations between the height of maximum velocity's position at each cross section (δ) and the distance of each cross section from the beginning of jump (
l) varied by the Fr number of incoming flow. For
Fr≥4.52, δ grew rapidly for the water surface from the beginning of jump, and their variation coefficient near bed (σ/
U) 0.3>0.4 (
U: velocity, σ: standard deviation). For
Fr=3.03, the increment of δ became moderate and (σ/
U)
0.3=0.2-0.3, and then for
Fr=1.75, (σ/
U)
0.3=0.1-0.2 and δ grew very slowly. The δ-l relations at the case of
Fr=1.75 in fl at bed and the cases of low
Fr number jumps in sloping bed were similar to the turbulent boundary layer developments in smooth surface open channel.
The area of surface roller of jump became narrow at
Fr=1.75, 4.52 and 6.02 and became wide at
Fr=3.03.
The vertical velocity distribition in the jump followed the 1/7 power law at 0<z<3 and the law of free jet at z>δ, where
Z is the height of position from bed.
2. The jumps in sloping bed were classified to 2 types according to the δ-
l relations. The direct jump type, where, δ grows rapidly for water surface on the sloping bed, or where δ does not grow so largely on the sloping bed but grows rapidly on the flat bed, and the submerged jump type, where δ scarcely grows on the sloping bed and grows very slowly on the flat bed.
The direct jump type occured when the turbulence near bed became high, that is, in general the
Fr number and
D/
d (
D: the height of jump beginning station from flat bed,
d: the depth of jump beginning station) were large provided the slope remained the same.
The submerged jump type occured at the contrary case.
The relations between the borders of Fr number,
D/
d of the both type and the slope were shown.
3. When the jump was the direct jump type, the vertical velocity distributions for 0<z<δ deviated from the 1/7 power law at the high turbulent stations but they followed the 1/7 power law at the low turbulent stations.
When the submerged type jump occured, the 1/7 power law was concluded perfectly.
For z>3 of the vertical velocity distribution, the same relation of free jet was concluded.
4. The
Um/
Uo,
U0.3/U
o (U
m: the maximum velocity of section,
U0.3: the velocity near bed of section, U
0: the mean velocity of the jump beginning station) were related to
l/
d. These relations were adjusted in the 2 groups of slopes 1/6.9-1/3 and slopes 1/10-1/20, flat bed. The
Um/
U0-
l/
d relations were settled on a single curve for each group having no relation to the slope,
Fr, and the jump type.
The
U0.3/U
0-
l/
d relations were adjusted in the same manner.
The experimental equations were obtained.
5. The various states of jump from a flat bed jump to a sloping bed jump were caused by regulating the downstream flow stage only.
The scoring characteristics of flat bed were compared with each other. The tested slopes were 1/1, 1/5 and 1/6. 9.
The flow states of each jump had some specialities, for example, in the case of high jump beginning station of 1/1 slope, the partial adverse fllow area was found on the flat bed near the toe of slope.
View full abstract