Velocity Distribution in Hydraulic Jump - nptel - Indian Institute of ...

Hydraulics Prof. B.S. Thandaveswara
29.4 Velocity Distribution in Hydraulic Jump
The approaching uniform flow velocity imparts some amount of energy to the ambient
fluid which changes the velocity distribution. After the jump, the variation of depth, flow
pattern, and air entrainment influence the velocity distribution. There has not been much
work on the velocity measurements particularly in the roller zone. Experiments by the
Miami conservancy District in 1917, clearly show that the approaching high velocity of
the water gradually diminishes through the jump.
Later Hubbard recorded the turbulent fluctuation in a hydraulic jump just downstream of
the roller, to compare the results of the air model investigated by Rouse et al.
However, it appears that it is Rajaratnam in 1965 who rationalised the analysis. He
conducted an extensive investigation of the mean velocity distribution in the jump
formed just below a sluice gate in a smooth channel in a Froude number range of 2.68
to 9.78. His measurements were confined to forward flow. He compared his results with
the wall jet and he was able to show the existence of similarity law of velocity
distribution. further, he concluded that the velocity in the boundary layer follows the
defect law and hydraulic jumps, the pressure gradient is adverse and its effect must be
felt as observed by Clauser.
Resch and Leutheusser in 1971-1972, have measured the turbulent velocity fluctuations
both in forward and backward flow of the jump.
An understanding of the velocity distribution is necessary when energy loss is to be
computed. However, it is usual to assume a uniform velocity distribution. Till recently
there had not been much work on velocity measurements in hydraulic jumps and
particularly in the roller zone. Miami Conservancy district conservancy report shows that
the velocity of the water gradually diminishes through the hydraulic jumps.
Hubbard and Rajaratnam investigated about the velocity distribution in jumps. The latter
conducted extensive investigations on the velocity distribution. His measuremets were
confined to forward flows in a Froude number range of 2.68 to 9.78. His analysis
followed the analogy of a wall jet.
Indian Institute of Technology Madras

Hydraulics Prof. B.S. Thandaveswara
In the following paragraphs the results of the Thandaveswara are reported in which an
attempt is is made to measure the velocity in the roller zone also.
In Figures a to f the normalised velocity ( V/ V1 max ) distribution along the jump have
been plotted against the normalsied depth ( y / y1 ) in which V1 max is the maximal
velocity of the appraching flow and y1 is the depth of the approaching flow. The velocity
profile rises sharply up to the maximum velocity of the flow and then decreases
gradually as to the depth increases and finally becomes zero. These velocity profiles
exhibits similarity with the wall jet velocity profile as discussed by Rajaratnam. In
backflow the roller zone, is shown in dotted lines in Figures a to f. The negative sign
indicates only the direction. These components are only approximate, as the roller is full
of eddies and even the presence of a pitot tube will cause disturbances and affect their
characteristics. Just downstream of the roller, the velocity profiles begin at a higher
level. In this region the flow becomes almost static and full of vortices. The presence of
vortices is discussed elsewhere. Farther downstream of this region the flow reverts to
nearly uniform flow.
In Figures g to h. the variation of the velocity profile along the jump is presented for the
PHJ. This also exhibits a sharp rise up to the wall turbulent zone. As observed in the
NHJ, there exists a zone near the bed where the flow is anticlockwise and the velocity
profile shown is only for the main flow direction. Later, flow returns to the normal
condition.
Indian Institute of Technology Madras

Hydraulics Prof. B.S. Thandaveswara
y
___
y1
10
Indian Institute of Technology Madras
8
6
4
10
y
___
y1
0 0 0 0 0 0 0 0
0
0
0 0.4 0.8 1.2
0
0 0.4 0.8 1.2
_____ v
v1max
(a)
0 0 0 0 0 0 0 0 0 0
12
Run R2
8
6
4
2
_____ v
v1max
(b)
Run R1

Hydraulics Prof. B.S. Thandaveswara
12
___ y
y1
Indian Institute of Technology Madras
16
14
10
8
6
4
2
0 0 0 0 0 0 0 0 0
Run R3
0
0 0.2 0.8
_____ v
v1max
Velocity Distribution in the Jump (NHJ)
(c)

Hydraulics Prof. B.S. Thandaveswara
Indian Institute of Technology Madras
y
___
y1
18
16
14
12
10
8
6
4
2
Run R4
0
0 0.4 0.8
_____ v
v1max
Velocity Distribution in the Jump (NHJ)
(d)

Hydraulics Prof. B.S. Thandaveswara
18
16
14
12
10
Indian Institute of Technology Madras
y
___
y1
0 0 0 0 0 0 0 0 0 0 0
20 Run R5
8
6
4
2
0
0 0.4 0.8
1.2
_____ v
v1max
Velocity Distribution in the Jumo (NHJ)
(e)

Hydraulics Prof. B.S. Thandaveswara
Indian Institute of Technology Madras
y
___
y1
16
14
12
10
8
6
4
2
0
0 0 0 0 0 0 0 0 0 0
Run R6
0 0.4 0.8
1.2
_____ v
v1max
Velocity Distribution in the Jump (NHJ)
(f)
0 0

Hydraulics Prof. B.S. Thandaveswara
Indian Institute of Technology Madras
y
___
y1
*
10
8
6
4
2
0 0 0 0 0 0 0 0 0
Run B0
0
0 0.4 0.8
1.2
_____ v
v1max
Velocity Distribution in the Jump (PHJ)
(g)

Hydraulics Prof. B.S. Thandaveswara
Indian Institute of Technology Madras
y
___
y1
*
8
6
4
2
0 0 0 0 0 0 0 0 0 0
Run B2
0
0 0.4 0.8
1.2
_____ v
v1max
Velocity Distribution in the Jump (PHJ)
(h)