Geoscience Reference
In-Depth Information
formula for free spillway, with straight insert on crest (Rogala et al.
1991
; Vischer
and Hager
1998
):
2
p
H
3
=
2
o
Q
¼ e
2
=
3
m
B
(1)
where
e
is the coefficient of side contraction weir,
e ¼
1.0;
m
is the discharge
coefficient,
m ¼
0.654;
B
is the spillway crest length,
B
¼
45.0 m;
H
o
is the energy
height calculated with relation to spillway crest.
For calculations, two characteristic damming levels in reservoir were taken.
They result from water level with regard to weir crest (309.30 m asl) and dam
crest, determining water layer thickness and the resultant energy of stream. The
calculation results are as follows:
55m
3
s
1
312
:
12 dam crest from downstream
ð
Þ
309
:
30
¼
2
:
82 m
!
Q
¼
411
:
58 m
3
s
1
312
:
00 dam crest from upstream
ð
Þ
309
:
30
¼
2
:
70 m
!
Q
¼
385
:
In the further analysis for flume parameters determination, the discharge equal to
385.58 m
3
s
1
was assumed.
In the calculations for the determination of flume parameters, an impact of
external forces, in compliance with Newton's second dynamic principle, should
be considered in two cross sections, 1-1 and 2-2, at distance d
x
, including gravity
force, material roughness of bed cross section, and resultant force of hydrostatic
pressures in the two cross sections mentioned above.
A gravity force is represented by horizontal component of water weight
W
between two cross sections, 1-1 and 2-2, given in the form:
W
sin
Y ¼ g
S
o
A
d
x
(2)
where
S
o
is the longitudinal slope of bottom line of flume,
A
is the wetted area
between cross sections 1-1 and 2-2,
is the weight density of water, and
Y
is the
inclination angle of bottom line of flume.
The force that results from an impact of roughness of the flume material is as
follows:
g
F
s
¼ g
AS
f
d
x
(3)
where
S
f
is the slope of energy line.
The force that results from differences of hydrostatic pressures in cross sec-
tions 1-1 and 2-2 can be written in the form:
P
1
P
2
¼g
A
d
y
(4)
where
P
1
is the force of hydrostatic pressure in cross section 1-1,
P
2
is the force of
hydrostatic pressure in cross section 2-2, and d
y
is the depth difference in cross
sections 1-1 and 2-2.
