Geoscience Reference
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The resultant change of momentum in time unit between cross sections 1-1 and
2-2 is equal to the sum of external forces and is described by the equation:
d M
d t ¼
P 1
P 2 þ
W sin Y
F s
(5)
d Q /d x and transformations, the following
equation is derived (Khatsuria 2005 ;¸ ent
After substitution of A
¼
Q / v and q
¼
urk 1994 ):
gA 2
d y
d x ¼
S o
S f
2
a
Qq
=
(6)
1
a
Q 2
=
gA 2 D
where
a
is the correction coefficient of kinetic energy (Saint Venant),
a ¼
1.10; q is
the rise of flow per length of flume, d Q /d x ; D is the hydraulic depth, D
¼
A / B ; and
B is the width of flume, B
15 m.
The above differential equation can be solved in two ways: either by applying
numerical methods available for equations of this type or by applying simplified
methods, which in general consist in introduction of finite differences in place of
differentials. For example, the equation determining a change of water levels Dy for
the length Dx is (Khatsuria 2005 ; Novak et al. 2007 ;¸ ent
¼
urk 1994 ):
¼ a
Q 1 ð
v 1 þ
v 2 Þ
v 2 ð
Q 2
Q 1 Þ
Dy
ð
v 2
v 1 Þþ
þ
S o Dx
S f Dx
(7)
g
ð
Q 1 þ
Q 2 Þ
Q 1
The analytical calculations applying the above formula confirmed a possibility
of improving the capacity ability of spillway to about 400 m 3 s 1 , but only for a
situation when it works as not-submerged. In the existing solutions, during water
inflow into a flume, a quick overfilling of flume and changes of weir work condi-
tions from not-submerged to submerged are observed. Hence, the results of calcula-
tions of capacity ability showed that for damming water in a reservoir of 312.00 m asl,
the maximum attainable capacity ability is equal only to 250 m 3 s 1 , that is, about
130 m 3 s 1 less than it results from the discharge curve that is currently valid for the
weir. The corrected discharge curve of the Złotniki reservoir's spillway, for its
present solutions, is shown in Fig. 2 .
4 Concept of Outlet Installation Reconstruction
In the concept of reconstructing the Złotniki reservoir's outlet installations, a safety
of reservoir was taken into account due to computational discharge values and
capacity ability of existing outlet installations (Machajski and Olearczyk 2009 ).
The consequences of computational discharges passage through the reservoir were
determined, analyzing possibilities of their reduction to safe discharges both for
downstream area and for reservoir (Jain 2001 ).
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