Geoscience Reference
In-Depth Information
a straight line was selected as the
x
value representing the behavior of the
lake. A line of best fit was inserted into the graph identified above using
and the equation of the trend line obtain from the computer.
The inverse of the slope of the line of best fit computed as (1
/m
)was
obtained as the
K
value. The Muskingum routing relationship was then
used to compute the values of the routed outflow
O
2
;
O
2
=
C
0
I
2
+
C
1
I
1
+
C
2
O
1
.
(5)
The
K
value obtained as the inverse of the slope “
m
”andthe
x
values
obtained were used to calculate the values of the Muskingham coecients
C
0
,
C
1
,and
C
2
,
:
C
0
=
−
Kx
+0
.
5∆
t
Kx
+0
.
5∆
t
,
K
−
Kx
+0
.
5∆
t
C
1
=
Kx
+0
.
5∆
t
,
(6)
K
−
K
−
Kx
−
0
.
5∆
t
C
2
=
Kx
+0
.
5∆
t
,
K
−
K
and ∆
t
have the units of time. The theoretical value of
K
is the time
required for an elemental (kinematic) wave to traverse the reach. It is
approximately the time interval between the inflow and outflow peaks.
Graphs of inflow, outflow, and routed outflow against time interval (months)
were plotted for all the years of interest.
2.3.2.
Reservoir routing
In reservoir routing, the Puls method was applied. The routing interval ∆
t
was taken as 5 h (18,000 s). The outlet at Albert Nile was assumed to take
on the behavior of a broad crested weir of which the outflow
Q
is given by
the relationship:
Q
=1
.
7
BH
1
.
5
,
(7)
where
B
is the breadth of the weir and was measured as 4 km, which is the
approximate width of Albert Nile at the outlet of Lake Albert.
H
is the
arbitrary elevation of the surface of the water above the crest of the weir.
The volume,
V
, of water flowing out was computed as the product of the
surface area of the lake obtained as approximately 5,335 km
2
and the eleva-
tion of the surface of the water above the crest of the weir,
H
(m). Arbitrary
values of
H
were used ranging from 0.0 to 1.5 m increasing in intervals of
0.05 m. For all the years of interest, the flow was routed through Lake Albert
