Accepted Papers - 3.pdf - UNESCO

the model may be represented as :
Maximize
Subject to
where
⎛ D + H ⎞
Vsc
= ⎜ ⎟[ CX
⎝ 3 ⎠
D 2
Vdug
= [ CX
3
To obtain the necessary conditions for
maxima / minima, the augmented Lagrange function
is derived as :
where ë is Lagrange multiplier differentiating
equation (13) with respect to H and λ, and applying
the necessary conditions for optimization the
following equation in terms of H is obtained as:
where,
P = 24Z + 2CXZ + 2XZ + 8DZ
Q = 4CX + 4X + 16DZ + 16
2
(C + 2) + 2Z(D + H) (2CX + X + 2Z(D + H))]
(C + 2) + 2DZ(2CX + X + 2DZ)]
3 2
AH + PH + QH + R = 0
25
A =
3
2
Z
2
...(9)
...( 10)
...( 11)
...(12)
...(3)
…(
4)
...(5)
….(6)
…(7)
1 2 2 2 2 4 2 2 2 4 3 2
R = - ( C DX + CDX + CD XZ + D XZ + D Z )
3
3 3 3 3
...(13)
X= bottom width (m), Y= bottom length (m), D=
excavated depth (m), H= height of embankment (m),
Z=side slopes (H : V), T = top width of the
embankment (m), V = storage capacity (m SC 3 ), Vdug = dug volume (m3 ), V = volume of embankment
emb
( m3 ), A = wetted surface area, m w 2 and A = s
exposed surface area (m2 ).
The value of the top width of the
embankment (T) is taken as 2 m for all sides of the
embankment. The bed length is transformed into
ratio (C) to facilitate the computation i.e. C = Y/X
where Y and X are bed length and bed width,
respectively.
General design procedure : The general steps
followed in the design of water harvesting
structures are :
a). Hydrologic design, b). Hydraulic design, and
c). Structural design.
Hydrologic design : It involves the estimation of
peak rate of runoff required to be passed safely
through a given structure and runoff volume or water
yield required to be stored in a pond. The choice of
design frequency depends upon the type of structure,
whether temporary, semi-permanent or permanent.
Intensity- duration- frequency relationship is
necessary to calculate risk and design a structure
that will accommodate the largest rain storm
expected during a particular length of time. Rational
method is generally used for the estimation of peak
rate of discharge.
2
2 1 3 2
VL(H.
...( Zemb8 = ) V2[{T
λsc)
+ = ZH} VH]
sc [{X(C - λ (V + 1) + dug 4Z(D−
+ VH)}]
emb + [4T ) H + 4TH Z + H Z ]
3
VHydraulic = Vemb
Design : Hydraulic design includes the
determination of a). storage capacity and storage
dimensions of water harvesting structure; and b).
fixing of spillway dimensions for safe disposal of
design peak flow (water should flow through the
structure safely without overtopping the bank and
when it leaves the structure its energy should be
dissipated).
342
dug …
The selection of site should begin with
preliminary studies of possible sites. The site should
have enough catchments of provide runoff sufficient
to fill the pond. The low point of a natural depression
is considered a good location. From economic point
of view, a pond should be located where a largest
volume can be obtained with least earthwork.
Location should also have a favorable outlet
condition for excess runoff disposal from the pond.
The sub-soil should allow minimum seepage as far
as possible. In case the seepage rate at the site are
excessive, good fill material or lining material
should be available in the vicinity. The design of
dugout pond for supplemental irrigation envisages
...(3)
( 4)
…