3.6 Evaluation of the Functioning of the Network
One of the five irrigation networks was considered in this
study for analysis. Analysis of the network was done by dividing the network
into various branches and taking into consideration the number of hydrants
which are opened upstream during irrigation. Hydraulic calculations were done
based on the formulas proposed by Zoungrana (2002) while heads losses were
calculated using the Hazem-William equation. Microsoft Excel software was used
for the hydraulic analysis.
3.6.1 Calculation of flow rates
If (en m3/h) is the nominal flow rate of one big gun,
n the number of opened big guns upstream and (m3/h) the flow rate
from the extremity of the downstream branch,
the flow rate entering the upstream branch, (m3/h) is
given by the formula:
(3.1)
The flow rate leaving the downstream branch is calculated by
respecting the loop rule of networks which is derived from the principle of
conservation of matter as:
? Flow entering = flow leaving (3.2)
Given that the network functions both in the transport and
distribution of water, the hydrants have almost equal flow rates. The flow rate
which results in the same head loss
4 ? Q
? otherwise known as the fictitious or simulated flow
rate,
? ?
? 10 ? 3600
D ? (m3/h), was calculated by the
formula presented by Zoungrana (2002):
(3.3)
3.6.2 Calculation of flow velocity and head losses.
Given that the flow rate in the conduits follows steady state
conditions for the same pipe diameters (i.e. the velocity in the fluid is the
same in both magnitude and direction at a given instant and in at every point
in the fluid), the flow velocity was calculated by applying the formula:
(3.4)
Where:
= Flow velocity (m/s)
= Flow rate considered (m3/h)
= internal diameter of the conduit (mm)
Also the velocity of flow in water supply conduits is always less
than or equal to 1.5m/s so knowing the diameter of the conduits, the velocity
of flow could be generated.
, but
Head losses were being calculated using the Hazem-William
equation
(3.5)
Where,
Linear head losses (m)
L= length of given branch (m)
Q= fictitious flow rate (lps)
C=150 for plastic pipes and 120 for steel pipes D= internal
diameter of pipe (mm)
Singular head losses due to T`s, bends, valves and elbows which
are difficult to calculate are estimated to be 10%
(3.6)
Total Head Losses, J, in a given branch is the sum of the linear
and singular head
losses
(3.7)
The ratio of this head loss on the length of a given branch gives
us the unit head losses given by:
(3.8)
Where,
j = unit head loss (m/m)
L = length of branch (m)
J = head loss in a given branch (m)
3.6.3 Determination of available and required
pressures
At the level of each hydrant, the available pressures and the
required pressures were calculated as follows:
(3.9)
Where,
available pressure upstream (m)
available pressure downstream (m)
upstream piezometric elevation (m)
downstream piezometric elevation (m) = head loss in a given
branch (m)
The required pressure downstream equals zero, if the number of
big guns at the
??
downstream hydrant equals zero or equal to the required pressure
upstream if the number of big guns at the downstream hydrant is different from
zero.
The pressures available upstream used in our calculations are
those of the technical slip of the principal conduits of PHP, version 2 of
16/02/01.
These calculations were done taking into consideration the
canon or the plot with the worst case (i.e. the furthest big gun on relatively
flat ground or the most elevated or both). The other systems such as the
microjet and undertree systems were been converted into the equivalent number
of big guns. This is because this system sets the ground base for the
conversion to other systems.
For undertree irrigation systems, the pressure required at the
entry of a lateral is given by the formula proposed by Azenkot (1999),
considering that the terrain is relatively flat.
hu = hs + 3/4F + r (3.10)
Where,
hu = pressure required at the entry of the
lateral (m) hs = nominal pressure of sprinkler (m)
F = correction factor
= linear head loss in the lateral (m)
r = height above the ground of the sprinkler
(m)
The pressure required at the center of the primary conduit is
calculated in the same way as that of the laterals and is given by:
hr = hu +3/4(Fr ) (3.11)
Where,
hr = required pressure at the centre of the lateral (m) Fr =
correction coefficient of the lateral
= head losses in the lateral (m)
? P avn ? Z av
The pressure available at the entry of the secondary conduit or
hydrant is given by equation 3.2:
= hr + + Zp - z (3.12)
Where,
= pressure required at the hydrant (m)
= head losses in the secondary conduit (m)
Zp = geometric elevation of the hydrant
z = geometric elevation of the plot with the worst case (m)
For irrigation plots totally covered by big guns, the required
pressure is calculated as above, the only exception being that the correction
factor is considered to be unity (1).
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