CIVIL WORKS GUIDELINES FOR MICRO-HYDROPOWER IN NEPAL
47
in the example. Then head loss in 1m length of canal for each
case should be calculated. The corresponding energy loss (or
power loss in most cases of micro-hydro) due to the head loss
over a year should be calculated. Then, the cost corresponding
to the energy loss should be calculated and the sum of energy
or power loss cost discounted over the plant’s economic life
(generally 15 years) for a discount rate (generally 10 %) is
determined. Note that the discount rate is the opportunity
cost of investment in the prevailing market and should be
greater than or at least equal to the prevailing lending rates
for infrastructure projects by the commercial banks of the
country. The longitudinal canal slope corresponding to the
minimum of sum of canal cost and energy loss cost as shown
in Figure 4.6 will be the optimum canal slope which
determines the canal size (depth and width).
Figure 4.6 Canal optimization
Canal optimization example
Design flow which was fixed earlier based on hydrology and
electricity demand , Q= 300 l/s =0.3 m3/s
Decide canal shape and lining method (according to site
condition): Rectangular, stone masonry (1:4) with base slab
and side walls, t=300 mm=0.3 m thick and free board,
F= 300 mm=0.3 m
Manning’s constant from table 4.1, n= 0.02
Assume an appropriate longitudinal slope of canal, S=1/500
(1 in 500) in this case
Select a width to depth ratio, B/D=r=2, (generally 2 is
optimum if site condition allows and should be lowered if
width is a constraint)
D
=
⎡
⎢
⎣⎢
Q
×n×
5
r3
(r +
1
×S
2)
2
2
3
3
⎤8
⎥
⎥⎦
=
⎡
⎢
0.3
×
0.02
×
(2
+
2)
2
3
⎣⎢
51
2 3 × (1/ 500) 2
3
⎤8
⎥
⎦⎥
=0.43m
Note that the above equation is derived from Manning’s
equation. Sizing and quantity calculations can be done
similar to this procedure for unlined or trapezoidal canal using
Manning’s equation.
Considering length of canal, L=1 m
Base slab:
B=r*D=2*0.43=0.86 m
Width, W=B+2*t=0.86+2*0.3=1.46 m
Quantity, Vb=W*t*L=1.46*0.3*1=0.44 m3
Walls:
Wall height, H=D+F=0.43+0.3=0.73 m
Quantity, Vw=2*t*H*L=2*0.3*0.73*1=0.44 m3
Total quantity, Vt=Vb+Vw=0.44+0.44=0.88 m3
Stone masonry rate, say Rm=4000 Rs/m3
Cost of canal, Cc=Vt*Rm=0.88*4000=Rs 3200
Head loss, HL=L*S=1*1/500=0.002 m
Overall efficiency, e=0.5, generally for micro-hydro
Power loss based on the power equation discussed in Chapter
1, PL=QgHLe=0.5*9.81*0.3*0.002=0.00294 kW=2.94 W
Power tariff, Rp =Rs 1.0 per kW/month (say)=NRs 12 per kW/
year
Energy/Power loss cost per annum, C=PL*Rp=2.94*12=Rs
35.28
If the tariff is based on energy i.e., Per kilo Watt Per hour
basis, then energy loss (EL, kWh) all around the year should
be calculated considering the plant factor (P) (generally 0.2 to
0.5 for micro hydro). Then energy loss should be multiplied
by energy rate (Re, Rs/kWh) to determine cost of loss over a
year (C).Thus, EL=8760*P*PLC=EL*Re
Assuming the following parameters for the financial analysis:
Plant’s economic life N=15 years
Discount rate, i=10%
Discount factor of annuity
DFA
=
(1 + i)N − i
i × (1 + i)N
=
(1 + 10%)15 −10%
10% × (1 + 10%)15
=9.76
Therefore power loss cost, Ce=C*DFA=35.28*9.76= Rs.
344.33
Now, total cost, Ct=Cc+Ce=3200+344.33=Rs. 3544.33
Similarly costs for various canal slopes should be calculated
and plotted to find the minimum total cost (as shown in
Figure 4.6). The corresponding canal longitudinal slope for
the minimum total cost will be the optimum slope.
4.3.2 MANNING’S EQUATION
The design of a headrace canal is based on Manning's equation.
Manning's equations for flow and velocity are as follows:
Q
=
AR2/3
n
S
V=
R2/3 S
n
where:
Q is the flow in the canal in m3/s
V is velocity in the canal in m/s