Inland Aquaculture Engineering (1984) 
DESIGN AND CONSTRUCTION OF FRESHWATER FISH FARMS 
Chapter 8. Hydraulic Formulas Used in Designing Fish Farms 
3. DESIGN FORMULAS FOR HYDRAULIC STRUCTURES 
3.7 Design Formulas for Siphons 


Diameter (mm) 
Length (m) 
Discharge (m^{3}/sec) 
a) Small, mobile 
25  120 
< 5 
0.00025  0.015 
b) Medium, movable 
120  200 
< 10 
0.015  0.050 
c) Large, stabile 
200  1 200 
< 100 
0.050  3.10 
Table 14 Recommended Minimum Velocities in Pipes for Siphons
Pipe diameter (mm) 
Velocity (m/sec) 
120 
1.0 
200 
1.5 
250 
1.55 
300 
1.6 
400 
1.7 
450 
1.8 
500 
1.9 
600 
2.2 
800 
2.4 
1 000 
2.6 
1 200 
2.6 
Calculating formulas
_{} 
(3.33) 
where
C = discharge coefficient
A = crosssectional area of the pipe, m^{2}
H = head, m
The discharge coefficient C can be calculated by the formula
_{} 
(3.34) 
where
l = friction factor = 0.02 (steel pipe)
1 = length of the siphon, m
d = diameter of the siphon, m
Sk = all local loss coefficients along the siphon
Table 19 lists local loss coefficients for a variety of the fixtures.
The allowable pressure head for siphon
_{} 
(3.35) 
where
_{}
Altitude in m 
0 
500 
1 000 
1 500 
2 000 
3 000 
_{} 
10.3 
9.8 
9.2 
8.6 
8.1 
7.2 
_{}
Water temperature °C 
10 
20 
30 
_{} 
0.123 
0.24 
0.43 
The allowable suction head of the siphon is:
_{} 
(3.36) 
where
v = velocity in the pipe, m/sec
_{}
The maximum allowable downstream head of the siphon is:
_{} 
(3.37) 
where
_{}
Depth of water above the entrance of the siphon
(a) Entrance with vertical axis
v  
D 
h  
(m/sec) 

(m) 
(m)  
1.5 
0.1 
 0.3 
2 D, but min. 
0.3 
1.5  2.5 
0.3 
 0.8 
1 D 
0.7 
> 2.5 
> 
1.0 
1.7 D 
2.0 
(b) Entrance with horizontal axis
_{} 
(3.38) 
where
k_{e} = entrance loss coefficient
(c) Entrance with inclined axis
_{} 
(3.39) 
where a = angle of the tilt in degree
Example 7
Design the siphon shown in Figure 17 for a discharge of 350 l/sec if water temperature is 30°C.
Solution
3 Considering the designed discharge Q = 0.35 m^{3}/sec the siphon is a large one. The velocity is calculated by the following formula assuming that its diameter is 400 mm.
_{}
As this velocity is higher than the recommended minimum one in Table 14 hence, the selected diameter is satisfactory.
The next step is to determine the water depth above the entrance of the siphon by using Equation (3.38)
_{}
v = 2.79 m 
k_{e} = 0.1 
then
_{}
The discharge coefficient of the siphon is defined from Equation (3.34)
_{}
l = 0.02
l = l_{1} + l_{2} + l_{3} + l_{4} + l_{5} + l_{6} = 1.80 + 14.0 + 8.70 + 13.0 + 5.0 + 1.50 = 44 m
d = 0.40 m
Computation of the local loss coefficient using Table 19
Diffusor inlet 
0.1 
Fraction bends (30°) 
4×0.09 = 0.36 
Fraction bends (90°) 
0.34 
Valve 
0.07 
Outlet diffusor 
0.5 

Sk = 1.37 
Substitution of the above values into the equation gives:
_{}
The allowable suction head of the siphon is obtained if we use Equation (3.35)
_{}
where
_{}
_{}
then
_{}
The suction head of the siphon is defined from Equation (3.36)
_{}
where
_{}
_{}
H_{s} = 7.35  1.03 = 6.32 m
H_{effs} = 550  545  5.0 m
The allowable downstream head of the siphon is determined from Equation (3.37)
_{}
where
_{}
_{}
H_{T} = 7.35 + 0.88 = 8.23 m
H_{effT} = 550  543 = 7.00 m
The design of the siphon is satisfactory because both H_{effs} and H_{effT} are below their allowable values.
The discharge of the siphon is defined by the formula (3.33)
_{}
where
C = 0.47
A = 0.126 m^{2}
H = 545  543 = 2.0 m
then
_{}
This is acceptable, since the designed Q = 0.35 m^{3}/sec.