Flow in the drip irrigation lines is hydraulically steady, spatially varied pipe flow with lateral out flows. The total discharge in the drip irrigation lines ( lateral, sub-main or main) decreases with respect to the length of line. The lateral and sub-main can be considered as having the same hydraulic characteristics and area designed to maintain the smallest pressure, the required pressure and the slope of the energy gradient line, which will give the total energy higher than that required at any sub-main for irrigation.
A drip irrigation system is made by a combination of different size of plastic pipes which are usually considered as smooth pipe. One empirically equation frequently used is the Hazen and Williams formula. Also, because of the possibility of laminar, turbulent or fully turbulent flow in trickle the Darcy Weisbach equation can be used to compute the head loss due to pipe friction.
Darcy Weisbach equation
Hf= 2fl v2
______
g.d
In which,
Hf= head loss in pipe, m
f= coefficient of friction for pipe
l= length of pipe, m
v= velocity of water in pipe, m/sec
g= acceleration due to gravity m/sec2
d= diameter of pipe, m
The Darcy- Weisbach friction factor, f for small diameter trickle irrigation tubing is related to the Reynolds number, (N.R). The Reynolds number, NR is computed with following equation.
NR= S D.V/ K.M
Where,
NR= Reynolds number
S= density of water, gm/cm3
D= diameter of pipe, cm,
V= Average velocity, cm/s
u = viscosity of fluid, n s/m2
K= unit constant (K =10 for S in gm/cm3, d in cm, v in cm/s)
The equation used to computer f depends on the magnitude of NR.
When Reynolds number is less than 2000 then flow is laminar, when NR is between 2000 to 10,000 flow is turbulent and when NR is greater than 10,000 flow is fully turbulent.
In general, the friction drop equation for pipe flow can be shown in simplified form as,
∆H= a. Qm. ∆L
Where,
∆H = is the total energy drop of pipe section, m
a = is constant for given pipe size
Q = is total discharge rate, lps
∆L= is length of pipe, m
m = 1 for laminar flow
m = 1.75 for turbulent flow in smooth pipe
m = 1.852 for turbulent flow using the Hazen and William formula
m= 2 for a fully turbulent flow
Where friction coefficient is constant,
Among all the equations, the Hazen and Williams formula is commonly and most frequently used.
The Hazen and William equation for smooth pipe is,
∆H= 1.526X 104 X (Q/C) 1.852 X D-4.871 X L
Where,
∆H= head loss in pipe, m
Q= total discharge in pipe, cum/hr
C= is Hazen and William constant (for smooth pipe C=150
D= is the diameter of pipe, cm
L= is the length of pipe, m
Since, the discharge in the cub –main and lateral, decreases with respect to length , the total energy drop will be less than, the one given by equation. Therefore, for lateral and sub-main head loss is calculated by introducing a F-values i.e called as outlet factor ( F).
∆H= 1.526 X 104 X (Q/C) 1.852 X D-4.871 X (L + le) X F
Where,
le = is the equivalent length of pipe or lateral , m
F= is outlet factor, and is depends on No of outlets.
Table: Values of Outlet Factor ( F) for Lateral or Pipe:
No of Outlet | F-Value | No of Outlet | F-Value |
1 | 1.00 | 12-15 | 0.40 |
2 | 0.65 | 16-20 | 0.39 |
3 | 0.55 | 21-30 | 0.38 |
4 | 0.50 | 31-36 | 0.37 |
5 | 0.47 | 37-40 | 0.36 |
6 | 0.45 | More than 40 | 0.35 |
7 | 0.44 |
|
|
8-9 | 0.42 |
|
|
10-11 | 0.41 |
|
|
Hydraulically, the pressure variation along a sub-main will cause a lateral flow variation along a Submain and pressure variation along a lateral will cause an emitter flow variation along the lateral through each emitter.
The pressure variation and emitter flow variation are related and can be expressed as ,
Q var= 1-(1-H var) 0.5
Where,
The emitter flow variation, q var is defined as;
Q var= q max -1 min / q max
In which,
q max= is the maximum emitter flow along the line, and
q min= is the minimum flow along the line, and
q var= should be less than 10% ( desirable)
The pressure variation, Hvar is defined as
H var = h max – h min / h max
In which,
h max and h min = are the maximum and minimum pressure variation respectively along the line and H var should be less than 20 percent.
In drip irrigation systems design, the design criterion is generally based on an emitter flow variation of less than 20 percent and pressure variation less than 10 percent i.e. acceptable limits.
