Discharge and pressure head relationship for a given set of sprinkler irrigation system



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HYDRO Himanshu

Table 1 Experimental Plot Detail and Specifications

Particulars

Dimensions/Numbers/Location

Area of Field (meter x meter)

50 x 25

Size of Plots (m x m)

25 x 25

No. of Plots

2 i.e. Plot – X and Plot – Y

No. of laterals in each plot

4 with 6 m length & 63 mm diameter

No. of manifold in each plot

1 with 18 m length & 63 mm diameter

No. of main

1 with 12 m length & 63 mm diameter

Sprinkler grid size (m x m)

12 x 12

No. of sprinkler in each plot

4

Sprinkler nozzle size (mm x mm)

5.1 x 3.1

Source of water

At middle top of the field

Capacity of the pump

1500 lit/min

Grid size for sample collection (m x m)

4 x 4

Grid size for evaluation (m x m)

2 x 2




Figure 1 Design Layout for the Sprinkler Irrigation System


Measurement of Discharge

Sprinklers are subjected to six different pressures (0.50, 0.60, 0.65, 0.75, 0.90 and 0.92 kg/cm2) using 63 mm HDPE diameter lateral. The water supplied for the experiment is a closed loop and regulated from the pump. A 63 mm diameter HDPE pipe is placed over stake assembly and sprinklers to confine the discharge into the plastic container directly. Irrigation water is supplied from a tube well. The water collected in the containers is measured with the help of measuring cylinder.




Development of a Relationship between Pressure Head and Discharge

According to Darcy – Weisbach equation


Hf = f∙L∙Q2 / 12.103∙D5
For fully developed turbulent flow, f is independent on Re. So for a given pipe,
Hf = K1∙Q2
Where K1 = f∙L / 12.103∙D5 = constant for given pipe in turbulent flow
Hf α Q2
But in laminar flow, f depends solely on Re.
f = 64 / Re
= 64∙μ / V∙D
= 64∙μ / (Q∙D / (π∙D2/4))
= 81.5286∙μ∙D / Q
Put the value of f in Darcy – Weisbach equation
Hence,
Hf = (81.5286∙μ∙D / Q) (L∙Q2 / 12.103∙D5)
= 6.7362 μ∙L∙Q / D4
So for a given pipe,
Hf = K2∙Q
Where K2 = 6.7362 μ∙L / D4= constant for given pipe in laminar flow
Hf α Q
For laminar flow
Hf α Q OR Q α Hf
For turbulent flow
Hf α Q2 OR Q α Hf1/2
But in actual practice we seldom have such exact flow conditions. So we can say
Q α Hfm (Where m = Power of pressure head loss)
In which m varies between 1 and 0.5 or even out of range.



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