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

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

H_f = f∙L∙Q² / 12.103∙D⁵
For fully developed turbulent flow, f is independent on Re. So for a given pipe,
H_f = K₁∙Q²
Where K₁ = f∙L / 12.103∙D⁵ = constant for given pipe in turbulent flow
H_f 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,
H_f = (81.5286∙μ∙D / Q) (L∙Q² / 12.103∙D⁵)
= 6.7362 μ∙L∙Q / D⁴
So for a given pipe,
H_f = K₂∙Q
Where K₂ = 6.7362 μ∙L / D⁴= constant for given pipe in laminar flow
H_f α Q
For laminar flow
H_f α Q OR Q α H_f
For turbulent flow
H_f α Q² OR Q α H_f^1/2
But in actual practice we seldom have such exact flow conditions. So we can say
Q α H_f^m (Where m = Power of pressure head loss)
In which m varies between 1 and 0.5 or even out of range.