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

RESULTS AND ANALYSIS


Measurement of Discharge

When the sprinkler system operated, discharges were measured for the pressures of 0.5, 0.6, 0.65, 0.75, 0.90 and 0.92 kg/cm² for the time duration of 1 minute per sprinkler.

The pressures were measured by the pressure gauge, for the time durations of 10 min, 20 min, 30 min, 1 hr, 1hr 30 min and 2 hr. The pressures were different in the Plot – X (Set – 1) and Plot – Y (Set – 2) as presented in Table 2.

Table 2 Pressure Variation for Different Time Durations in Plot – X and Plot – Y

Time Duration for System Operation	Pressure, kg/cm^2
	Plot - X	Plot – Y
10 minute	0.75	0.50
20 minute	0.65	0.60
30 minute	0.90	0.90
1 hour	0.90	0.90
1 hour 30 minute	0.92	0.92
2 hour	0.90	0.90

For the six different pressures, discharges were measured for 1 minute per sprinkler which relieved from the sprinkler head’s spray nozzle and impact nozzle shown in Table 3.

Table 3 Measured Discharges for the Six Different Pressures at a Sprinkler for 1 Minute

Pressure,_kg/_cm_2'>Pressure, kg/ cm^2	Pressure head, m	Discharge, ml/min
		Impact Nozzle	Spray Nozzle	Total
0.50	5.0	8920	3120	12040
0.60	6.0	10250	3550	13800
0.65	6.5	10900	3780	14680
0.75	7.5	12200	4290	16490
0.90	9.0	15600	5440	21040
0.92	9.2	15950	5560	21510

Now the total discharges (irrigation water applied) in Plot – X and Plot – Y was calculated by multiplying the sprinkler number to 1 minute discharge and time duration of sprinkler system operated.

Total discharge in one plot = No. of sprinklers x measured discharge for 1 minute x time duration of sprinkler system operated

= 4 no. (Same number in both plot) x measured one minute discharge x time duration of sprinkler system operated

Table 4 Total Irrigation Water Applied and Discharge in Plot – X and Plot - Y for Different Time Durations

Pressure, Kg/cm^2	Plot – X	0.75	0.65	0.90	0.90	0.92	0.90
	Plot – Y	0.50	0.60	0.90	0.90	0.92	0.90
Pressure head, m	Plot - X	7.5	6.5	9.0	9.0	9.2	9.0
	Plot - Y	5.0	6.0	9.0	9.0	9.2	9.0
Discharge at 1 sprinkler, lpm	Plot – X	16.490	14.680	21.040	21.040	21.510	21.040
	Plot – Y	12.040	13.800	21.040	21.040	21.510	21.040
Number of sprinkler	Plot – X	4	4	4	4	4	4
	Plot – Y	4	4	4	4	4	4
Time duration for system operation	Plot – X	10 min	20 min	30 min	1 hr	1 hr 30 min	2 hr
	Plot – Y	10 min	20 min	30 min	1 hr	1 hr 30 min	2 hr
Total Volume of water applied, l	Plot - X	659.60	1174.40	2524.80	5049.60	7743.60	10099.20
	Plot - Y	481.60	1104.00	2524.80	5049.60	7743.60	10099.20
Total discharge, lph	Plot - X	3957.6	3523.2	5049.6	5049.6	5162.4	5049.6
	Plot - Y	2889.6	3312	5049.6	5049.6	5162.4	5049.6

In this the discharge rate increased with the pressure increased from 0.50 to 0.92 kg/cm². At maximum pressure of 0.92 kg/cm² the discharge obtained is 5162.4 lph and at minimum pressure of 0.50 kg/cm² the discharge obtained is 2889.6 lph.

Relationship between Pressure Head and Discharge

The relationship between pressure head and discharge was found by plotting the pressure head Vs discharge graph shown in Figure 2 for Plot – X and Figure 3 for Plot – Y.

Table 5 Pressure Head and Discharge in Plot – X for Different Time Durations

Duration	10 min	20 min	30 min	1 hr	1 hr 30 min	2 hr
Pressure Head, m	7.5	6.5	9	9	9.2	9
Total Discharge, lph	3957.6	3523.2	5049.6	5049.6	5162.4	5049.6

Figure 2 Pressure Head and Discharge Relationship in Plot – X for Different Time Durations

The relationship is given by,

Q α H_f^m
Q = K∙H_f^m
Where, K = 900 and Slope, m = (log 10590) – (log 900) = 1.071
Q = 900∙H_f^1.071
Q α H_f^1.071

Hence, discharge is proportional to 1.071 power of the head loss.

Table 6 Pressure Head and Discharge in Plot – Y for Different Time Durations

Duration	10 min	20 min	30 min	1 hr	1 hr 30 min	2 hr
Pressure Head, m	5	6	9	9	9.2	9
Total Discharge, lph	2889.6	3312	5049.6	5049.6	5162.4	5049.6

Figure 3 Pressure Head and Discharge Relationship in Plot – Y for Different Time Durations
Where, k = 600 and Slope, m = (log 10400) – (log 600) = 1.24
Q = 600∙H_f^1.24
Q α H_f^1.24
Hence, discharge is proportional to 1.24 power of the head loss.


Conclusions

The relationship between pressure and discharge is determined, which comes out to be non-linear. Minimum and maximum discharges are 2890 lph and 5162 lph observed at pressures 0.50 and 0.92 kg/cm² respectively. The relationship between pressure head and discharge is given as,

For plot – X, Q α H_f^1.071
For plot – Y, Q α H_f^1.24
Thus the pressure discharge relationship varies for the same set of sprinkler irrigation system. It can be concluded that discharge is directly proportional to head loss raised to power m. The power m varies from 1.07 to 1.24 for a given set of 12m x 12m grid of sprinkler irrigation system.


References

Bharti, J. P., Pandey, V. K. and Bagde, H. D., (2008), “Moisture Distribution Pattern Under Pressurized Irrigation Systems In Sandy Clay Loam Soil”, Journal of Indian Water Resources Society, Vol. 28, No. 1.

Phathare, J. S. (1993), “Studies on Moisture Distribution in Trickle Irrigation”, M. Tech. Thesis Submitted to MPAU, Rahuri, (M. S.)