The drip irrigation efficiency ($E_d$) is the product of application efficiency ($E_a$) and system efficiency ($E_s$).

Drip Irrigation Parameters

• Application Efficiency ($E_a$): $0.9$
• Minimum Flow Rate ($q_{min}$): $45 \ L\cdot h^{-1}$
• Maximum Flow Rate ($q_{max}$): $65 \ L\cdot h^{-1}$
• Average Flow Rate ($q_{avg}$): $50 \ L\cdot h^{-1}$
• Manufacturer's Coefficient of Variation ($CV_m$): $0.07$

Calculate Observed Flow Variation ($CV_{obs}$)

The observed coefficient of variation ($CV_{obs}$) reflects the flow rate variability in the field:

$CV_{obs} = \frac{q_{max} - q_{min}}{2 \times q_{avg}}$

$CV_{obs} = \frac{65 \ L\cdot h^{-1} - 45 \ L\cdot h^{-1}}{2 \times 50 \ L\cdot h^{-1}} = \frac{20}{100} = 0.2$

Calculate Total Coefficient of Variation ($CV_{total}$)

The total variation combines manufacturer and observed variations:

$CV_{total} = \sqrt{CV_{obs}^2 + CV_m^2}$

$CV_{total} = \sqrt{(0.2)^2 + (0.07)^2} = \sqrt{0.04 + 0.0049} = \sqrt{0.0449} \approx 0.2119$

Calculate System Efficiency ($E_s$)

System efficiency is derived from the total variation:

$E_s = \frac{100}{1 + CV_{total}}$

$E_s = \frac{100}{1 + 0.2119} \approx \frac{100}{1.2119} \approx 82.51\%$

Calculate Drip Irrigation Efficiency ($E_d$)

The final drip irrigation efficiency is calculated as:

$E_d = E_a \times E_s$

$E_d = 0.9 \times 0.8251 \approx 0.7426$

The drip irrigation efficiency is approximately $74.26\%$.