• Field water application efficiency (\( \eta_f \)) is expressed mathematically as: \[ \eta_f = \frac{\text{Net irrigation depth}}{\text{Gross irrigation depth}} \times 100 \]
• The parameters given are: Net irrigation depth = 8 cm, and field application efficiency = 75% (or 0.75).
• Calculating gross amount:
  \[ \text{Gross irrigation depth} = \frac{8}{0.75} = \frac{800}{75} = 10.667\text{ cm} \]
• Therefore, the gross depth of water to apply is 10.66 cm (Option 1).

Analysis of irrigation terms:

• Duty: Defined as the area of land (in hectares) irrigated per unit discharge of water (1 cumec flowing continuously during base period). It represents the ratio of irrigated area to volume/rate of water supplied (\(D = \text{Area} / \text{Discharge}\)).
• Delta: The total depth of water (in cm or meters) required by a crop during its entire life cycle in the field.
• Base period: The total duration (in days) between the first watering at sowing and the final watering before harvest.
• Irrigation quotient: Not a standard technical parameter in irrigation engineering.

Analysis of slope in border irrigation:

• 0.05 - 0.20%: In border strip irrigation, slopes must ensure uniform water advance without causing soil erosion or ponding; 0.05% to 0.20% is the safe recommended longitudinal slope range for medium soils.
• 0.20 - 0.40%: Excessive for erodible loam soils.
• 0.40 - 0.60%: Causes rapid flow and rill erosion in borders.
• 0.60 - 0.80%: Unsafe slope exceeding hydraulic design standards for surface irrigation.