Depth at canal outlet considering efficiencies: Irrigation efficiency is 80%, conveyance losses are 20%, and the actual depth needed on the field is 16 cm. What depth of water must be supplied at the canal outlet?

Introduction / Context:
Designing irrigation supplies requires accounting for losses and application efficiency. The canal outlet must deliver more water than the crop actually stores in the root zone due to conveyance and application losses along the path from outlet to field and within the field itself.

Given Data / Assumptions:

• Field requirement (actual stored depth) = 16 cm.
• Field (application) efficiency η_field = 80% = 0.8.
• Conveyance losses = 20% ⇒ conveyance efficiency η_conv = 0.8.

Concept / Approach:
The delivered depth at the canal outlet must cover both the field application inefficiency and conveyance losses. Therefore, the depth at outlet equals the required stored depth divided by the product of efficiencies.

Step-by-Step Solution:
1) Water at field inlet needed = actual depth / η_field = 16 / 0.8 = 20 cm.2) Water at canal outlet = field inlet depth / η_conv = 20 / 0.8 = 25 cm.3) Therefore, required depth at outlet = 25 cm.

Verification / Alternative check:
Combine efficiencies directly: Overall efficiency η_total = η_field * η_conv = 0.8 * 0.8 = 0.64. Outlet depth = 16 / 0.64 = 25 cm, which confirms the stepwise calculation.

Why Other Options Are Wrong:

• 10 cm and 15 cm: too small; they ignore one or both loss components.
• 20 cm: accounts only for field efficiency, not conveyance.
• 30 cm: exceeds the necessary depth for the stated efficiencies.

Common Pitfalls:

• Multiplying instead of dividing by efficiencies.
• Using percentages as whole numbers (e.g., 80 instead of 0.8).

Final Answer:
25 cm.