Reservoir sedimentation arithmetic: A reservoir accumulates on average 0.15 million m³ of sediment per year. Dead storage = 8 million m³, total capacity = 36 million m³. Which statement is correct regarding siltation timeline and onset of useful-capacity loss?

Introduction / Context:
Long-term reservoir performance depends on sediment inflow. Designers distinguish between dead storage (for sediment deposition) and useful or live storage (for supply and power). Simple arithmetic checks help screen timelines before detailed sediment routing is performed.

Given Data / Assumptions:

• Average sediment deposition rate = 0.15 million m³/year.
• Dead storage = 8 million m³; Total capacity = 36 million m³.
• Assume uniform annual deposition and full trapping.

Concept / Approach:

Two timelines matter: time to fill dead storage and time to fill total capacity. Useful (live) storage begins to decline once dead storage is consumed. Theoretical “complete siltation” is total capacity divided by the annual deposition rate.

Step-by-Step Solution:

Verification / Alternative check:

Even if annual silt volume changes seasonally, the arithmetic average still centers near these values, unless trap efficiency or density changes are accounted for in a more advanced model.

Why Other Options Are Wrong:

• (b) overestimates the onset of live storage loss.
• (c) cannot be true since (b) is wrong.
• (d) is false because (a) is correct.
• (e) is false; live storage is preserved until dead storage fills.

Common Pitfalls:

• Confusing dead storage fill time with total siltation time.
• Ignoring that trap efficiency may reduce actual deposition in some cases.

Final Answer:

The reservoir will theoretically be completely silted in 240 years.