Question

A reservoir is contemplated on a stream that has an average annual runoff of 350×106 m3. Measurements indicate that the average sediment inflow is 200,000 metric tons per year. Assume that a cubic meter of settled sediment will dry out to a weight of 9,600 N/m3. If the reservoir's initlal capacity is 42×106 m3, determine the life of the reservoir if its life ends when it is 80% full of sediment and plot the reservoir capacity as a function of time. Use the median curve in Figure 7.12 of the handout and capacity intervals of 8.4×106 m3. Note that 1 metric ton equals 1,000 kg.

Answer 1

To determine the life of the reservoir until it reaches 80% full of sediment, we need to calculate the sediment deposition rate and the time it takes to reach the desired sediment capacity.

Given:
- Average annual runoff: 350 × 10^6 m^3
- Average sediment inflow: 200,000 metric tons per year
- Weight of settled sediment: 9,600 N/m^3
- Initial capacity of the reservoir: 42 × 10^6 m^3
- Reservoir capacity intervals: 8.4 × 10^6 m^3

First, we need to convert the sediment inflow from metric tons to cubic meters per year. Since 1 metric ton equals 1,000 kg and the weight of settled sediment is 9,600 N/m^3, we can calculate the sediment deposition rate (SDR) in cubic meters per year:

SDR = (Sediment inflow in metric tons * 1,000 kg/ton) / (Weight of settled sediment in N/m^3)

Next, we can calculate the sediment capacity required to reach 80% of the reservoir's capacity:

Sediment capacity = Initial capacity of the reservoir * 0.8

Now, we can calculate the life of the reservoir using the sediment deposition rate and the sediment capacity:

Life of the reservoir = (Sediment capacity - Initial capacity of the reservoir) / SDR

To plot the reservoir capacity as a function of time, we can use the median curve from Figure 7.12 and the capacity intervals. By incrementing the time in regular intervals and calculating the corresponding sediment capacity, we can create a time vs. capacity plot until the reservoir reaches its life expectancy.

Please note that without specific values for the capacity intervals and the data from Figure 7.12, it is not possible to provide a detailed plot or numerical results.