River A & B flow into river C. River A is 40 ft wide and is flowing at an average of 2.47 mph. River B is 25 ft wide and has a flow rate of 1125 cubic feet per second. Assume all rivers have a uniform depth of 15 ft. If river C is 100 ft wide, what is its average velocity [kilometers per second]?

To find the average velocity of river C, we need to calculate the total volume of water flowing into it from rivers A and B, and then divide it by the cross-sectional area of river C.

1. Calculate the total flow rate of water from river A:
- Width of river A = 40 ft
- Average velocity of river A = 2.47 mph

To find the flow rate, we need to multiply the cross-sectional area by the velocity:
Flow rate of river A = width * depth * velocity
= 40 ft * 15 ft * 2.47 mph

2. Calculate the total flow rate of water from river B:
- Width of river B = 25 ft
- Flow rate of river B = 1125 cubic ft/s

The flow rate of river B is already given, so we don't need to perform any calculations.

3. Calculate the total flow rate of water into river C:
Total Flow rate into river C = Flow rate of river A + Flow rate of river B

4. Calculate the cross-sectional area of river C:
- Width of river C = 100 ft
- Depth of river C = 15 ft

Cross-sectional area of river C = width * depth
= 100 ft * 15 ft

5. Calculate the average velocity of river C:
Average velocity of river C = Total Flow rate into river C / Cross-sectional area of river C

Given that 1 mile is equal to 1.60934 kilometers and 1 hour is equal to 3600 seconds, you can convert the average velocity from mph to km/s.

Please provide the values for the depth and width of river C to proceed with the calculations.

To calculate the average velocity of river C in kilometers per second, we first need to find the volume of water flowing in river A and river B per unit of time.

1. Finding the volume of water flowing in river A:
Since river A is 40 ft wide, has a depth of 15 ft, and is flowing at an average velocity of 2.47 mph, we can calculate its flow rate in cubic feet per second as follows:

Flow rate (cubic feet per second) = width (ft) * depth (ft) * velocity (ft/sec)
= 40 ft * 15 ft * (2.47 mi/hr * 1 hr/3600 sec) * (5280 ft/mi)
= 40 ft * 15 ft * (2.47/3600) * 5280 ft
≈ 401.44 cubic feet per second

2. Finding the volume of water flowing in river B:
River B has a flow rate of 1125 cubic feet per second, so we don't need to make any further calculations.

3. Finding the total volume of water flowing in river C:
River C is formed by the confluence of river A and river B. Therefore, the total volume of water flowing in river C would be the sum of the volumes of river A and river B:

Total volume of water in river C (cubic feet per second) = volume of river A (cubic feet per second) + volume of river B (cubic feet per second)
= 401.44 cubic feet per second + 1125 cubic feet per second
= 1526.44 cubic feet per second

4. Converting the volume flow rate from cubic feet per second to cubic meters per second:
Since we want to express the average velocity of river C in kilometers per second, we need to convert the flow rate from cubic feet per second to cubic meters per second.

1 cubic meter = 35.3147 cubic feet

Flow rate (cubic meters per second) = Flow rate (cubic feet per second) / 35.3147

Flow rate (cubic meters per second) = 1526.44 cubic feet per second / 35.3147
≈ 43.24 cubic meters per second

5. Calculating the average velocity of river C:
Finally, we can calculate the average velocity of river C using the flow rate and width of river C:

Average velocity of river C (kilometers per second) = Flow rate (cubic meters per second) / (width (ft) * 0.3048 m/ft)

Average velocity of river C (kilometers per second) = 43.24 cubic meters per second / (100 ft * 0.3048 m/ft)
= 43.24 / 30.48
≈ 1.419 kilometers per second

Therefore, the average velocity of river C is approximately 1.419 kilometers per second.