Calculate the average discharge of the Mississippi River at New Orleans (in cubic feet per second) given the following parameters: (show your work)
Average velocity: 25 miles per hour Average width: 2,000 feet Average depth: 90 feet
Discharge = velocity (/) x river width (ft) x river depth (ft)
*Remember, you will need to convert miles-per-hour to feet-per-second to obtain the proper units for discharge (ft3/) There are 5,280 feet in a mile
The Correct Answer and Explanation is :
To calculate the average discharge of the Mississippi River at New Orleans, we can use the formula:
[
\text{Discharge} = \text{velocity} \times \text{width} \times \text{depth}
]
However, the velocity is given in miles per hour, but we need it in feet per second to match the units of width and depth. Let’s walk through the steps.
Step 1: Convert velocity from miles per hour to feet per second
We know the following:
- 1 mile = 5,280 feet
- 1 hour = 3,600 seconds
The average velocity of the river is 25 miles per hour. To convert it to feet per second:
[
\text{Velocity (ft/s)} = 25 \, \text{miles per hour} \times \frac{5,280 \, \text{feet}}{1 \, \text{mile}} \times \frac{1 \, \text{hour}}{3,600 \, \text{seconds}}
]
[
\text{Velocity (ft/s)} = 25 \times \frac{5,280}{3,600} = 25 \times 1.4667 = 36.667 \, \text{ft/s}
]
Step 2: Calculate discharge
We now have the following values:
- Velocity = 36.667 feet per second
- Width = 2,000 feet
- Depth = 90 feet
Substitute these values into the discharge formula:
[
\text{Discharge} = 36.667 \, \text{ft/s} \times 2,000 \, \text{ft} \times 90 \, \text{ft}
]
[
\text{Discharge} = 36.667 \times 180,000 = 6,600,060 \, \text{ft}^3/\text{s}
]
Final Answer:
The average discharge of the Mississippi River at New Orleans is approximately 6.6 million cubic feet per second.
Explanation:
Discharge represents the volume of water flowing through a river at any given time, and it is calculated as the product of the river’s velocity, width, and depth. In this case, the velocity was first converted from miles per hour to feet per second to ensure consistency with the width and depth measurements, both of which are in feet. The resulting discharge provides a measure of how much water flows through the river at New Orleans every second, which is essential for understanding the river’s role in transportation, ecology, and hydrology.