Final answer:
The lake level of Lake Mead will rise approximately 0.510 feet, or about 6.12 inches, per 24-hour day during flood conditions when the net inflow rate is accounted for.
Step-by-step explanation:
To determine how many feet per 24-hour day Lake Mead's level will rise, we must calculate the difference between the inflow and the outflow of water and then convert this volume to a change in lake height, considering the lake's surface area.
Firstly, we find the net flow rate into Lake Mead by subtracting the outflow from the dam from the inflow rate of the Colorado River:
- Inflow: 45,000 cfs (cubic feet per second)
- Outflow: 8,000 cfs
- Net inflow: 45,000 cfs - 8,000 cfs = 37,000 cfs
Next, we convert the net inflow rate into cubic feet per day:
- 37,000 cfs * 86,400 seconds/day = 3,196,800,000 cubic feet/day
Since the surface area of Lake Mead is given as approximately 225 square miles, we convert this to square feet for consistency in units:
- 225 square miles * 27,878,400 square feet/square mile = 6,272,640,000 square feet
Finally, we calculate the rise in water level by dividing the total volume of water added to the lake in one day by the lake's surface area:
- Rise in lake level per day = 3,196,800,000 cubic feet/day ÷ 6,272,640,000 square feet = 0.510 feet/day
Therefore, the lake level will rise approximately 0.510 feet, or about 6.12 inches, per 24-hour day during flood conditions.