Question

Experts estimate that when levees break in the aftermath of a​ hurricane, water can flow into a city at a peak rate of 10 billion gallons per day. There are 7.5 gallons in 1 cubic foot. Use this information to complete parts​ (a) and​ (b) below.


a. Find the flow rate in units of cubic feet per second, compare this flow rate to a river with an average flow rate of 30,000cfs.

b. The water level rose approximately_____ ft.

Answer 1

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Experts estimate that when levees break in the aftermath of a hurricane, water can flow into a city at a peak rate of 10 billion gallons per day. There are 7.5 gallons in 1 cubic foot. Use this information to complete parts (a) and (b) below. Click the loon to view the USCS measurements a. Find the flow rate in units of cubic feet per second (cs). Compare this flow rate to a river with an average flow rate of 35,000 cfs. The flow rate is cfs, which is approximately % of the flow rate of the river (Round to the nearest whole number as needed.) b. Assume that the flooded part of the city had an area of 8 square miles Estimate how much in foot) the water level rose in one day at the given flow rate. The water level rose approximately (Round to the nearest tenth as needed.)

Solution:

Water can flow into a city at a peak rate of 10 billion gallons per day. If there are 7.5 gallons in 1 cubic foot, then we would convert 10 billion gallons to cubic foot. It becomes

7.5 gallons = 1 cubic foot

10^9 gallons = x cubic foot

Cross multiplying, it becomes

7.5x = 10^9

x = 10^9/7.5

x = 1333333333.3 cubic feet per day

a) we would convert 1333333333.3 cubic feet per day to cubic feet per second. Since

24 hours = 1 day

60 minutes = 1 hour

60 seconds = 1 minute

Then, the number of seconds in a day is

24 × 60 × 60 = 86400 seconds

Converting 1333333333.3 cubic feet per day to cubic feet per second, it becomes

1333333333.3/86400 = 15432.1 cubic feet per second

comparing this flow rate to a river with an average flow rate of 35,000cfs, it is lower.

15432.1/35000 × 100 = 44.1%

b) 1 mile = 5280 feet

1 square mile = 27878400 square feet

8 square miles = 8 × 27878400 = 223027200 square feet

The height

The number of foot by which the water level rose in one day is

1333333333.3/223027200 = 6 feet per day

Answer 2

Following are the solution to the given points:

For point a:

Water enters a metropolis at a peak pace of 8 billion gallons per day.

$\to 7.5 \ gallons = 1 \ foot^3 \\\\ \to 1 \ gallon = \frac{1}{7.5} \ foot^3$

by which we get

$\to 8 \text{billion gallons} = (\frac{8}{7.5}) \ \text{billion cubic foot}$ now to convert this rate into per second we will convert it

$\to (\frac{8}{(7.5 \times 24123456 \times 60 \times 60)})$ billion cubic foot per second Now we know billion means $10^{9}$ so putting it above and simplifying we get

$\to rate = 12345.67\ CFS$

Now we how to find how much is this percentage of $30000\ \ CFS$

Calculating the percentage value:

$\to (\frac{12345.67}{30000}) \times 100 \\\\ \to (\frac{12345.67}{300})\\\\ \to (\frac{1234567}{30000})\\\\ \to (\frac{411522.333}{10000})\\\\ \to 41.1522333\\\\ \to 41.15\%$

For point b:

$\to 1 \ mile = 5280\ ft\\\\ \to 1 \ \text{square mile} = 27878400\ ft^2\\\\ \to 8\ \text{square miles} = 8 \times 27878400 = 223027200\ ft^2$

Calculating the height with the number of feet by which the water level rose in one day is:

$\to \frac{1333333333.3}{223027200} \\\\ \to 6 \ \frac{feet}{day}$

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