A water system of 2 in.(inside diameter) pipe, having a length of 1/4 mile, is to be flushed with a volume of water equal to twice that contained in the system. how much water (gallons) must be flushed through the system? (note: one cubic foot=7.481gal.)
if the pipe is full, it contains
pi * 2^2 * 1/4 * 5280 * 12 = 199051 in^3 = 115.19 ft^3
So, we want twice that, or
230.38 * 7.481 = 723.5 gal
rats. divide that by 4, since I was using radius=2, not diameter
To determine the amount of water that needs to be flushed through the system, we can follow these steps:
Step 1: Find the volume of water contained in the system
The volume of a cylindrical pipe can be calculated using the formula:
V = π * r^2 * h
where:
V = volume
π = 3.14159
r = radius (half of the inside diameter)
h = length of the pipe
Given that the inside diameter is 2 inches, the radius (r) is equal to 1 inch or 1/12 feet. The length of the pipe is 1/4 mile, which is equal to 1320/4 feet.
V = 3.14159 * (1/12)^2 * (1320/4)
Step 2: Calculate the volume of water to be flushed
The volume to be flushed is twice the volume contained in the system:
Flushed Volume = 2 * V
Step 3: Convert the flushed volume to gallons
Since one cubic foot is equal to 7.481 gallons:
Flushed Volume (in gallons) = Flush Volume (in cubic feet) * 7.481
Let's calculate the flushed volume:
V = 3.14159 * (1/12)^2 * (1320/4)
Flushed Volume = 2 * V
Flushed Volume (in gallons) = Flush Volume (in cubic feet) * 7.481
Now we can compute the results.
To solve this problem, we'll first need to calculate the volume of water contained in the system using the given information. Then, we'll find out the volume of water required for flushing, which is twice the volume of water contained in the system. Finally, we'll convert the volume from cubic feet to gallons using the conversion factor provided.
1. Calculate the volume of water in the system:
- Diameter of the pipe = 2 inches
- Radius of the pipe = diameter divided by 2 = 2 inches / 2 = 1 inch = 1/12 feet
- Length of the pipe = 1/4 mile = 1/4 * 5280 feet = 1320 feet
The volume of the pipe can be calculated using the formula for the volume of a cylinder: V = πr^2h
where V is the volume, r is the radius, and h is the height.
V = π * (1/12 ft)^2 * 1320 ft
V ≈ 172.78 cubic feet
2. Calculate the volume of water required for flushing:
The volume of water required for flushing is twice the volume of water contained in the system, so:
Volume of flushing water = 2 * 172.78 cubic feet
Volume of flushing water ≈ 345.56 cubic feet
3. Convert the volume from cubic feet to gallons:
We know that 1 cubic foot is equal to 7.481 gallons.
Volume of flushing water in gallons = Volume of flushing water in cubic feet * 7.481
Volume of flushing water in gallons ≈ 345.56 cubic feet * 7.481
Volume of flushing water ≈ 2584.27 gallons (rounded to two decimal places)
Therefore, approximately 2584.27 gallons of water must be flushed through the system.