QuestionAugust 25, 2025

1.30 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?

1.30 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?
1.30 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?

Solution
4.0(274 votes)

Answer

Approximately 431.97 gallons must be flushed through the system. Explanation 1. Calculate the Volume of Water in the Pipe The volume V of a cylinder is given by **V = \pi r^2 h**, where r is the radius and h is the height (or length). Convert 2 inches to feet for diameter, so r = \frac{1}{6} ft. Convert \frac{1}{4} mile to feet: h = \frac{1}{4} \times 5280 = 1320 ft. Thus, V = \pi \left(\frac{1}{6}\right)^2 \times 1320. 2. Calculate the Volume of Water to be Flushed Since the system needs to be flushed with twice the volume contained, multiply the calculated volume by 2. 3. Convert Cubic Feet to Gallons Use the conversion factor: **1 cubic foot = 7.48052 gallons**. Multiply the total volume in cubic feet by this factor to convert to gallons.

Explanation

1. Calculate the Volume of Water in the Pipe<br /> The volume $V$ of a cylinder is given by **$V = \pi r^2 h$**, where $r$ is the radius and $h$ is the height (or length). Convert 2 inches to feet for diameter, so $r = \frac{1}{6}$ ft. Convert $\frac{1}{4}$ mile to feet: $h = \frac{1}{4} \times 5280 = 1320$ ft. Thus, $V = \pi \left(\frac{1}{6}\right)^2 \times 1320$.<br /><br />2. Calculate the Volume of Water to be Flushed<br /> Since the system needs to be flushed with twice the volume contained, multiply the calculated volume by 2.<br /><br />3. Convert Cubic Feet to Gallons<br /> Use the conversion factor: **1 cubic foot = 7.48052 gallons**. Multiply the total volume in cubic feet by this factor to convert to gallons.
Click to rate:

Similar Questions