Considering friction, how many 6 inch water lines would be required to carry the same amount of water as one 12 inch water line?

To determine how many 6-inch water lines would be required to carry the same amount of water as one 12-inch water line, we first need to consider the relationship between the diameter of the pipe and the flow capacity, which is influenced by the cross-sectional area.

The cross-sectional area of a circular pipe is calculated using the formula ( A = \pi (d/2)^2 ), where ( d ) is the diameter of the pipe.

1. Calculate the area of the 12-inch line:

[

A_{12} = \pi \left( \frac{12}{2} \right)^2 = \pi (6)^2 = 36\pi , \text{square inches}

]

2. Calculate the area of a 6-inch line:

[

A_{6} = \pi \left( \frac{6}{2} \right)^2 = \pi (3)^2 = 9\pi , \text{square inches}

]

3. To find out how many 6-inch lines are needed to match the area of one 12-inch line, you set up the equation:

[

n \cd