What is the equivalent number of 1-¼" copper pipes to equal the cross-sectional area of one 4-inch copper pipe?

To determine the equivalent number of 1-¼" copper pipes that match the cross-sectional area of one 4-inch copper pipe, we first need to calculate the cross-sectional areas based on the diameters of the pipes.

The formula for the cross-sectional area (A) of a pipe is given by:

[ A = \pi \left(\frac{d}{2}\right)^2 ]

Where ( d ) is the diameter of the pipe.

Calculate the cross-sectional area of the 4-inch copper pipe:

1. Convert 4 inches to feet to maintain consistency in measurement, if necessary, though we'll keep it in inches for simplicity.

2. The radius would be ( \frac{4}{2} = 2 ) inches.

3. Thus, the area of the 4-inch pipe becomes:

[ A_{4in} = \pi (2)^2 = \pi (4) \approx 12.57 \text{ square inches} ]

Next, calculate the cross-sectional area of a 1-¼" copper pipe:

1. The radius for a 1-¼" pipe is ( \frac{1.25}{2} = 0.625 ) inches.

2