Question

Increasing this To this Increases the capacity

pipe diameter diameter by a factor of
(inches) (inches)
4 6 2.25
4 8 4.00
6 8 1.78
6 10 2.78
6 12 4.00
8 10 1.56
8 12 2.25
8 15 3.52
10 12 1.44
10 15 2.25
12 15 1.56

You need to replace a 4 inch sewer pipe with a 6 inch sewer pipe. If velocity is the same in both pipes the new pipe will be able to carry 2.25 times as much material."
a. True
b. False
c. Cannot determine with the info given.

Answer 1

The statement is true; increasing the diameter of a pipe from 4 to 6 inches increases capacity by 2.25 times if the velocity remains the same.

Step-by-step explanation:

The question relates to the fluid dynamics principle that the carrying capacity of a pipe is related to its cross-sectional area. According to the data provided in the question, increasing the diameter of a pipe from 4 inches to 6 inches increases the capacity by a factor of 2.25. Given that the velocity remains constant, the capacity of the pipe is proportional to its cross-sectional area, which is dependent on the square of the diameter. Since the area increases by a factor larger than the increase in diameter, the new 6-inch pipe will indeed be able to carry 2.25 times as much material as the 4-inch pipe, if the velocity remains unchanged.