Question

Water flows at a speed of 15 m/s through a pipe that has a radius of 0.40 m. The water then flows through a smaller pipe at

a speed of 45 m/s. What is the radius of the smaller pipe?

Answer 1

Explanation: The volume flow rate of the water remains constant as it flows from the larger pipe to the smaller pipe. Therefore, we can use the equation:

A1v1 = A2v2

where A1 and v1 are the cross-sectional area and velocity of the larger pipe, and A2 and v2 are the corresponding values for the smaller pipe.

The cross-sectional area of a pipe is given by the formula:

A = πr^2

where r is the radius of the pipe.

Substituting the given values, we get:

π(0.4)^2(15) = π(r^2)(45)

Simplifying and solving for r, we get:

r = 0.13 m

Therefore, the radius of the smaller pipe is 0.13 m.