Final answer:
To find the velocity of water in an 18-inch pipeline, we calculate the cross-sectional area of the pipe and use the flowrate to find that the velocity is approximately 3.39 feet per second (fps).
Step-by-step explanation:
The question involves calculating the velocity of water flowing through a pipeline. To find the velocity, we must use the formula for flowrate (Q), which relates to velocity (v) and the cross-sectional area of the pipe (A):
Q = A * v
First, we find the area of the pipeline.
The diameter of the pipe is 18 inches; we need to convert this into feet to be consistent with the flowrate units:
18 inches = 1.5 feet (since 1 foot = 12 inches)
The radius (r) is half the diameter, so r = 1.5 feet / 2 = 0.75 feet.
The area (A) of the pipe's cross-section is π * r2:
A = π * (0.75 feet)2
Now we can solve for the velocity (v):
6 ft3/s = π * (0.75 feet)2 * v
We rearrange to solve for v:
v = 6 ft3/s / (π * (0.75 feet)2)
After calculating, we find that v ≈ 3.39 fps.
Therefore, the correct answer is (a) 3.39 fps.