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Flowrate is 6 ft3/s through an 18-inch pipeline flowing full. Find the velocity?

a. 3.39 fps
b. 10.59 fps
c. 2.69 fps
d. 1.98 fps

1 Answer

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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.

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