Question

quiz # 3
november 5, 2025 10 minutes name: ...

1. consider the piping system shown below. the average speed of water flowing through the 14 - inch - diameter section of the piping system is 6 ft/s. what is the volume flow rate of water in the piping system? express the volume flow rate in ft³/s
2. compute the future value of a $25,000 deposit made today, after twelve years, in a account that pays an interest rate of 5% that compounds annually. how much int will be paid to this account?

Explanation:

Step1: Convert diameter to radius in feet

The diameter \(d = 14\) inches. Since \(1\) foot \(= 12\) inches, \(d=\frac{14}{12}\text{ft}\), and the radius \(r=\frac{d}{2}=\frac{14}{2\times12}=\frac{7}{12}\text{ft}\)

Step2: Calculate the cross - sectional area

The formula for the area of a circle is \(A=\pi r^{2}\). Substituting \(r = \frac{7}{12}\text{ft}\), we get \(A=\pi\times(\frac{7}{12})^{2}=\frac{49\pi}{144}\text{ft}^{2}\)

Step3: Use the volume flow rate formula

The volume flow rate formula is \(Q = A\times v\), where \(v = 6\text{ft/s}\). Substituting \(A=\frac{49\pi}{144}\text{ft}^{2}\) and \(v = 6\text{ft/s}\)

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Answer:

The volume flow rate of water in the piping system is approximately \(6.41\text{ft}^{3}/\text{s}\)