   # Consider the piping system shown in the accompanying figure. The speed of water flowing through the 4 in. diameter section of the piping system is 3 ft/s. What is the volume flow rate of water in the piping system? Express the volume flow rate in ft 3 s , gpm, and L/s. For the case of steady flow of water through the piping system, what is the speed of water in the 3 in. diameter section of the system? ### Engineering Fundamentals: An Intro...

5th Edition
Saeed Moaveni
Publisher: Cengage Learning
ISBN: 9781305084766

#### Solutions

Chapter
Section ### Engineering Fundamentals: An Intro...

5th Edition
Saeed Moaveni
Publisher: Cengage Learning
ISBN: 9781305084766
Chapter 8, Problem 26P
Textbook Problem
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## Consider the piping system shown in the accompanying figure. The speed of water flowing through the 4 in. diameter section of the piping system is 3 ft/s. What is the volume flow rate of water in the piping system? Express the volume flow rate in ft 3 s , gpm, and L/s. For the case of steady flow of water through the piping system, what is the speed of water in the 3 in. diameter section of the system? To determine

Find the volume flow rate of water and the speed of water in the 3 in. diameter section of the system.

### Explanation of Solution

Given data:

Refer to the Figure  problem 8.26 in the textbook for the piping system.

The speed of water in 4 in. diameter section is 3fts.

Formula used:

Write the expression for the volume flow rate.

Q=VaverageAc (1)

Here,

Ac is cross-sectional area, and

Vaverage is average velocity.

Write the expression for the average velocity.

Vaverage=π4d2 (2)

Here,

d is diameter, which is given as 4 in.

Calculation:

Substitute equation (2) in (1),

Q=(π4d2)Vaverage (3)

Substitute 3fts for Vaverage and 4 in. for d,

Q=π4(4in)2(3fts)=π4(4×0.0833ft)2(3fts)[1in=0.0833ft]

Q=0.262ft3s (4)

Convert the unit of Q in equation (4) from ft3s to gpm.

Q=0.262ft3s(7.48gal1ft3)(60s1min)    [1min=60s,and1ft3=7.48gal]118gpm

Convert the unit of Q in equation (4) from ft3s to Ls

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