220 Chapter 8 Time and Time-Related Parameters
In fact, some flow-measuring devices make use of Equa-
tion (8.12) to determine the volume flow rate of
a fluid by first measuring the fluid’s average velocity and
the cross-sectional area of the flow. Finally, note that in
Chapter 9 we will explain another closely defined variable, mass flow rate of a flowing
material, which provides a measure of time rate of mass flow through pipes or other carrying con-
duits.Example 8.4 Consider the piping system shown in Figure 8.10. The average speed of water flowing through
the 12-inch-diameter section of the piping system in 5 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 average speed of water in the
6-inch-diameter section of the system?We can determine the volume flow rate of water through the piping system using
Equation (8.12).For the steady flow of water through the piping system the volume flow rate is constant. This
fact allows us to calculate the speed of water in the 6-inch section of the pipe.From the results of this example you can see that when you reduce the pipe diameter by a fac-
tor of 2, the water speed in the reduced section of the pipe increases by a factor of 4.average speed20 ft/s
3.926 ft
3
/s 1 average speed2ap
4
b10.5 ft 2
2Q3.926 ft
3
/s 1 average velocity 21 cross-sectional area of flow 2Q 1 3.926 ft
3
/s2a28.3168 L
1 ft
3 b111.2 L/sQ 1 3.926 ft
3
/s2a7.48 gal
1 ft
3 ba60 s
1 min
b1762 gpm
Q volume flow rate 1 5 ft/s2a
p
4
b11 ft 2
2
3.926 ft
3
/svolume flow rate 1 average velocity 21 cross-sectional area of flow 2
12 in. 5 ft/s 6 in.
■Figure 8.10 The piping system of Example 8.4.
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀