CHAPTER 8
385
When the pipes are connected in series, the flow rate through
the entire system remains constant regardless of the diameters
of the individual pipes. For a pipe that branches out into two
(or more) parallel pipes and then rejoins at a junction down-
stream, the total flow rate is the sum of the flow rates in the
individual pipes but the head loss in each branch is the same.
When a piping system involves a pump and/or turbine, the
steady-flow energy equation is expressed as
When the useful pump head h
pump, u
is known, the mechanical
power that needs to be supplied by the pump to the fluid and
the electric power consumed by the motor of the pump for a
specified flow rate are determined from
W
#
pump, shaft
r
V
#
gh
pump, u
h
pump
and W
#
elect
r
V
#
gh
pump, u
h
pump–motor
P
2
rg
a
2
V
2
2
2g
z
2
h
turbine, e
h
L
P
1
rg
a
1
V
2
1
2g
z
1
h
pump, u
where h
pump–motor
is the efficiency of the pump–motor combi-
nation, which is the product of the pump and the motor effi-
ciencies.
The plot of the head loss versus the flow rate
V
.
is called
the system curve. The head produced by a pump is not a con-
stant, and the curves of h
pump, u
and h
pump
versus
V
.
are called
the characteristic curves. A pump installed in a piping sys-
tem operates at the operating point, which is the point of
intersection of the system curve and the characteristic curve.
Flow measurement techniques and devices can be consid-
ered in three major categories: (1) volume (or mass) flow rate
measurement techniques and devices such as obstruction
flowmeters, turbine meters, positive displacement flowme-
ters, rotameters, and ultrasonic meters; (2) point velocity
measurement techniques such as the Pitot-static probes, hot-
wires, and LDV; and (3) whole-field velocity measurement
techniques such as PIV.
The emphasis in this chapter has been on flow through
pipes. A detailed treatment of numerous types of pumps and
turbines, including their operation principles and performance
parameters, is given in Chap. 14.
REFERENCES AND SUGGESTED READING
1. H. S. Bean (ed.). Fluid Meters: Their Theory and
Applications, 6th ed. New York: American Society of
Mechanical Engineers, 1971.
2. M. S. Bhatti and R. K. Shah. “Turbulent and Transition
Flow Convective Heat Transfer in Ducts.” In Handbook of
Single-Phase Convective Heat Transfer, ed. S. Kakaç, R.
K. Shah, and W. Aung. New York: Wiley Interscience,
1987.
3. C. F. Colebrook. “Turbulent Flow in Pipes, with Particular
Reference to the Transition between the Smooth and
Rough Pipe Laws,” Journal of the Institute of Civil
Engineers London. 11 (1939), pp. 133–156.
4. C. T. Crowe, J. A. Roberson, and D. F. Elger. Engineering
Fluid Mechanics, 7th ed. New York: Wiley, 2001.
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Practice of Laser-Doppler Anemometry, 2nd ed. New
York: Academic, 1981.
6. R. W. Fox and A. T. McDonald. Introduction to Fluid
Mechanics, 5th ed. New York: Wiley, 1999.
7. Fundamentals of Orifice Meter Measurement. Houston,
TX: Daniel Measurement and Control, 1997.
8. S. E. Haaland. “Simple and Explicit Formulas for the
Friction Factor in Turbulent Pipe Flow,” Journal of Fluids
Engineering, March 1983, pp. 89–90.
9. I. E. Idelchik. Handbook of Hydraulic Resistance, 3rd ed.
Boca Raton, FL: CRC Press, 1993.
10. W. M. Kays and M. E. Crawford. Convective Heat and
Mass Transfer, 3rd ed. New York: McGraw-Hill, 1993.
11. R. W. Miller. Flow Measurement Engineering Handbook,
3rd ed. New York: McGraw-Hill, 1997.
12. L. F. Moody. “Friction Factors for Pipe Flows,”
Transactions of the ASME 66 (1944), pp. 671–684.
13. B. R. Munson, D. F. Young, and T. Okiishi. Fundamentals
of Fluid Mechanics, 4th ed. New York: Wiley, 2002.
14. O. Reynolds. “On the Experimental Investigation of the
Circumstances Which Determine Whether the Motion of
Water Shall Be Direct or Sinuous, and the Law of
Resistance in Parallel Channels.” Philosophical
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pp. 935–982.
15. H. Schlichting. Boundary Layer Theory, 7th ed. New
York: McGraw-Hill, 1979.
16. R. K. Shah and M. S. Bhatti. “Laminar Convective Heat
Transfer in Ducts.” In Handbook of Single-Phase
Convective Heat Transfer, ed. S. Kakaç, R. K. Shah, and
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17. P. L. Skousen. Valve Handbook. New York: McGraw-Hill,
1998.
18. P. K. Swamee and A. K. Jain. “Explicit Equations for
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