Page 860 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Appendix D: Fluid Mechanics—Reviews of Selected Topics 815

in which Bernoulli: The Bernoulli equation accounts for the various
V is the volume of flow that has passed the propeller forms of energy in fluid flow; Daniel Bernoulli,
3
3
(m ) or (ft ) 1700–1782 is credited with formulating the Ber-
3
3
Q is the flow in pipe (m =s) or (ft =s) noulli theorem, but the fact is that he did not quite
t is the time for flow of volume, V (s) achieve this as we know it today, according to Rouse
v(pipe) is the velocity of water flowing within pipe
(m=s) or (ft=s) and Ince (1957, pp. 91–100).
2
2
A(pipe) is the cross-sectional area of pipe (m ) or (ft ) Cycle: A process in which the initial and final states are
k(meter) is the coefficient of proportionality between identical (Shapiro, 1958, p. 24).
velocity in pipe and rotational speed of propeller Darcy–Weisbach: (1) Refers to equation for headloss in pipe
2
(m=s=rev) or (ft=s=rev) flow, i.e., h L ¼ f(L=D)(v =2g). (2) Julius Weisbach
k(meter) is the coefficient of proportionality to calibrate (1806–1871) was a professor of mathematics at the
3
flow meter (m =rev) Freiberg School of Mines; his main interests were in
N is the number of revolutions of propeller associated hydraulics and geodesy. He published in 1877 a com-
with volume V (rev) prehensive treatise on hydraulics that Rouse and Ince
(1957) credit as modernizing the topic and as being
From Equation D.83, the number of revolutions is con- the model for twentieth century texts on fluid mech-
verted to the flow volume reading on the register. Cali- anics. He was the first to write the foregoing headloss
bration of each flow meter must be done before
installation to determine k . The flow reading is by a equation and to understand the friction factor. (The
0
digital register located at the top of the meter. Inside the foregoing from Rouse and Ince, 1957). The connec-
meter, a coupling connects the propeller to the internal tion between Darcy and Weisbach was not indicated.
mechanism and may be direct drive or magnetic drive, as (3) See also Brown (2000) for comprehensive history
described by Huth. The magnetic drive eliminates the of the Darcy-Weisbach equation.
need for packing seals and thus water is not likely to Entropy: Defined mathematically as DS ¼ (q=T) rev ; concep-
enter the register. tually entropy increase is associated with increased
The bearings of the propeller meter may be water lubri- ‘‘disorder.’’
cated ceramic sleeve bearings or stainless steel ball bear- Extensive property: Quantity depends upon mass, e.g.,
ings. The ceramic sleeve type requires less maintenance V, E, H, G, etc.
and has longer life than the stainless steel bearings (Huth,
Friction factor: The Darcy–Weisbach friction factor, f. The
1990). Also, according to Huth (1990), the meters can be
Moody diagram is the source for f data currently.
equipped to measure flow as well as volume. Clogging
Gas constant: The universal gas constant is the constant in
due to debris is a possible problem and so installing pro-
peller meters on the upstream side of the sand bed is not the ideal gas equation; in SI units, R ¼ 8.314 510
1
1
advised if a debris hazard is present. Nm K mol . Also, R ¼ k (Boltzmann constant)
N (Avogadro’s number).
Head: Specific energy of terms in the Bernoulli relation, i.e.,
Nm=(kg g)
ACKNOWLEDGMENTS Header: A pressurized conduit that serves a collection of
On thermodynamics and discussion of compressors, Dr. Paul smaller conduits that are connected, usually in a
Wilbur, professor of mechanical engineering, provided orien- ‘‘T’’ format, to the larger conduit. The header con-
tation on practical aspects of compressor selection and helped duit is the main feed for a manifold.
in reviewing the thermodynamics of compressors. He is a Heat capacity: Two kinds of heat capacity are
faculty member at Colorado State University. c p : defined as the rate of change of enthalpy with temperature
Dr. Larry Weber, director, and Cornelia Mutel, archivist at constant volume, i.e., (qH=qT) V
and historian, IIHR-Hydroscience & Engineering at the c V : defined as the rate of change of internal energy with
University of Iowa, answered the question of exactly where temperature at constant pressure, i.e., (qE=qT) p
and when Dr. Hunter Rouse received his doctorate in Ger- Hydraulic grade line: Locus of points defined by (z þ p=g)
many. It turns out that his doctoral studies were under Profes- along a pipeline.
sor Theodor Rehbock, a well-known hydraulic engineer and Hydraulic loading rate: Defined as flow divided by area
academic. Mutel also provided the photograph of Dr. Rouse, of cross section, i.e., v ¼ Q=A; same as superficial
obtained from the Archives of IIHR-Hydroscience & Engin- velocity.
eering. Hydraulics: That branch of engineering describing the flow
of liquids in terms of the associated dependent and
independent variables.
Intensive property: Quantity that is independent of mass,
GLOSSARY
e.g., temperature, pressure, partial molar free energy,
density, etc.
Absolute temperature: Defined: T(K) ¼ 273.15þ 8C; T(R) ¼
459.6 þ 8F. Interstitial velocity: Defined as flow divided by pore area of
Adiabatic: Zero heat transfer during a change of state. cross section, i.e., v ¼ Q=(AP).