Page 131 - Water Engineering Hydraulics, Distribution and Treatment

Chapter5
Water Hydraulics, Transmission, and
Appurtenances
5.1 FLUID MECHANICS, HYDRAULICS, AND gravity of a given oil is 0.755, its specific weight is 0.755 ×
3
3
WATER TRANSMISSION (62.4 lb/ft ) = 47.11 lb/ft .
The mass of a body (rho), which is termed density, can
5.1.1 Fluid Mechanics and Hydraulics
be expressed by the following equation:
Fluids are substances that are capable of flowing and that

conform to the shape of the vessel in which they are con- = (5.3)
g
tained. Fluids may be divided into liquids and gases. Liquids
are practically incompressible, whereas gases are compress- In the US customary system of units, the density of
ible. Liquids occupy definite volumes and have free sur- water is (62.4lb∕ft )∕(32.2ft∕s ) = 1.94 slug/ft .Inthe
3
2
3
faces, whereas gases expand until they occupy all portions of metric system, the density of water is 1 g∕cm = 1kg∕L =
3
◦
any containing vessels. Water, wastewater, oil, and so on are 1,000 kg∕m = 1 tonne/m at 4 C.
3
3
liquids. Fluid flow may be steady or unsteady, uniform or nonuni-
Fluid mechanics is a branch of applied mechanics deal-
form. Steady flow occurs at any point if the velocity of suc-
ing with the behavior of fluids (liquids and/or gases) at rest
cessive fluid particles is the same at successive instants, that
and in motion. The principles of thermodynamics must be
is, if the fluid velocity is constant with time. The uniform
included when an appreciable compressibility does occur.
flow occurs when the velocity of successive fluid particles
Hydraulics is a branch of fluid mechanics dealing with the
does not change with distance. This book introduces mainly
behavior of particularly incompressible water, wastewater,
the fundamentals of the steady and uniform flows involving
liquid sludge, and so on.
water and wastewater.
The characteristics of gases are determined by Boyle’s In steady flow, the mass of fluid passing any and all
and Charles’s laws: sections in a stream of fluid per unit of time is the same.
For incompressible fluids, such as water and wastewater, the
P V ∕T = R (5.1)
a s a g
following principle of conservation of mass governs:
2
where P = absolute pressure = P gauge + P atm ,lb/ft ; V =
s
a
3
1∕ = specific volume, ft /lb; T = absolute temperature = A v = A v = Constant = Q (5.4)
1 1
2 2
a
◦
◦
◦
T + 460 F; R = gas constant, ft∕ F;T = temperature, F;
g
3
1
2
= specific weight, lb/ft ; and where A and A are, respectively, the cross-sectional areas
2
2
(ft or m ) at section 1 and section 2; v and v are, respec-
2
1
= 1∕V = P ∕R T (5.2) tively, the average velocity of the stream (ft/s or m/s) at
g a
a
s
3
3
section 1 and section 2; and Q is the flow rate (ft /s or m /s).
The specific weight, , of a substance is the weight of a
The Bernoulli equation results from application of the
unit volume of the substance. The specific (unit) weight of principle of conservation of energy to fluid flow, and is writ-
3
water is 62.4 lb/ft for ordinary temperature variations.
ten between two points in a hydraulic system:
The specific gravity of a substance is that pure number,
which denotes the ratio of the weight of a substance to the H + H − H − H = H B (5.5a)
l
e
a
A
weight of an equal volume of a substance taken as a standard.
◦
◦
Solids and liquids are referred to water (at 39.2 F = 4 C) as H + H = H + (H + H ) = H + h f (5.5b)
A
l
B
a
B
e
standard, whereas gases are referred to air free of hydrogen H = P ∕ + v ∕2g + Z A (5.6a)
2
A
A
◦
◦
and carbon dioxide (at 32 F = 0 C and at 1 atmosphere = A
2
2
14.7lb∕in. pressure) as standard. For example, if the specific H = P ∕ + v ∕2g + Z B (5.6b)
B
B
B
Water Engineering: Hydraulics, Distribution and Treatment, First Edition. Nazih K. Shammas and Lawrence K. Wang.
© 2016 John Wiley & Sons, Inc. Published 2016 by John Wiley & Sons, Inc.
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