branching pipes design
TRANSCRIPT
ÇUKUROVA UNIVERSITY
ENGINEERING AND ARCHITECTURE FACUTY
DEPARTMENT OF MECHANICAL ENGINEERING
ENGINEERING PROJECT - I
BRANCHING PIPES DESIGN
BY
2008595015 CANER KİBAR
ADVISOR
ASSOC. PROF. AHMET PINARBAŞI
JANUARY 2012
ADANA
ACKNOWLEDGEMENT
I would like to thank to my advisor Assoc. Prof. Ahmet PINARBAŞI for his guidance,
patience and supports during whole study process. Without his leadership, this book couldn’t
be written.
Also I want to thank to Prof. Dr. Beşir ŞAHİN and Prof. Dr. Hüseyin AKILLI for their
great expressions at Fluid Mechanics lectures. I used basic fluid mechanics principles many
times in this book and I owe this opportunity to them.
II
CONTENTS
ACKNOWLEDGEMENT.......................................................................................................IILIST OF FIGURES................................................................................................................IVLIST OF TABLES...................................................................................................................VCHAPTER 1..............................................................................................................................61.INTRODUCTION..................................................................................................................6CHAPTER 2..............................................................................................................................72. FUNDAMENTAL PRINCIPLES........................................................................................7
2.1.Energy And Hydraulic Grade Lines.............................................................................72.2.Laminar or Turbulent Flow...........................................................................................92.3.Losses And Calculations...............................................................................................11
2.3.1.Head Loss................................................................................................................112.3.2. Minor Loss.............................................................................................................182.3.3. Other Local Losses................................................................................................29
CHAPTER 3............................................................................................................................323. THE ANALYSIS OF PIPING SYSTEM AND PUMP SELECTION...........................32
3.1. Pipe Design...................................................................................................................323.1.1. Pipe Materials........................................................................................................323.1.2. Pressure Class Guidelines....................................................................................323.1.3. Limiting Velocities................................................................................................33
3.2. Pipe Systems.................................................................................................................343.2.1. Single Pipes............................................................................................................343.2.2. Multiple Pipe Systems...........................................................................................35
3.3. Pump Characteristics and Selection...........................................................................393.3.1.Pump Characteristics............................................................................................393.3.2. Pump Selection......................................................................................................403.3.3. Revision of Energy Equation...............................................................................44
CHAPTER 4............................................................................................................................454. BRANCHING PIPES DESIGN.........................................................................................45
4.1. Problem Statement.......................................................................................................454.2. Calculation of Project..................................................................................................47
REFERANCES.......................................................................................................................53
III
LIST OF FIGURES
Figure 2.1 – Representation of the energy line and hydraulic grade line. ................................. 8 Figure 2.2 - Experiment to illustrate type of flow. ..................................................................... 9 Figure 2.3 - Time dependence of fluid velocity at a point. ...................................................... 10 Figure 2.4 – The Moody Chart. ................................................................................................ 16 Figure 2.5 - Entrance flow conditions and loss coefficient ...................................................... 20 Figure 2.6 - Flow pattern and pressure distribution for a sharp-edged entrance. .................... 21 Figure 2.7 - Exit flow conditions and loss coefficient. ............................................................ 22 Figure 2.8 – Loss coefficient for a sudden contraction ............................................................ 22 Figure 2.9 – Loss coefficient for a sudden expansion .............................................................. 23 Figure 2.10 - Control volume used to calculate the loss coefficient for a sudden expansion. . 23 Figure 2.11 - Loss coefficient for a typical conical diffuser. ................................................... 25 Figure 2.12 - Character of the flow in a 900 bend and the associated loss coefficient ............. 26 Figure 2.13 - Character of the flow in a 900 mitered bend ....................................................... 27 Figure 2.14 – Boundary layer seperation ................................................................................. 29 Figure 2.15 – Local losses in pipe flow ................................................................................... 30 Figure 3.1 – Series and paralel pipe systems ........................................................................... 36 Figure 3.2 – Multiple pipe loop system. .................................................................................. 38 Figure 3.3 – Pump selection for a single pump ........................................................................ 41 Figure 3.4 – Selection of paralel pumps .................................................................................. 43 Figure 4.1 – Shematic Representation of Branching Pipes Water Supply System .................. 45 Figure 4.2 – Feasibility of Pump with Checking Power-Flow Rate Comparison .................... 52 Figure 4.3 - Feasibility of Pump with Checking Head Loss-Flow Rate Comparison ............. 52
IV
LIST OF TABLES
Table 2.1 – Equivalent roughness for new pipes. .................................................................... 15 Table 2.2 - Loss coefficients for pipe components. ................................................................. 28 Table 2.3 - KL values for practical calculations ....................................................................... 30 Table 3.1 – Three most common types of problems ................................................................ 35 Table 4.1. – Necessary Informations of Branching Pipes System ........................................... 46 Table 4.2. – Flow Rate Distribution and Other Informations of Pipes .................................... 49
V
CHAPTER 1
1.INTRODUCTION
At the start of this book “the branching” term should be well understood before investigate the
branching pipes system and due to achieve to aim of project. In a branching system a number
of pipes are connected to the main to form the topology of a tree. Assuming that the flow is
from the main into the smaller laterals it is possible to calculate the flow rate in any pipe as
the sum of the downstream consumptions or demands. If the laterals supply water to the main,
the same might be done. In either case by proceeding from the outermost branches toward the
main or “root of the tree” the flow rate can be calculated, and from the flow rate in each pipe
the head loss can be determined using the Darcy-Weisbach or Hazen-Williams equation. In
analyzing a pipe network containing a branching system, only the main is included with the
total flow rate specified by summing from the smaller pipes. Upon completing the analysis the
pressure head in the main will be known. By substracting individual head losses from this
known head, the heads (or pressures) at any point throughout the branching system can be
determined.
As they are mentioned above, before the analysis of design problem some basic principles
will be explained and examined at next chapters such as energy and hydraulic grade lines,
type of losses and their formulas, pump theory and characteristics, flow characteristics which
are foundations of the material in this book.
6
CHAPTER 2
2. FUNDAMENTAL PRINCIPLES
2.1.Energy And Hydraulic Grade Lines
The Hydraulic Grade Line and Energy Line are simply graphical forms of the Bernoulli
Equation. The Bernoulli equation is actually an energy equation representing
the partitioning of energy for an inviscid, incompressible, steady flow. The sum of
the various energies of the fluid remains constant as the fluid flows from one section to
another.
A useful interpretation of the Bernoulli equation can be obtained through the use of
the concepts of the hydraulic grade line (HGL) and the energy line (EL). These ideas
represent a geometrical interpretation of a flow and can often be effectively used to better
grasp the fundamental processes involved.
The Bernoulli equation can be obtained by integrating “F=m.a” along a stream line and it is:
(2.1)
For steady, inviscid, incompressible flow the total energy remains constant along a
streamline. The concept of “head” was introduced by dividing each term in Eq. 2.1 by the
specific weight, “γ=ρ.g”, to give the Bernoulli equation in the following form:
(2.2)
Each of the terms in this equation has the units of length (feet or meters) and represents a
certain type of head. The Bernoulli equation states that the sum of the pressure head, the
velocity head, and the elevation head is constant along a streamline. This constant is called the
total head, H.
The energy line is a line that represents the total head available to the fluid. As shown
in Fig. 2.1, the elevation of the energy line can be obtained by measuring the stagnation
pressure with a Pitot tube. (A Pitot tube is the portion of a Pitot-static tube that measures the
stagnation pressure.) The stagnation point at the end of the Pitot tube provides
a measurement of the total head (or energy) of the flow. The static pressure tap connected
to the piezometer tube shown, on the other hand, measures the sum of the pressure
head and the elevation head, “p/γ + z”, This sum is often called the piezometric head. The
static pressure tap does not measure the velocity head.
7
Figure 2.1 – Representation of the energy line and hydraulic grade line.
According to Eq. 2.2, the total head remains constant along the streamline. Thus, a pitot tube
at any other location in the flow will measure the same total head, as is shown in the figure.
The elevation head, velocity head, and pressure head may vary along the streamline, however.
The locus of elevations provided by a series of pitot tubes is termed the energy line,
EL. The level provided by a series of piezometer taps is termed the hydraulic grade line,
HGL. Under the assumptions of the Bernoulli equation, the energy line is horizontal. If the
fluid velocity changes along the streamline, the hydraulic grade line will not be horizontal.
If viscous effects are important, the total head does not remain constant due to a loss in energy
as the fluid flows along its streamline. This means that the energy line is no longer horizontal.
8
2.2.Laminar or Turbulent Flow
Figure 2.2 - (a) Experiment to illustrate type of flow. (b) Typical dye streaks.
The flow of a fluid in a pipe may be laminar flow or it may be turbulent flow. Osborne
Reynolds (1842–1912), a British scientist and mathematician, was the first to distinguish the
difference between these two classifications of flow by using a simple apparatus as shown
in Fig. 8.3a. If water runs through a pipe of diameter D with an average velocity V, the
following characteristics are observed by injecting neutrally buoyant dye as shown. For
“small enough flowrates” the dye streak (a streakline) will remain as a well-defined line as it
flows along, with only slight blurring due to molecular diffusion of the dye into the
surrounding water. For a somewhat larger “intermediate flowrate” the dye streak fluctuates in
time and space, and intermittent bursts of irregular behavior appear along the streak. On the
other hand, for “large enough flowrates” the dye streak almost immediately becomes blurred
and spreads across the entire pipe in a random fashion. These three characteristics, denoted as
laminar, transitional, and turbulent flow, respectively, are illustrated in Fig. 2.2b.
The curves shown in Fig. 2.3 represent the x component of the velocity as a function
of time at a point A in the flow. The random fluctuations of the turbulent flow (with the
associated particle mixing) are what disperse the dye throughout the pipe and cause the
blurred appearance illustrated in Fig. 2.2b. For laminar flow in a pipe there is only one
component of velocity, V=uî. For turbulent flow the predominant component of velocity is
also along the pipe, but it is unsteady and accompanied by random components normal to the
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pipe axis, V=uî+vj+wk. Such motion in a typical flow occurs too fast for our eyes to follow.
Slow motion pictures of the flow can more clearly reveal the irregular, random, turbulent
nature of the flow.
Figure 2.3 - Time dependence of fluid velocity at a point.
Dimensional quantities should not be label as being “large” or “small,” such as “small enough
flowrates” in the preceding paragraphs. Rather, the appropriate dimensionless quantity should
be identified and the “small” or “large” character attached to it. A quantity is “large” or
“small” only relative to a reference quantity. The ratio of those quantities results in a
dimensionless quantity. For pipe flow the most important dimensionless parameter is the
Reynolds number, Re—the ratio of the inertia to viscous effects in the flow. Re= ρVD/ μ
where V is the average velocity in the pipe. That is, the flow in a pipe is laminar, transitional,
or turbulent provided the Reynolds number is “small enough,” “intermediate,” or “large
enough.” It is not only the fluid velocity that determines the character of the flow—its density,
viscosity, and the pipe size are of equal importance. These parameters combine to produce the
Reynolds number. The distinction between laminar and turbulent pipe flow and its
dependence on an appropriate dimensionless quantity was first pointed out by Osborne
Reynolds in 1883.
The Reynolds number ranges for which laminar, transitional, or turbulent pipe flows
are obtained cannot be precisely given. The actual transition from laminar to turbulent flow
may take place at various Reynolds numbers, depending on how much the flow is disturbed
by vibrations of the pipe, roughness of the entrance region, and the like. For general
engineering purposes (i.e. without undue precautions to eliminate such disturbances), the
following values are appropriate: The flow in a round pipe is laminar if the Reynolds number
10
is less than approximately 2100. The flow in a round pipe is turbulent if the Reynolds number
is greater than approximately 4000. For Reynolds numbers between these two limits, the
flow may switch between laminar and turbulent conditions in an apparently random fashion
(transitional flow).
2.3.Losses And Calculations
2.3.1.Head Loss
The head loss in a pipe is a result of the viscous shear stress on the wall. Because of viscosity,
there is friction within the fluid as well as friction of the fluid against the piping or ducting
walls. This friction converts into heat some of the pressure energy of the flowing fluid and
raises the temperature of the fluid and piping. This phenomenon can be critical in the
operation of some quipment.
The energy equation for incompressible, steady flow between two locations can be written as:
(2.3)
Recall that the kinetic energy coefficients, α1 and α2, compensate for the fact that the velocity
profile across the pipe is not uniform. For uniform velocity profiles α=1, whereas for any
nonuniform profile, α >1.
The head loss term, hL, accounts for any energy loss associated with the flow. This loss is a
direct consequence of the viscous dissipation that occurs throughout the fluid in the pipe. For
the ideal (inviscid) cases α1 = α2 = 1, hL = 0 and the energy equation reduces to the familiar
bernoulli equation, Eq. 2.1.
Even though the velocity profile in viscous pipe flow is not uniform, for fully developed
flow it does not change from section (1) to section (2) so that α1 = α2. Thus, the kinetic
energy is the same at any section (α1.V12/2 = α2. V2
2/2) and the energy equation becomes:
(2.4)
Consider a volume element of fluid which is flowing in a circular pipe, with coordinate x in
the flow direction and r radially, lenght, L and diameter, D. With the definitions of wall shear
11
stress (τw), net pressure force in element is (P1- P2= γ. hL), net shear force in the element is
(τw.π.D), force balance for equilibrium yields:
(2.5)
Substituting the equations 2.4 and 2.5, frictional head loss can be written as:
(2.6)
It is the shear stress at the wall (which is directly related to the viscosity and the shear stress
throughout the fluid) that is responsible for the head loss. A closer consideration of the
assumptions involved in the derivation of Eq. 2.6 will show that it is valid for both laminar
and turbulent flow.
As is discussed above, the pressure drop and head loss in a pipe are dependent on the wall
shear stres, τw, between the fluid and pipe surface. A fundamentaldifference between laminar
and turbulent flow is that the shear stress for turbulent flow is a function of the density of the
fluid, ρ. For laminar flow, the shear stress is independent of the density, leaving the viscosity,
μ, as the only important fluid property. Thus, the pressure drop, Δp, for steady,
incompressible turbulent flow in a horizontal round pipe of diameter D can be written in
functional form as Δp=f(V,D,L,ε,μ,ρ) where V is the average velocity, L is the pipe length,
and ε is a measure of the roughness of the pipe wall. It is clear that Δp should be a function of
V, D, and L. The dependence of Δp on the fluid properties μ and ρ is expected because of the
dependence of τ on these parameters.
Although the pressure drop for laminar pipe flow is found to be independent of the roughness
of the pipe, it is necessary to include this parameter when considering turbulent flow. For
turbulent flow there is a relatively thin viscous sublayer formed in the fluid near the pipe wall.
In many instances this layer is very thin; δs/D<<1, where δs is the sublayer thickness. If a
typical wall roughness element protrudes sufficiently far into (or even through) this layer, the
structure and properties of the viscous sublayer (along with Δp and τw) will be different than if
the wall were smooth. Thus, for turbulent flow the pressure drop is expected to be a function
of the wall roughness. For laminar flow there is no thin viscous layer thus, relatively small
roughness elements have completely negligible effects on laminar pipe flow. Of course, for
12
pipes with very large wall roughness, (ε/D>0.1), the flowrate may be a function of the
roughness.
The list of parameters given in Δp=f(V,D,L,ε,μ,ρ) is apparently a complete one. experiments
have shown that other parameters (such as surface tension, vapor pressure, etc.) do not affect
the pressure drop for the conditions stated (steady, incompressible flow; round, horizontal
pipe). Since there are seven variables (k=7) which can be written in terms of the three
reference dimensions MLT (r=3), Δp=f(V,D,L,ε,μ,ρ) can be written in dimensionless form in
terms of k-r=4 dimensionless groups. One such representation is:
This result differs from that used for laminar flow in two ways. First, it have been chosen to
make the pressure dimensionless by dividing by the dynamic pressure, ρV2/2, rather than a
characteristic viscous shear stress, μV/D. This convention was chosen in recognition of the
fact that the shear stress for turbulent flow is normally dominated by τturb, which is a stronger
function of the density than it is of viscosity. Second, it have been introduced two additional
dimensionless parameters, the Reynolds number, Re= ρVD/ μ, and the relative roughness, ε/D
which are not present in the laminar formulation because the two parameters, ρ and ε are not
important in fully developed laminar pipe flow.
As was done for laminar flow, the functional representation can be simplified by imposing
the reasonable assumption that the pressure drop should be proportional to the pipe length.
(Such a step is not within the realm of dimensional analysis. It is merely a logical assumption
supported by experiments.) The only way that this can be true is if the L/D dependence is
factored as:
the quantity ΔpD/(LρV2/2) is termed the friction factor, f. Thus, for a horizontal pipe:
(2.7) where
13
For laminar fully developed flow, the value of f is simply f=64/Re, independent of ε/D. For
turbulent flow, the functional dependence of the friction factor on the Reynolds number and
relative toughness, f=ϕ(Re, ε/D), is a rather complex one that cannot, as yet, be obtained from
a theoretical analysis. The results are obtained from an exhaustive set of experiments and
usually presented in terms of a curve-fitting formula or the equivalent graphical form.
The energy equation for steady incompressible flow is:
where hL is the head loss between sections (1) and (2). With the assumption of a constant
diameter ( D1=D2 so that V1=V2), horizontal (z1=z2) pipe with fully developed flow (α1= α2),
this becomes Δp=p1-p2=γ hL, which can be combined with Eq. 2.7 to give
(2.8)
Equation 2.8, called the Darcy-Weisbach equation, is valid for any fully developed, steady,
incompressible pipe flow-whether the pipe is horizontal or on a hill-. On the other hand, Eq.
2.7 is valid only for horizontal pipes. In general, with V1=V2 the energy equation gives
Part of the pressure change is due to the elevation change and part is due to the head loss
associated with frictional effects, which are given in terms of the friction factor, f.
It is sometimes useful to write the Darcy equation in terms of discharge Q, (using Q = AV)
or with a %1 error
It is not easy to determine the functional dependence of the friction factor on the Reynolds
number and relative roughness. Much of this information is a result of experiments conducted
by J. Nikuradse in 1933 and amplified by many others since then. One difficulty lies in the
determination of the roughness of the pipe. Nikuradse used artificially roughened pipes
produced by gluing sand grains of known size onto pipe walls to produce pipes with
sandpaper-type surfaces. The pressure drop needed to produce a desired flowrate was
14
measured and the data were converted into the friction factor for the corresponding Reynolds
number and relative roughness. The tests were repeated numerous times for a wide range of
Re and ε/D to determine the f=ϕ(Re, ε/D) dependence.
In commercially available pipes the roughness is not as uniform and well defined as in the
artificially roughened pipes used by Nikuradse. However, it is possible to obtain a measure of
the effective relative roughness of typical pipes and thus to obtain the friction factor. Typical
roughness values for various pipe surfaces are given in Table 2.1. Figure 2.4 shows the
functional dependence of f on Re and ε/D and is called the Moody chart in honor of L. F.
Moody, who, along with C. F. Colebrook, correlated the original data of Nikuradse in terms
of the relative roughness of commercially available pipe materials. It should be noted that the
values of ε/D do not necessarily correspond to the actual values obtained by a microscopic
determination of the average height of the roughness of the surface. They do, however,
provide the correct correlation for f=ϕ(Re, ε/D)
Table 2.1 – Equivalent roughness for new pipes.
It is important to observe that the values of relative roughness given pertain to new, clean
pipes. After considerable use, most pipes (because of a buildup of corrosion or scale) may
have a relative roughness that is considerably larger (perhaps by an order of magnitude) than
that given. Very old pipes may have enough scale buildup to not only alter the value of ε but
also to change their effective diameter by a considerable amount.
The following characteristics are observed from the data of Fig. 2.4. For laminar flow,
f=64/Re, which is independent of relative roughness. For very large Reynolds numbers,
f=ϕ(Re, ε/D), which is independent of the Reynolds number. For such flows, commonly
15
termed completely turbulent flow (or wholly turbulent flow), the laminar sublayer is so thin
(its thickness decreases with increasing Re) that the surface roughness completely dominates
the character of the flow near the wall. Hence, the pressure drop required is a result of an
inertia-dominated turbulent shear stress rather than the viscosity-dominated laminar shear
Figure 2.4 – The friction factor as a function of Reynolds number and relative roughness for
round pipes. – The Moody Chart.
16
stress normally found in the viscous sublayer. For flows with moderate values of Re, the
friction factor is indeed dependent on both the Reynolds number and relative roughness
f=ϕ(Re, ε/D). The gap in the figure for which no values of f are given ( 2100<Re<4000 range)
is a result of the fact that the flow in this transition range may be laminar or turbulent (or an
unsteady mix of both) depending on the specific circumstances involved.
Note that even for smooth pipes (ε=0) the friction factor is not zero. That is, there is a head
loss in any pipe, no matter how smooth the surface is made. This is a result of the no-slip
boundary condition that requires any fluid to stick to any solid surface it flows over. There is
always some microscopic surface roughness that produces the no-slip behavior (and thus f 0)
on the molecular level, even when the roughness is considerably less than the viscous
sublayer thickness. Such pipes are called hydraulically smooth.
Various investigators have attempted to obtain an analytical expression for f=ϕ(Re, ε/D). Note
that the Moody chart covers an extremely wide range in flow parameters. The nonlaminar
region covers more than four orders of magnitude in Reynolds number – from Re=4.103 to
Re=108. Obviously, for a given pipe and fluid, typical values of the average velocity do not
cover this range. However, because of the large variety in pipes (D), fluids (ρ and μ) and
velocities (V), such a wide range in Re is needed to accommodate nearly all applications of
pipe flow. In many cases the particular pipe flow of interest is confined to a relatively small
region of the Moody chart, and simple semiempirical expressions can be developed for those
conditions. The Moody chart is universally valid for all steady, fully developed,
incompressible pipe flows. The following equation from Colebrook is valid for the entire
nonlaminar range of the Moody chart
(2.9)
In fact, the Moody chart is a graphical representation of this equation, which is an empirical
fit of the pipe flow pressure drop data. Equation 2.9 is called the Colebrook formula. The
turbulent portion of the Moody chart is represented by the Colebrook formula. A difficulty
with its use is that it is implicit in the dependence of f. That is, for given conditions (Re and
ε/D) it is not possible to solve for f without some sort of iterative scheme. With the use of
modern computers and calculators, such calculations are not difficult. A word of caution is in
order concerning the use of the Moody chart or the equivalent Colebrook formula. Because of
17
various inherent inaccuracies involved (uncertainty in the relative roughness, uncertainty in
the experimental data used to produce the Moody chart, etc.), the use of several place
accuracy in pipe flow problems is usually not justified. As a rule of thumb, a 10% accuracy is
the best expected.
Note: The f value shown above is different to that used in American practice. Their
relationship is f American = 4f. Sometimes the f is replaced by the Greek letter λ, where
λ= f American = 4f. Consequently great care must be taken when choosing the value of f with
attention taken to the source of that value.
2.3.2. Minor Loss
Losses occur in straight pipes (major losses) and pipe system components (minor losses). the
head loss in long, straight sections of pipe can be calculated by use of the friction factor
obtained from either the Moody chart or the Colebrook equation. Most pipe systems,
however, consist of considerably more than straight pipes. These additional components
(valves, bends, tees, and the like) add to the overall head loss of the system. Such losses are
generally termed minor losses, with the apparent implication being that the majority of the
system loss is associated with the friction in the straight portions of the pipes, the major
losses. In many cases this is true. In other cases the minor losses are greater than the major
losses. In this section, how to determine the various minor losses that commonly occur in pipe
systems will be indicated.
The head loss associated with flow through a valve is a common minor loss. The purpose of a
valve is to provide a means to regulate the flowrate. This is accomplished by changing the
geometry of the system (i.e. closing or opening the valve alters the flow pattern
through the valve), which in turn alters the losses associated with the flow through the valve.
The flow resistance or head loss through the valve may be a significant portion of the
resistance in the system. In fact, with the valve closed, the resistance to the flow is infinite –
the fluid cannot flow. Such minor losses may be very important indeed. With the valve wide
open the extra resistance due to the presence of the valve may or may not be negligible.
It is not difficult to realize that a theoretical analysis to predict the details of such flows to
obtain the head loss is not, as yet, possible. Thus, the head loss information for essentially all
components is given in dimensionless form and based on experimental data. The most
common method used to determine these head losses or pressure drops is to specify the loss
coefficient, KL, which is defined as
18
so that or
(2.10)
Losses due to pipe system components are given in terms of loss coefficients. The pressure
drop across a component that has a loss coefficient of KL=1 is equal to the dynamic pressure,
ρV2/2.
The actual value of is strongly dependent on the geometry of the component considered. It
may also be dependent on the fluid properties. It is, KL=ϕ(geometry, Re) where Re=ρVD/ μ is
the pipe Reynolds number. For many practical applications the Reynolds number is large
enough so that the flow through the component is dominated by inertia effects, with viscous
effects being of secondary importance. This is true because of the relatively large
accelerations and decelerations experienced by the fluid as it flows along a rather curved,
variable-area (perhaps even torturous) path through the component. In a flow that is
dominated by inertia effects rather than viscous effects, it is usually found that pressure drops
and head losses correlate directly with the dynamic pressure. This is the reason why the
friction factor for very large Reynolds number, fully developed pipe flow is independent of
the Reynolds number. The same condition is found to be true for flow through pipe
components. Thus, in most cases of practical interest the loss coefficients for components are
a function of geometry only, KL=ϕ(geometry, Re).
Minor losses are sometimes given in terms of an equivalent length, Leq. In this terminology,
the head loss through a component is given in terms of the equivalent length of pipe that
would produce the same head loss as the component. That is,
or
where D and f are based on the pipe containing the component. The head loss of the pipe
system is the same as that produced in a straight pipe whose length is equal to the pipes of the
original system plus the sum of the additional equivalent lengths of all of the components of
19
the system. Most pipe flow analyses, including those in this book, use the loss coefficient
method rather than the equivalent length method to determine the minor losses.
Many pipe systems contain various transition sections in which the pipe diameter changes
from one size to another. Such changes may occur abruptly or rather smoothly through some
type of area change section. Any change in flow area contributes losses that are not accounted
for in the fully developed head loss calculation (the friction factor). The extreme cases involve
flow into a pipe from a reservoir (an entrance) or out of a pipe into a reservoir (an exit).
Figure 2.5 - Entrance flow conditions and loss coefficient (a) Reentrant, KL =0.8, (b) sharp-
edged, KL =0.5, (c) slightly rounded, KL =0.2 (d) well-rounded, KL =0.04
A fluid may flow from a reservoir into a pipe through any number of different shaped
entrance regions as are sketched in Fig. 2.5. Each geometry has an associated loss coefficient.
A typical flow pattern for flow entering a pipe through a square-edged entrance is sketched in
Fig. 2.6. A vena contracta region may result because the fluid cannot turn a sharp right-angle
corner. The flow is said to separate from the sharp corner. The maximum velocity at section
(2) is greater than that in the pipe at section (3), and the pressure there is lower. If this high-
speed fluid could slow down efficiently, the kinetic energy could be converted into pressure
(the Bernoulli effect), and the ideal pressure distribution indicated in Fig. 2.6 would result.
The head loss for the entrance would be essentially zero.
20
Figure 2.6 - Flow pattern and pressure distribution for a sharp-edged entrance.
Minor head losses are often a result of the dissipation of kinetic energy. Although a fluid may
be accelerated very efficiently, it is very difficult to slow down (decelerate) a fluid efficiently.
Thus, the extra kinetic energy of the fluid at section (2) is partially lost because of viscous
dissipation, so that the pressure does not return to the ideal value. An entrance head loss
1pressure drop2 is produced as is indicated in Fig. 2.6. The majority of this loss is due to
inertia effects that are eventually dissipated by the shear stresses within the fluid. Only a small
portion of the loss is due to the wall shear stress within the entrance region. The net effect is
that the loss coefficient for a square-edged entrance is approximately KL =0.50. One-half of a
velocity head is lost as the fluid enters the pipe. If the pipe protrudes into the tank (a reentrant
entrance) as is shown in Fig. 2.5a, the losses are even greater.
An obvious way to reduce the entrance loss is to round the entrance region as is shown in Fig.
2.5c, thereby reducing or eliminating the vena contracta effect. A significant reduction in KL
can be obtained with only slight rounding.
21
Figure 2.7 - Exit flow conditions and loss coefficient. (a) Reentrant, KL =1.0 (b) sharp-edged,
KL=1.0, (c) slightly rounded, KL=1.0, (d) well-rounded, KL=1.0.
A head loss (the exit loss) is also produced when a fluid flows from a pipe into a tank as is
shown in Fig. 2.7. In these cases the entire kinetic energy of the exiting fluid (velocity V1) is
dissipated through viscous effects as the stream of fluid mixes with the fluid in the tank and
eventually comes to rest( V2=0). The exit loss from points (1) and (2) is therefore equivalent
to one velocity head, or KL=1.
Figure 2.8 – Loss coefficient for a sudden contraction
22
Figure 2.9 – Loss coefficient for a sudden expansion
Losses also occur because of a change in pipe diameter as is shown in Figs. 2.8 and 2.9. The
sharp-edged entrance and exit flows discussed in the previous paragraphs are limiting cases of
this type of flow with either A1/A2= , or A1/A2=0, respectively. The loss coefficient for a
sudden contraction, KL=hL/(V2/2g), is a function of the area ratio, A1/A2 , as is shown in Fig.
2.8. The value of KL changes gradually from one extreme of a sharp-edged entrance (A1/A2=0
with KL=0.50) to the other extreme of no area change (A1/A2=1 with KL=0).
In many ways, the flow in a sudden expansion is similar to exit flow. As is indicated in Fig.
2.10, the fluid leaves the smaller pipe and initially forms a jet-type structure as it enters the
larger pipe. Within a few diameters downstream of the expansion, the jet becomes dispersed
across the pipe, and fully developed flow becomes established again. In this process [between
sections (2) and (3)] a portion of the kinetic energy of the fluid is dissipated as a result of
viscous effects. A square-edged exit is the limiting case with A1/A2=0.
Figure 2.10 - Control volume used to calculate the loss coefficient for a sudden expansion.
23
A sudden expansion is one of the few components (perhaps the only one) for which the loss
coefficient can be obtained by means of a simple analysis. To do this the continuity and
momentum equations for the control volume shown in Fig. 2.10 are considered and the energy
equation applied between (2) and (3). It’s assumed that the flow is uniform at sections (1), (2),
and (3) and the pressure is constant across the left-hand side of the control volume
(pa=pb=pc=p1). The resulting three governing equations (mass, momentum, and energy) are
and
These can be rearranged to give the loss coefficient, KL=hL/(V2/2g), as
This result, plotted in Fig. 2.9, is in good agreement with experimental data. As with so many
minor loss situations, it is not the viscous effects directly (i.e. the wall shear stres) that cause
the loss. Rather, it is the dissipation of kinetic energy (another type of viscous effect) as the
fluid decelerates inefficiently.
The losses may be quite different if the contraction or expansion is gradual. Typical results for
a conical diffuser with a given area ratio, A1/A2, are shown in Fig. 2.11. (A diffuser is a
device shaped to decelerate a fluid.) Clearly the included angle of the diffuser, θ, is a very
important parameter. For very small angles, the diffuser is excessively long and most of the
head loss is due to the wall shear stress as in fully developed flow. For moderate or large
angles, the flow separates from the walls and the losses are due mainly to a dissipation of the
kinetic energy of the jet leaving the smaller diameter pipe. In fact, for moderate or large
values of θ (i.e. θ>350 for the case shown in Fig. 2.11), the conical diffuser is, perhaps
unexpectedly, less efficient than a sharp-edged expansion which has KL=1. There is an
optimum angle (θ 80 for the case illustrated) for which the loss coefficient is a minimum. The
24
relatively small value of θ for the minimum KL results in a long diffuser and is an indication
of the fact that it is difficult to efficiently decelerate a fluid.
It must be noted that the conditions indicated in Fig. 8.29 represent typical results only. Flow
through a diffuser is very complicated and may be strongly dependent on the area ratio A1/A2,
specific details of the geometry, and the Reynolds number. The data are often presented in
terms of a pressure recovery coefficient, Cp=(p2-p1)/ (ρV21/2), which is the ratio of the static
pressure rise across the diffuser to the inlet dynamic pressure.
Figure 2.11 - Loss coefficient for a typical conical diffuser.
Flow in a conical contraction (a nozzle; reverse the flow direction shown in Fig. 2.11) is less
complex than that in a conical expansion. Typical loss coefficients based on the downstream
(high-speed) velocity can be quite small, ranging from KL=0.02 for θ=300, to KL=0.07 for
θ=600 for example. It is relatively easy to accelerate a fluid efficiently.
Bends in pipes produce a greater head loss than if the pipe were straight. The losses are due to
the separated region of flow near the inside of the bend (especially if the bend is sharp) and
the swirling secondary flow that occurs because of the imbalance of centripetal forces as a
result of the curvature of the pipe centerline. These effects and the associated values of KL for
large Reynolds number flows through a 900 bend are shown in Fig. 2.12.
25
Figure 2.12 - Character of the flow in a 900 bend and the associated loss coefficient
For situations in which space is limited, a flow direction change is often accomplished by use
of miter bends, as is shown in Fig. 2.13, rather than smooth bends. The considerable losses in
such bends can be reduced by the use of carefully designed guide vanes that help direct the
flow with less unwanted swirl and disturbances.
Another important category of pipe system components is that of commercially available pipe
fittings such as elbows, tees, reducers, valves, and filters. The values of KL for such
components depend strongly on the shape of the component and only very weakly on the
Reynolds number for typical large Re flows. Thus, the loss coefficient for a 900 elbow
depends on whether the pipe joints are threaded or flanged but is, within the accuracy of the
data, fairly independent of the pipe diameter, flow rate, or fluid properties (the Reynolds
number effect). Typical values of KL for such components are given in Table 2.2. These
typical components are designed more for ease of manufacturing and costs than for reduction
of the head losses that they produce. The flowrate from a faucet in a typical house is sufficient
whether the value of for an elbow is the typical KL=1.5, or it is reduced to KL=0.2 by use of a
more expensive long-radius, gradual bend (Fig. 2.12).
26
Figure 2.13 - Character of the flow in a 900 mitered bend and the associated loss coefficient:
(a) without guide vanes, (b) with guide vanes
A valve is a variable resistance element in a pipe circuit. Valves control the flowrate by
providing a means to adjust the overall system loss coefficient to the desired value. When the
valve is closed, the value of KL is infinite and no fluid flows. Opening of the valve reduces
producing the desired flowrate. Loss coefficients for typical valves are given in Table 2.2. As
with many system components, the head loss in valves is mainly a result of the dissipation of
kinetic energy of a high-speed portion of the flow.
27
Table 2.2 - Loss coefficients for pipe components.
28
2.3.3. Other Local Losses
Large losses in energy usually occur only where flow expands. The mechanism at work in
these situations is that as velocity decreases (by continuity) so pressure must increase (by
Bernoulli). When the pressure increases in the direction of fluid outside the boundary layer
has enough momentum to overcome this pressure that is trying to push it backwards. The
fluid within the boundary layer has so little momentum that it will very quickly be brought to
rest, and possibly reversed in direction. If this reversal occurs it lifts the boundary layer away
from the surface as shown in Figure 8. This phenomenon is known as boundary layer
separation.
Figure 2.14 – Boundary layer seperation
At the edge of the separated boundary layer, where the velocities change direction, a line of
vortices occur (known as a vortex sheet). This happens because fluid to either side is moving
in the opposite direction. This boundary layer separation and increase in the turbulence
because of the vortices results in very large energy losses in the flow. These separating/
divergent flows are inherently unstable and far more energy is lost than in parallel or
convergent flow.
Some common situation where significant head losses occur in pipe are shown in Fig. 2.15.
29
Figure 2.15 – Local losses in pipe flow
The values of KL for these common situations are shown in Table 2.3. It gives value that are
used in practice.
Table 2.3 - KL values for practical calculations
30
The summation of all friction and local losses in a pipe system can be expressed as:
(2.11)
(2.12)
(2.13)
It is important to use the correct pipe diameter for each pipe section and local loss. In the past
some have expressed the local losses as an equivalent pipe length: L/d = KL /f. It simply
represents the length of pipe that produces the same head loss as the local or minor loss. This
is a simple, but not a completely accurate method of including local losses. The problem with
this approach is that since the friction coefficient varies from pipe to pipe, the equivalent
length will not have a unique value. When local losses are truly minor, this problem becomes
academic because the error only influences losses which make up a small percentage of the
total. For cases where accurate evaluation of all losses is important, it is recommended that
the minor loss coefficients KL be used rather than an equivalent length.
The challenging part of making minor loss calculations is obtaining reliable values of KL. The
final results cannot be any more accurate than the input data. If the pipe is long, the friction
losses may be large compared with the minor losses and approximate values of KL will be
sufficient. However, for short systems with many pipe fittings, the local losses can represent a
significant portion of the total system losses, and they should be accurately determined.
Numerous factors influence KL. For example, for elbows, KL is influenced by the shape of the
conduit (rectangular vs. circular), by the radius of the bend, the bend angle, the Reynolds
number, and the length of the outlet pipe. For dividing or combining tees or Y-branches, the
percent division of ßow and the change in pipe diameter must also be included when
estimating KL. One factor which is important for systems where local losses are significant is
the interaction between components placed close together. Depending on the type, orientation,
and spacing of the components, the total loss coefficient may be greater or less than the
simple sum of the individual KL values.
31
CHAPTER 3
3. THE ANALYSIS OF PIPING SYSTEM AND PUMP SELECTION
3.1. Pipe Design
3.1.1. Pipe Materials
Materials commonly used for pressure pipe transporting liquids are ductile iron, concrete,
steel, fiberglass, PVC, and polyolefin. Specifications have been developed by national
committees for each of these pipe materials. The specifications discuss external loads, internal
design pressure, available sizes, quality of materials, installation practices, and information
regarding linings. Standards are available from the following organizations:
American Water Works Association (AWWA)
American Society for Testing and Materials (ASTM)
American National Standards Institute (ANSI)
Federal Specifications (FED)
Plastic Pipe Institute (PPI)
Turkish Institute of Standarts (TSE)
In addition, manuals and other standards have been published by various manufacturers and
manufacturer‘s associations. All of these specifications and standards should be used to guide
the selection of pipe material. ANSI contains a description of each of these pipe materials and
a list of the specifications for the various organizations which apply to each material. It also
discusses the various pipe-lining materials available for corrosion protection.
For air- and low-pressure liquid applications one can use unreinforced concrete, corrugated
steel, smooth sheet metal, spiral rib (sheet metal), and HDPE (high-density polyethylene)
pipe. The choice of a material for a given application depends on pipe size, pressure
requirements, resistance to collapse from internal vacuums, external loads, resistance to
internal and external corrosion, ease of handling and installing, useful life, and economics.
3.1.2. Pressure Class Guidelines
Procedures for selecting the pressure class of pipe vary with the type of pipe material.
Guidelines for different types of materials are available from AWWA, ASTM, ANSI, FED,
PPI, TSE and from the pipe manufacturers. These specifications should be obtained and
studied for the pipe materials being considered.
32
The primary factors governing the selection of a pipe pressure class are (1) the maximum
steady state operating pressure, (2) surge and transient pressures, (3) external earth loads and
live loads, (4) variation of pipe properties with temperature or long-time loading effects, and
(5) damage that could result from handling, shipping, and installing or reduction in strength
due to chemical attack or other aging factors. The influence of the first three items can be
quantified, but the last two are very subjective and are generally accounted for with a safety
factor which is the ratio of the burst pressure to the rated pressure. There is no standard
procedure on how large the safety factor should be or on how the safety factor should be
applied. Some may feel that it is large enough to account for all of the uncertainties. Past
failures of pipelines designed using this assumption prove that it is not always a reliable
approach. The procedure recommended by the author is to select a pipe pressure class based
on the internal design pressure (IDP) defined as
in which Pmax is the maximum steady state operating pressure, Ps is the surge or water hammer
pressure, and SF is the safety factor applied to take care of the unknowns (items 3 to 5) just
enumerated. A safety factor between 3 and 4 is typical.
The maximum steady state operating pressure (Pmax) in a gravity flow system is usually the
difference between the maximum reservoir elevation and the lowest elevation of the pipe. For
a pumped system it is usually the pump shutoff head calculated based on the lowest elevation
of the pipe.
Surge and transient pressures depend on the specific pipe system design and operation.
Accurately determining Ps requires analyzing the system using modern computer techniques.
Selection of wall thickness for larger pipes is often more dependent on collapse pressure and
handling loads than it is on burst pressure. A thin-wall, large-diameter pipe may be adequate
for resisting relatively high internal pressures but may collapse under negative internal
pressure or, if the pipe is buried, the soil and groundwater pressure plus live loads may be
sufficient to cause collapse even if the pressure inside the pipe is positive.
3.1.3. Limiting Velocities
There are concerns about upper and lower velocity limits. If the velocity is too low, problems
may develop due to settling of suspended solids and air being trapped at high points and along
33
the crown of the pipe. The safe lower velocity limit to avoid collecting air and sediment
depends on the amount and type of sediment and on the pipe diameter and pipe profile.
Velocities greater than about 1 m/sec are usually sufficient to move trapped air to air release
valves and keep the sediment in suspension. Problems associated with high velocities are (1)
erosion of the pipe wall or liner (especially if coarse suspended sediment is present), (2)
cavitation at control valves and other restrictions, (3) increased pumping costs, (4) removal of
air at air release valves, (5) increased operator size and concern about valve shaft failures due
to excessive flow torques, and (6) an increased risk of hydraulic transients. Each of these
should be considered before making the final pipe diameter selection. A typical upper velocity
for many applications if 6 m/sec. However, with proper pipe design and analysis (of the
preceding six conditions), plus proper valve selection, much higher velocities can be tolerated.
A typical upper velocity limit for standard pipes and valves is about 6 m/sec. However, with
proper design and analysis, much higher velocities can be tolerated.
3.2. Pipe Systems
Pipe systems may contain a single pipe with components or multiple interconnected pipes.
3.2.1. Single Pipes
The nature of the solution process for pipe flow problems can depend strongly on which of
the various parameters are independent parameters (“given”) and which is the dependent
parameter (“determine”). The three most common types of problems are shown in Table 3.1
in terms of the parameters involved. It is assumed that the pipe system is defined in terms of
the length of pipe sections used and the number of elbows, bends, and valves needed to
convey the fluid between the desired locations. In all instances it is assumed the fluid
properties are given.
In a Type I problem the desired flowrate or average velocity is specified and the necessary
pressure difference or head loss is determined.
In a Type II problem the applied driving pressure (or, alternatively, the head loss) is specified
and the flowrate is determined.
In a Type III problem the pressure drop and the flowrate is specified and the diameter of the
pipe needed is determined.
34
Table 3.1 – Three most common types of problems
Pipe flow problems in which it is desired to determine the flowrate for a given set of
conditions (Type II problems) often require trial-and-error solution techniques. This is
because it is necessary to know the value of the friction factor to carry out the calculations,
but the friction factor is a function of the unknown velocity (flowrate) in terms of the
Reynolds number.
In pipe flow problems for which the diameter is the unknown (Type III), an iterative
technique is required. This is, again, because the friction factor is a function of the diameter -
through both the Reynolds number and the relative roughness. Thus, neither 4ρQ/πμD nor ε/D
are known unless D is known.
3.2.2. Multiple Pipe Systems
In many pipe systems there is more than one pipe involved. The complex system of tubes in
our lungs or the maze of pipes in a city’s water distribution system are typical of such
systems. The governing mechanisms for the flow in multiple pipe systems are the same as for
the single pipe systems discussed in this chapter. However, because of the numerous
unknowns involved, additional complexities may arise in solving for the flow in multiple pipe
systems. Some of these complexities are discussed under this title.
The simplest multiple pipe systems can be classified into series or parallel flows, as are shown
in Fig. 8.35. The nomenclature is similar to that used in electrical circuits. Indeed, an analogy
35
between fluid and electrical circuits is often made as follows. In a simple electrical circuit,
there is a balance between the voltage (V), current (i), and resistance (R) as given by Ohm’s
law: V=i.R. In a fluid circuit there is a balance between the pressure drop (Δp), the flowrate or
velocity (Q or V), and the flow resistance as given in terms of the friction factor and minor
loss coefficients (f and KL). For simple flow [Δp=f.(L/D).(ρV2/2)], it follows that Δp=Q2.R,
where R, a measure of the resistance to flow, is proportional to f.
Figure 3.1 – (a) Series and (b) paralel pipe systems
The main differences between the solution methods used to solve electrical circuit problems
and those for fluid circuit problems lie in the fact that Ohm’s law is a linear equation
(doubling the voltage doubles the current), while the fluid equations are generally nonlinear
(doubling the pressure drop does not double the flowrate unless the flow is laminar). Thus,
although some of the standard electrical engineering methods can be carried over to help
solve fluid mechanics problems, others cannot.
One of the simplest multiple pipe systems is that containing pipes in series, as is shown in
Fig. 3.1a. Every fluid particle that passes through the system passes through each of the pipes.
Thus, the flowrate (but not the velocity) is the same in each pipe, and the head loss from point
A to point B is the sum of the head losses in each of the pipes. The governing equations can
be written as follows:
36
and
where the subscripts refer to each of the pipes. In general, the friction factors will be different
for each pipe because the Reynolds numbers (Rei=ρViDi/μ) and the relative roughnesses
(εi/Di) will be different. If the flowrate is given, it is a straightforward calculation to determine
the head loss or pressure drop (Type I problem). If the pressure drop is given and the flowrate
is to be calculated (Type II problem), an iteration scheme is needed. In this situation none of
the friction factors, fi, are known, so the calculations may involve more trial-and-error
attempts than for corresponding single pipe systems. The same is true for problems in which
the pipe diameter (or diameters) is to be determined (Type III problems).
Another common multiple pipe system contains pipes in parallel, as is shown in Fig. 3.1b. In
this system a fluid particle traveling from A to B may take any of the paths available, with the
total flowrate equal to the sum of the flowrates in each pipe. However, by writing the energy
equation between points A and B it is found that the head loss experienced by any fluid
particle traveling between these locations is the same, independent of the path taken. Thus, the
governing equations for parallel pipes are
and
Again, the method of solution of these equations depends on what information is given and
what is to be calculated.
Another type of multiple pipe system called a loop is shown in Fig. 3.2. In this case the
flowrate through pipe (1) equals the sum of the flowrates through pipes (2) and (3), or
Q1=Q2+Q3. As can be seen by writing the energy equation between the surfaces of each
reservoir, the head loss for pipe (2) must equal that for pipe (3), even though the pipe sizes
and flowrates may be different for each. That is,
for a fluid particle traveling through pipes (1) and (2), while
for fluid that travels through pipes (1) and (3). These can be combined to give hL2=hL3.
37
Figure 3.2 – Multiple pipe loop system.
This is a statement of the fact that fluid particles that travel through pipe (2) and particles that
travel through pipe (3) all originate from common conditions at the junction (or node, N) of
the pipes and all end up at the same final conditions.
These informations have been introduced for a purpose of a pre-study to branching pipe
subject. Branching pipe will be explained at Chapter 4.
The analysis of piping networks, no matter how complex they are, is based on two simple
principles:
1- Conservation of mass throughout the system must be satisfied. This is done by
requiring the total flow into a junction to be equal to the total flow out of the juction
for all junctions in the system. Also, the flow rate must remain constant in pipes
connected series regardless of the changes in diameters.
2- Pressure drop (and thus head loss) between two junctions must be the same for all
paths between the two juctions. This is because pressure is a point of function and it
cannot have two values at specified point. In practice this rule is used by requiring that
the algebraic sum of head losses in a loop (for all loops) be equal to zero. (A head loss
is taken to be positive for flow in the clockwise direction and negative for flow in
counterclockwise direction.)
38
3.3. Pump Characteristics and Selection
3.3.1.Pump Characteristics
The actual head rise, ha, gained by fluid flowing through a pump can be determined with an
experimental arrangement with using the energy equation with hp=hs-hL where hs is the shaft
work head and is identical to and hL is the pump head loss.
(3.1)
with sections (1) and (2) at the pump inlet and exit, respectively. The head, is the same as
used with the energy equation, where hp is interpreted to be the net head rise actually gained
by the fluid flowing through the pump, i.e. hp= hs-hL. Typically, the differences in elevations
and velocities are small so that:
(3.2)
The power, W, gained by the fluid is given by the equation
(3.3)
and this quantity, expressed in terms of horsepower is traditionally called the water
horsepower. Thus;
(3.4)
Note that if the pumped fluid is not water, the γ appearing in Eq. 3.4 must be the specific
weight of the fluid moving through the pump.
In addition to the head or power added to the fluid, the overall efficiency, η, is of interest,
where
(3.5)
39
The overall pump efficiency is affected by the hydraulic losses in the pump, as previously
discussed, and in addition, by the mechanical losses in the bearings and seals. There may also
be some power loss due to leakage of the fluid between the back surface of the impeller hub
plate and the casing, or through other pump components. This leakage contribution to the
overall efficiency is called the volumetric loss. Thus, the overall efficiency arises from three
sources, the hydraulic efficiency, ηh, the mechanical efficiency, ηm, and the volumetric
efficiency, ηv, so that η= ηh. ηm. ηv
3.3.2. Pump Selection
Optimizing the life of a water supply system requires proper selection, operation, and
maintenance of the pumps. During the selection process, the designer must be concerned
about matching the pump performance to the system requirements and must anticipate
problems that will be encountered when the pumps are started or stopped and when the pipe is
filled and drained. The design should also consider the effect of variations in flow
requirements, and also anticipate problems that will be encountered due to increased future
demands and details of the installation of the pumps.
Selecting a pump for a particular service requires matching the system requirements to the
capabilities of the pump. The process consists of developing a system equation by applying
the energy equation to evaluate the pumping head required to overcome the elevation
difference, friction, and minor losses. For a pump supplying water between two reservoirs, the
pump head required to produce a given discharge can be expressed as
or
in which the constant C is defined by Eq. 2.13. Figure 3.3 shows a system curve for a pipe
having an 82-meter elevation lift and moderate friction losses. If the elevation of either
reservoir is a variable, then there is not a single curve but a family of curves corresponding to
differential reservoir elevations.
40
Figure 3.3 – Pump selection for a single pump
The three pump curves shown in Figure 3.3 represent different impeller diameters. The
intersections of the system curve with the pump curves identify the ßow that each pump will
supply if installed in that system. For this example both A and B pumps would be a good
choice because they both operate at or near their best efficiency range. Figure 3.3 shows the
head and flow that the B pump will produce when operating in that system are 97 m and 450
L/m. The net positive suction head (NPSH) and brake horsepower (bhp) are obtained as
shown in the figure.
The selection process is more complex when the system demand varies, either due to
variations in the water surface elevation or to changing flow requirements. If the system must
operate over a range of reservoir elevations, the pump should be selected so that the system
curve, based on the mean (or the most frequently encountered) water level, intersects the
pump curve near the midpoint of the best efficiency range. If the water level variation is not
too great, the pump may not be able to operate efficiently over the complete flow range.
The problem of pump selection also becomes more difficult when planning for future
demands or if the pumps are required to supply a varying flow. If the flow range is large,
multiple pumps or a variablespeed drive may be needed. Recent developments in variable-
41
frequency drives for pumps make them a viable alternative for systems with varying ßows.
Selection of multiple pumps and the decision about installing them in parallel or in series
depend on the amount of friction in the system. Parallel installations are most effective for
low-friction systems. Series pumps work best in high-friction systems. For parallel pump
operation the combined two pump curve is constructed by adding the flow of each pump.
Such a curve is shown in Figure 3.4 (labeled 2 pumps). The intersection of the two-pump
curve with the system curve identifies the combined flow for the two pumps. The pump
efficiency for each pump is determined by projecting horizontally to the left to intersect the
single-pump curve. For this example, a C pump, when operating by itself, will be have an
efficiency of 83%. With two pumps operating, the efficiency of each will be about 72%. For
the two pumps to operate in the most efficient way, the selection should be made so the
system curve intersects the single-pump curve to the right of its best efficiency point.
Starting a pump with the pipeline empty will result in filling at a very rapid rate because
initially there is little friction to build backpressure. As a result, the pump will operate at a
ßow well above the design flow. This may cause the pump to cavitate, but the more serious
problem is the possibility of high pressures generated by the rapid filling of the pipe.
Provisions should be made to control the rate of filling to a safe rate. Start-up transients are
often controlled by starting the pump against a partially open discharge valve located near the
pump and using a bypass line around the pump. This allows the system to be filled slowly and
safely. If the pipe remains full and no air is trapped, after the initial filling, subsequent start-up
of the pumps generally does not create any serious problem. Adequate air release valves
should be installed to release the air under low pressure.
42
Figure 3.4 – Selection of paralel pumps
For some systems, stopping the pump, either intentionally or accidentally, can generate high
pressures that can damage the pipe and controls. If the design process does not consider these
potential problems, the system may not function trouble free. Downtime and maintenance
costs may be high. Not all systems will experience start-up and shutdown problems, but the
design should at least consider the possibility. The problem is more severe for pipelines that
have a large elevation change and multiple high points. The magnitude of the transient is
related to the length and profile of the pipeline, the pump characteristics, the magnitude of the
elevation change, and the type of check valve used. The downsurge caused by stopping the
pump can cause column separation and high pressures due to flow reversals and closure of
the check valves. Surge-protection equipment can be added to such systems to prevent
damage and excessive maintenance.
Selection of the proper pump will improve reliability, extend the economic life of the system,
and reduce maintenance. Failure to complete a transient analysis and include the required
controls will have the opposite effect. A system is only as good as it is designed to be.
43
3.3.3. Revision of Energy Equation
When a piping system involves a pump, the steady-flow energy equation on a unit mass basic
can be expressed as:
where =Wpump/g is the useful pump head delivered to the fluid and hL is the total head
loss in piping (including minor losses if they are significant) between points (1) and (2). The
pump head is zero if the piping system does not involve a pump.
Many practical piping systems involve a pump to move a fluid from one reservoir to another.
Taking points (1) and (2) to be free surfaces of the reservoirs, the energy equation in this case
reduces for useful pump head:
since the velocities at free surfaces are negligible and the pressures are atmospheric pressure.
Therefore, the useful pump head is equal to the elevation difference between the two
reservoirs plus the head loss. If the head loss is negligible compared to , the useful
pump head is simply equal to elevation difference between two reservoirs.
44
CHAPTER 4
4. BRANCHING PIPES DESIGN
4.1. Problem Statement
Figure 4.1. – Shematic Representation of Branching Pipes Water Supply System
45
As it shown in Figure 4.1 the basic structure of four branched system is being considered at
this chapter. This system can be a pilot project to industry applications such as water demand
of workers which are working on different elevations at big construction fields, AC plants and
cooling towers, river water pumping, agricultural farming etc. In objective case, they have the
same principle and similar aim which is selection of suitable pump.
In this system, there is water usage at each tank which is shown in informations as outer
volume flow rate.
When looked to the catalogs for select a suitable pump, it is clearly seen that two distinct
property is needed which are required volume flow rate and head loss of pump. Before
proceeding to calculation subject of these two properties, necessary informations and
explanations of abbreviations are given below.
WSElnormal : Normal Water Surface Elevation
WSElmin : Minimum Water Surface Elevation
Qout : Outer Volume Flow Rate
QP : Volume Flow Rate of Pump
L : Length of Pipe
D : Diameter of Pipe
ε : Roughness of Pipe
A : Cross-Section Area
f : Friction Factor
V : Volume
Tank A Tank B Tank C Tank D
WSElnormal 32 m 28 m 24 m 18 m
WSElmin 22 m 20 m 16 m 12 m
Diameter (d) 16 m 10 m 8 m 10 m
Qout 0,08 m3/s 0,06 m3/s 0.04 m3/s 0,06 m3/s
Table 4.1. – Necessary Informations of Branching Pipes System
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4.2. Calculation of Project
First of all it is known that QP and hp must be determined for selection of pump and so, as a
start, QP can be calculated as:
QP = QA + QB + QC
Determination of volume flow rate of Tank A:
Qout,A = 0,08 m3/s = 288 m3/h
Volume of water which is out of tank after eight hour:
Vout,A =
Vout,A = 2304 m3
Volume of water between normal elevation and minimum elevation:
VA =
VA =
VA = 2010,61 m3
Amount of water requirement from pump to Tank A during eight hour:
Vreq,A = Vout,A – VA
Vreq,A = 2304 – 2010,61 m3
Vreq,A = 293,39 m3
QA = Vreq,A / 8 hr
QA = 0,010 m3/s = 36,673 m3/hr
Determination of volume flow rate of Tank B:
Qout,B = 0,06 m3/s = 216 m3/h
Volume of water which is out of tank after eight hour:
Vout,B =
Vout,B = 1728 m3
Volume of water between normal elevation and minimum elevation:
VB =
47
VB =
VB = 628,31 m3
Amount of water requirement from pump to Tank B during eight hour:
Vreq,B = Vout,B – VB
Vreq,B = 1728 – 628,31 m3
Vreq,B = 1099,69 m3
QB = Vreq,B / 8 hr
QB = 0,038 m3/s = 137,46 m3/hr
Determination of volume flow rate of Tank C:
Qout,C = 0,04 m3/s = 144 m3/h
Volume of water which is out of tank after eight hour:
Vout,C =
Vout,C = 1152 m3
Volume of water between normal elevation and minimum elevation:
VC =
VC =
VC = 402,12m3
Amount of water requirement from pump to Tank C during eight hour:
Vreq,C = Vout,C – VC
Vreq,C = 1152 – 402,12 m3
Vreq,C = 749,88 m3
QC = Vreq,C / 8 hr
QC = 0,026 m3/s = 93,73 m3/hr
After these determinations volume flow rate of pump can be easily calculated:
QP = QA + QB + QC
QP = 0,010 m3/s + 0,038 m3/s + 0,026 m3/s
QP = 0.074 m3/s = 266,4
According to previous page calculations, flow rate distribution on each pipe can be shown.
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Pipe 1 Pipe 2 Pipe 3 Pipe 4 Pipe 5
Length (L) 1000 m 1400 m 1800 m 2200 m 1600 m
Diameter (D) 0,35 m 0,35 m 0,2 m 0,3 m 0,3 m
Roughness (ε) 3,0 mm 3,0 mm 3,0 mm 3,0 mm 3,0 mm
Flow Rate (Q) 0,074 m3/s 0,074 m3/s 0,038 m3/s 0,010 m3/s 0,026 m3/s
Table 4.2. – Flow Rate Distribution and Other Informations of Pipes
Second step is calculation of head loss of pump and on this purpose, Bernoulli equation must
be written between Tank A which is at the highest elevation of the system and Tank D.
Where ρwater = 1000 kg/m3 , zD = WSElnormal,D and zA = WSElnormal,A.Also Noting that the fluid at
both surfaces of tanksa re open to atmosphere and thus PD = PA = Patm. And because of the
velocities at wide tanks can be assumed as zero, VD = VA = 0. So, Bernoulli equation yields:
hpump = (zA – zD) + hL,total
Here it is, elevation differences are known but not hL,total. Calculation of this loss is:
hL,total = hL,major + hL,minor
hL,major =
Before identify friction coefficient f, first look to the flow in pipes which is laminar or
turbulent with Reynold number. μ = 1,002x10-3 kg/m.s
V1 =
49
V2 =
V3 =
V4 =
V5 =
As it can seen all of the Reynold number of pipes are higher than critical Re value and thus
flow is turbulent. Which means Moody diagram should be used to find friction factor, f.
50
hL,major =
hL,major = 38,473 m
hL,minor =
Where KL = 1,5 from Table 2.3 for branch tol ine condition and so:
hL,minor = 0,045 + 0,045 + 0,111 + 0,001 + 0,01
hL,minor = 0,212
hL,total = hL,major + hL,minor = 38,473 + 0,212 = 38,685 m
hpump = (zA – zD) + hL,total
hpump = (32 – 18) + 38,685
hpump = 52,685 m
With the help of Figure 3.3 and Standard pump selection program, pump can be selected as:
SNM 100 – 200 (3000) Singlestage Centrifugal Pump
QP = 266,4 m3/hr
hmax = 70 m
ηpump = 80%
N = 3000 rpm
Wpump,shaft =
51
Figure 4.2. – Feasibility of Pump with Checking Power-Flow Rate Comparison
Figure 4.3. - Feasibility of Pump with Checking Head Loss-Flow Rate Comparison
52
REFERENCES
1. Munson, B.R. Young D.F. and Okiishi T.H. Fundamentals of Fluid Mechanics, 4th
Ed., John Wiley & Sons Inc., New York, 2002.
2. Hinze, J. O. Turbulence, 2nd Ed., McGraw-Hill, New York, 1975.
3. White, F. M. Fluid Mechanics, 4th Ed. McGraw-Hill, New York, 1979.
4. Moody, L. F. Friction Factors for Pipe Flow, Transactions of the ASME, Vol.66.1944
5. Streeter, V. L. and Wylie, E. B. Fluid Mechanics, 8th Ed. McGraw-Hill, New York,
1985.
6. Jeppson, R. W. Analysis of Flow in Pipe Networks, Ann Arbor Science Publishers,
Ann Arbor, Mich., 1976.
7. Hydraulic Institute, Engineering Data Book, 1st Ed., Cleveland Hydraulic Institute,
1979.
8. Karassick, I. J. Pump Handbook, 2nd Ed., McGraw-Hill, New York, 1985.
9. Nikuradse, J. Stomungsgesetz in Rauhen Rohren, VDIForschungsch, No. 361
10. Riley, W. F. and Sturges, L. D. Engineering Mechanics:Dynamics, 2nd Ed., Wiley,
New York, 1996.
11. Çengel, Y. A. and Cimbala, J. M. Fluid Mechanics, 4th Ed., McGraw-Hill, New York.
12. Thorley, A. R. D. Fluid Transients in Pipeline Systems, D&L, England, 1991.
13. Watters, G. Z. Analysis and Control of Unsteady Flow in Pipelines, 2nd Ed.,
Butterworths, Massachusetts, 1984.
14. Chaudry, M. H. Applied Hydraulic Transients, 2nd Ed., Van Nostrand Reinhold, New
York, 1987.
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