Chapter 6 - Hydraulic Machinery
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Transcript of Chapter 6 - Hydraulic Machinery
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CHAPTER 6
HYDRAULIC MACHINERY
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2INTRODUCTION
What is turbine?
Turbine is a hydraulic machine that utilises the energy of fluids to move other types of machineries.
An example of turbine usage can be seen in a hydroelectric power plant.
Turbines are generally divided into Impulse and Reaction turbines.
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3INTRODUCTION
Impulse turbines
This turbine derive its energy
from a jet of water exiting out of
a nozzle and shooting at the
blades of the turbine. The most
common type is Pelton Wheel
Turbine and its suitable for
medium head and low
discharge.
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4INTRODUCTION
Reaction turbines
A reaction turbine derives its power from the equal
and opposite reactive power of fluid passing between
its blades and classified in 3 types of flows which are
radial, axial and mixed flow. Two popular types are
the Francis turbine and the propeller turbine.
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5INTRODUCTION
Francis turbines are effective on a very wide range of
heads (medium head) and are very much used in spite
of their relatively high cost. Usually work in radial flow
but also can in mixed flow.
A propeller (Kaplan) turbine is an axial flow machine
with its runner confined in a closed conduit. A propeller
turbine is often set on a vertical axis, and can also be
set on a horizontal axis or a slightly inclined axis. A
propeller turbine is suitable for operation with low head
and large amount of discharge.
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6What is pump?
Pump is a hydraulic machine which supply energy
to fluid in certain operation.
An example of pump usage can be seen in such as
in water distribution system.
Pumps are generally divided into positive
displacement and rotodynamic pumps.
INTRODUCTION
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7Rotodynamic pumps consist of a rotating device known as an impeller. The fluid that needs to be pumped enters a casing near the shaft of the impeller. Vanesattached to the spinning impeller increases the velocity of the pumped fluid and moves the fluid out through an outlet.
The most common and popular pump under the rotodynamic pump category is the centrifugal pumpand the propeller pumps.
INTRODUCTION
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8Centrifugal pumps produce radial flow and
mixed flow according to the fluid path. Thus,
centrifugal pumps are also referred to as
radial and mixed flow pumps.
Meanwhile, propeller pumps also consist of
an impeller, which produces axial flow for the
fluid.
INTRODUCTION
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9POWER AND EFFICIENCY OF PUMP
Figure below shows the process of pump in a operation.
The mechanical energy through the shaft and impeller is
converted to fluid energy. The difference between the total
energy heads at the intake and discharge flanges of the
pump is denoted as net head, H developed in the pump.
The intake end (inlet flow), of a pump is commonly known
as a suction end while the discharge end (outlet flow) of a
pump is called a delivery end.
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10
POWER AND EFFICIENCY OF PUMP
The equation below shows the relationship between a
suction head and a discharge head.
g
Vz
P
g
Vz
PHHH ss
sdd
dsd
22'
22
Where:
b = width
Vf= V sin = flow velocity
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11
POWER AND EFFICIENCY OF PUMP
The power absorbed by the water from the actions of an
impeller is given as shown on the right.
Power at suction end also known as power in while
power at discharge end is called power out.
Where:
Vu = V cos = swirl velocity
= rate of shaft rotation in radians per second
Ps = Pi Pd = Po
Note :
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12
POWER AND EFFICIENCY OF PUMP
power Brakeshafttheintopowerfluidthetodeliveredpower
0
Hmv
s
dO
P
P
The overall efficiency of a pump is given as,
However, the sum of hydraulic, volumetric and
mechanical efficiency also yields the overall efficiency
for a pump. Thus, the overall efficiency of a pump
can also be written shown below.
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13
EXAMPLE 10.1
A centrifugal pump is needed to supply 23m3/s ofwater for a city. This operation will utilise a net head Hof 20 m with a specific speed N of 450 rpm. Given thatthe inflow power Ps is 5000 kW, calculate
a) Outflow power, Pdb) The overall efficiency, oAssume that the density of water is 1000 kg/m3 at 5oC.
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14
EXAMPLE 10.1
Outflow Power, Po
= 1000 X 9.81 X 23 X 20
= 4512.6 kW
'QHPo
100% x i
oo
P
P
o
100%5000
6.4512x
Overall Efficiency
= 90.3%
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15
CHARACTERISTICS OF PUMP CURVE
The efficiency of a pump varies considerably
depending upon the conditions under which it must
operate. It is important to have information regarding
the performance of various pumps when selecting a
pump for a given situation. Though some centrifugal
pumps are driven by variable speed motors, the usual
mode of operation of pump is at constant speed.
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16
CHARACTERISTICS OF PUMP CURVE
The characteristic curve of
pump and other performance
curves for a typical mixed-
flow centrifugal pump are
shown in figure on the right.
Curves such as shown in the
figure are usually determined
by pump manufacturers
through laboratory testing.
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17
CHARACTERISTICS OF PUMP CURVE
Relationship between power input, P, efficiency, and head, H starts when intake pipe valve closed,
impeller will spin the water until pressure at pump
output point increase to maximum head (shut-off
head).
Then when the valve open, water will flow through
the pipe and the head of pump will decrease.
With addition of flow rate, the pump efficiency will
increase until reach maximum and then decrease to
end of operation.
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18
CHARACTERISTICS OF PUMP CURVE
Intersection between head and power corresponds to
the point of optimum efficiency is the best point to
use pump or BEP (best efficiency point).
This particular pump has a normal capacity or rated
capacity of 10 500 gpm when developing a normal
head of 60 ft at an opening speed of 1450 rpm.
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19
CAVITATION
An important factor in the satisfactory operation of apump is the avoidance of cavitation, both for the goodefficiency and for the prevention of impeller damage.
As liquid passes through the impeller of a pump, thereis a change in pressure. If the absolute pressure ofthe liquid drops the vapour pressure, cavitation willoccur.
The region of vaporization hinders the flow andplaces a limit on the capacity of the pump.
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20
As the fluid moves further into a region of higher
pressure, the bubbles collapse and the implosion of
the bubbles may cause pitting of the impeller.
Cavitation is most likely to occur near the point of
discharge (periphery) of radial flow and mixed flow
impellers, where velocities are highest.
It may also occur on the suction side of the impeller,
where the pressures are the lowest.
CAVITATION
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21
PARALLEL PUMP
However, the head, h (pressure head) is same in
both pumps and will be the net head of combined
discharge.
If two similar pumps A and B are connected in
parallel, the combined discharge will be the sum of
individual discharges QA and QB.
Qtotal = QA + QB
htotal = hA = hB
Qtotal = QA + QB
htotal = hA = hB
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22
SERIES PUMP
If two similar pumps 1 and 2 are connected in
series, the discharge will not change and the head
will added up.
Qtotal = QA = QB
htotal = hA + hB
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23
SIMILITUDE
Similitude is also used in the design and analysis
of turbines and pump.
Similarity laws help us interpret the results of model studies. The relation between model and prototype is classified into three:
Geometry Similarity, Kinematics Similarity and Dynamic Similarity
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24
SIMILITUDEGEOMETRY SIMILARITY - The prototype and model
have identical shapes but differ only in size.
KINEMATIC SIMILARITY - ratio of velocities at all
corresponding points in flow are the same and
involve length and time.
DYNAMIC SIMILARITY-Two systems have
dynamic similarity if, in addition to dynamic
similarity, corresponding forces are in the
same ratio in both.
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25
SCALE RATIO
MODEL (m)
- Similar with object/structure required in certain
scale ratio.
- tested in laboratory and similar in real
phenomenon.
- not necessary its smaller than prototype
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26
SCALE RATIO
PROTOTAIP (p) - object/actual structure- tested in actual phenomenon, example:
structure in open channel, ship etc
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27
ADVANTAGES USING SIMILARITY
1. Performances of object can be predicted.2. Economy and easy to build, where design
of model can be done many times until reach a certain values.
3. Nonfunctional structure also can be measured such as dam.
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28
SIMILARITY (PUMP)
In similarity relations, the basic repeating variables are
rotative speed (N) and pump diameter (D). Therefore,
the similitude laws for head (H), discharge (Q), and
power (P) can be expressed as below.
2222
mp
p
mm
m
ND
H
ND
H
3535
ppp
p
mmm
m
ND
P
ND
P
33
pp
p
mm
m
DN
Q
DN
Q
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29
SIMILARITY (PUMP)
From the given laws of similitude, we conclude that any
two homologous pumps would have the same specific
speed (Ns).
Therefore, the relationship between a prototype pump
and its geometric model satisfy the following equation.
sp/p
pp
/m
mmsm N
H
QN
H
QNN
4343
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30
Two homologous pumps A and B use an operation
at the speed of 600 rpm. Pump A has an impeller
with a 50 cm diameter and discharges 0.4 m3/s of
water under a net head of 50 m. Determine the
size of pump B and its net head if it is to discharge
0.3m3/s.
EXAMPLE 10.2
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31
EXAMPLE 10.2
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32
SIMILARITY (TURBINE)
The characteristic relationships between a turbine
model and its prototype can be expressed in terms of
variables as shown below.
p
pp
m
mm
H
DN
H
DN
33
pp
p
mm
m
DN
Q
DN
Q
3535
pp
p
mm
m
ND
P
ND
P
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33
SIMILARITY (TURBINE)
Thus, we conclude that two homologous turbines have
the same specific speed Ns. Therefore
sp/p
pp
/m
mmsm N
H
PN
H
PNN
4545
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34
A 1:5 model of turbine develops 2 kW of power at
400 rpm under head of 3.0 m. What is the specific
speed? Assuming the overall efficiency of 0.85 for
both the model and prototype, calculate the
rotational speed, power and discharge of the
prototype when run under a head of 20 m?
EXAMPLE 10.3
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35
EXAMPLE 10.3
3.1433
24004/54/5
m
mm
SH
PNN
rpmN
N
p
p
6.206
20
)5(
3
)1)(400(
Specific Speed
Speed
p
pp
m
mm
H
DN
H
DN
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36
EXAMPLE 10.4
kWP
Pk
p
p
2.861
)6.206()5()400()1(
23535
Power
Discharge
mmom HQP
3535
pp
p
mm
m
ND
P
ND
P
smQ
Qxx
m
m
/0799.0
)3)()(85.0)(100081.9(10002
3
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37
EXAMPLE 10.4
33
pp
p
mm
m
DN
Q
DN
Q
Discharge
smQ
Qx
Q
p
p
p
/159.5
2582510998.1
)5)(6.206()1)(400(
0799.0
3
4
33
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38
UNIT QUANTITIES
(a)Unit Discharge
Unit discharge Qu is defined as the flow rate of a geometrically similar turbine which is run under a head of 1 m
SIMILARITY (TURBINE)
H
QQu
1
1
H
Q
2
2
H
Q
If comparing between 2 turbine, the equation will be as below.
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39
UNIT QUANTITIES
(b)Unit Speed
Unit speed Nu is defined as the speed of a
geometrically similar turbine which is run under a
head of 1 m
SIMILARITY (TURBINE)
If comparing between 2 turbine, the equation will be as
below.
H
NNu
1
1
H
N
2
2
H
N
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40
UNIT QUANTITIES
(c)Unit Power
Unit power Pu is defined as the power of a geometrically similar turbine which is run under a head of 1 m
SIMILARITY (TURBINE)
If comparing between 2 turbine, the equation will be as
below.
2/3H
PPu
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41
A Francis turbine produces 6750 kW at 300 rpm
under a net head of 45 m with an overall efficiency
of 85%. Determine the revolution per-minute (rpm),
discharge and brake power of the same turbine
under a net head of 60 m under homologous
conditions.
EXAMPLE 10.5
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42
EXAMPLE 10.5
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43
EXAMPLE 10.5