ME9
ME9
FLUID MACHINERY
FLUID MACHINERY
“The school system has it‟s own definition of what
“The school system has it‟s own definition of what
a ge
a geni
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t may not be the s
the same de
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tion of your
of your ge
geni
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us.
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Dif ferent genius come
ferent genius comes out in
s out in diff
diff e
erent environments.
rent environments.
Thomas Edison‟s genius came out in a
Thomas Edison‟s genius came out in a
labor
labor atory an
atory an d Stev
d Steve
e
Jobs ge
Jobs geni
ni us
us
came out in his family‟s garage where he started
came out in his family‟s garage where he started
Appl
Appl e
e computers.
computers. M
M ark Z
ark Z uckerberg create
uckerberg created Facebook in hi
d Facebook in hi s
s
college do
college dorm
rm room
room as
as he create
he created a way for
d a way for hi
hi s fellow students
s fellow students
to connect and communi
to connect and communi cate
cate..
”
”
- Robert T.
CHAPTER 1 CHAPTER 1
Basic Energy Equations
Basic Energy Equations
1. Pressure head, h 1. Pressure head, hPP Figure 1.1 Figure 1.1 P = P = ρρff
h hPP, h, hPP = =
Where, P = gage pressure Where, P = gage pressure
h
hPP = pressure head = pressure head
ɣ
ɣ
= weight density= weight densityɣ
ɣ
ff = weight density of fluid = (S.G.)( = weight density of fluid = (S.G.)(ɣ
ɣ
waterwater))Where,
Where,
ɣ
ɣ
ww = 9.81 = 9.81
= 62.4 = 62.4
Exercise #1:
Exercise #1: What is the pressure of a 100 cmWhat is the pressure of a 100 cm column of water?
column of water?
2. Velocity head, h
2. Velocity head, h V V - Torri - Torricelli’s Theorem:celli’s Theorem:
“The velocity of a liquid which discharges under a “The velocity of a liquid which discharges under a
head is equal to the velocity of a body which falls head is equal to the velocity of a body which falls in the same head
in the same head.”.”
h hvv = =
, v =, v =
Where, hWhere, hvv = velocity head = velocity head
v = velocity of fluid v = velocity of fluid g = 9.81 g = 9.81
= 32.2 = 32.2
Exercise #2:Exercise #2: Determine the velocity of the liquid in aDetermine the velocity of the liquid in a tank at the bottom, given that surface h = 7m.
3. Volume flow, Q 3. Volume flow, Q Figure 1.2 Figure 1.2 Q = (A Q = (A
v) = v) =
Where, A = cross-sectional area Where, A = cross-sectional area
v = velocity v = velocity
Q = volume flow rate Q = volume flow rate Flow through nozzle:
Flow through nozzle: Q = C
Q = Cdd
A A
v vWhere, v = Where, v =
C
Cdd = coefficient of discharge = coefficient of discharge
Exercise #3:
Exercise #3: Water is flowing through a cast iron Water is flowing through a cast iron pipe at the rate of 3500 GPM. The inside diameter of pipe at the rate of 3500 GPM. The inside diameter of pipe is 6 in. Find the flow velocity.
pipe is 6 in. Find the flow velocity.
4. Power of a jet, P 4. Power of a jet, P Figure 1.3 Figure 1.3 P = P =
ɣ
ɣ
Q Q
h h Where, P = Power Where, P = Powerɣ
ɣ
= Weight density = = Weight density = ρρgg 5. For bubbles5. For bubbles
Figure 1.4 Figure 1.4
A. T = c (Isothermal) if T is not given: A. T = c (Isothermal) if T is not given:
P
P11VV11 = P = P22VV22
B. Use any process if T is given: B. Use any process if T is given:
= =
Where, P
Where, P11 = =
ɣ
ɣ
h + Ph + Patmatm *absolute *absolute PPP
6. Bernoulli’s Energy Theorem
6. Bernoulli’s Energy Theorem - - neglectingneglecting friction, the total head or total amount of energy friction, the total head or total amount of energy per unit weight, is the same at every point in the per unit weight, is the same at every point in the path of flow. path of flow. Figure 1.5 Figure 1.5 h hTT = h = hPP + h + hvv + z + z
Where, z = elevation head Where, z = elevation head
Using continuity flow equation: Using continuity flow equation:
Q
Q11 = Q = Q22 or A or A11vv11 = A = A22vv22
+ +
+ z + z11 = =
+ +
+ z + z227. Viscosity,
7. Viscosity,
–– resistance to flow or the resistance to flow or the property to resist shear deformation.property to resist shear deformation. A. Absolute or dynamic viscosity,
A. Absolute or dynamic viscosity,
–– viscosity viscosity which is determined by direct measurement of shear which is determined by direct measurement of shear resistance in resistance in
or or
.. B. Kinematic Viscosity,B. Kinematic Viscosity,
–– absolute viscosity absolute viscosity divided the density individed the density in
..8
8. Reynold’s Number, N. Reynold’s Number, NR R
N
NRR = =
(dimensionles
(dimensionless)
s)
Where, N
Where, NRR < 2000 - Laminar Flow < 2000 - Laminar Flow N
NRR > 4000 - Turbulent Flow > 4000 - Turbulent Flow
v = velocity of fluid v = velocity of fluid
D = internal diameter of pipe D = internal diameter of pipe Exercise #4:
Exercise #4: Water is flowing in a pipe with radius Water is flowing in a pipe with radius of 30 cm at a velocity of 5 m/s. The viscosity of of 30 cm at a velocity of 5 m/s. The viscosity of water is 1.17 Pa-s. What is the Reynolds Number? water is 1.17 Pa-s. What is the Reynolds Number?
9. Friction head loss, h
9. Friction head loss, hLL
A.
A. Using Morse Equation:Using Morse Equation:
h
hLL = =
B.
B. Using Darcy’s Equation:Using Darcy’s Equation:
h
Where, h
Where, hLL = friction head loss = friction head loss
f = coefficient of friction or friction factor f = coefficient of friction or friction factor L = pipe length L = pipe length g = 9.81 g = 9.81
= 32.2 = 32.2
C.C. Pressure drop in the pipe, PPressure drop in the pipe, Pdd
P
Pdd = =
ɣ
ɣ
hhLLExercise #5:
Exercise #5: Water is flowing at a rate of 3,500 GPM.Water is flowing at a rate of 3,500 GPM. The inside radius is 8 cm and coefficient of friction The inside radius is 8 cm and coefficient of friction is 0.0181. What is the pressure drop over a length of is 0.0181. What is the pressure drop over a length of 50 m?
50 m?
Venturi-meter
Venturi-meter - is used to measure the volume of - is used to measure the volume of flow.
flow.
Pitot tube - is used to measure the velocity of Pitot tube - is used to measure the velocity of flow.
flow.
Q = A
Q = A11vv11 = A = A22vv22
For circular cross-section: A =
For circular cross-section: A =
For rectangular
For rectangular cross-section
cross-section:
:
A = bhA = bh Where,Where, ρρ = =
in
in
A. If
A. If venturi-meter is horizontal:
venturi-meter is horizontal:
Figure 1.6 Figure 1.6
= =
B. If venturi-meter is vertical B. If venturi-meter is vertical Figure 1.7 Figure 1.7
= =
- (z - (z11 - z - z22)) Where, PWhere, P11 = inlet pressure = inlet pressure
P
P22 = throat pressure = throat pressure
Exercise #6:
Exercise #6: A perfect venturi with throatA perfect venturi with throat diameter of 2 in. is placed horizontally in a pipe diameter of 2 in. is placed horizontally in a pipe with 2 inches is placed horizontally in a pipe with 2 inches is placed horizontally in a pipe with 6 inches inside diameter. What is the with 6 inches inside diameter. What is the difference between the pipe and venturi throat difference between the pipe and venturi throat static pressure if the mass flow rate of water is static pressure if the mass flow rate of water is 100 lb/sec?
100 lb/sec?
Bouyancy
Bouyancy - Archimedes Principle: A body partly or- Archimedes Principle: A body partly or wholly submerged in a liquid is buoyed up by a force wholly submerged in a liquid is buoyed up by a force equal to the weight of the liquid displaced.
equal to the weight of the liquid displaced. A. Weight of object in air
A. Weight of object in air
Figure 1.8 Figure 1.8
W
Woo = =
ooVVooWhere,
Where,
oo = weight density of object = SG = weight density of object = SGoo
wwV
Voo = total volume of object = total volume of object
B. If the object is floating B. If the object is floating
Figure 1.9 Figure 1.9 BF = bouyant force = W
BF = bouyant force = Woo = =
ɣ
ɣ
ffVVdd = =ɣ
ɣ
ooVVooWhere,
Where, ρρff = density of fluid = SG = density of fluid = SGff
ρρwwV
Vdd = volume displaced = volume displaced
V
Exercise #7:
Exercise #7: A 2 meter rod floats vertically in water.A 2 meter rod floats vertically in water. It has a 7 cm
It has a 7 cm22 cross sectional and a specific gravity cross sectional and a specific gravity
of 0.6. What length, L, is submerged? of 0.6. What length, L, is submerged?
C. If the object is submerged C. If the object is submerged
Figure 1.9.1 Figure 1.9.1 BF = BF =
ɣ
ɣ
ffVVoo W Woo = =ɣ
ɣ
ooVVoo R + BF = W R + BF = WooWhere, R = weight of object in water Where, R = weight of object in water
V Voo = V = Vdd
Exercise #8:
Exercise #8: What is the buoyant force of a bodyWhat is the buoyant force of a body that weighs 100 kg in air and 70 kg in water?
L
L ao Tz
ao Tzu, the Chin
u, the Chin es
ese
e fou
fou nder of Taoi
nder of Taoi s
sm
m
in t
in t he 5th Ce
he 5th Centu
ntu ry BC, state
ry BC, stated:
d:
“If you give a man a fish, you feed him for a day.
“If you give a man a fish, you feed him for a day.
If you teac
If you teach a man to fish y
h a man to fish you feed h
ou feed him for a lifetime.”
im for a lifetime.”
“
“
Ar
Ar e
e our schools fail
our schools fail in
in g to te
g to teach pe
ach people to
ople to fi
fi s
sh?
h?
Or ar
Or ar e o
e our
ur s
schools teac
chools teachi
hi ng students
ng students that th
that th ey
ey are
are
e
entitl
ntitl e
ed to their daily f
d to their daily f ish?
ish?
II s this why th
s this why th ere are more and more peo
ere are more and more people are
ple are
de
depe
pendent upon th
ndent upon th e
e gove
govern
rn ment for
ment for lili fe s
fe support
upport ?
?
”
”
- RTK
- RTK
“
“
Ask not what your country can do for you -
Ask not what your country can do for you
-Ask what
Ask what
you can d
you can do for your c
o for your country.”
ountry.”
- President John Kennedy
- President John Kennedy
CHAPTER 2 CHAPTER 2
Hydro-electric Power
Hydro-electric Power
Hydraulics - branch of mechanics which deals with the Hydraulics - branch of mechanics which deals with the laws governing the behavior of water and other
laws governing the behavior of water and other liquids in the states of rest and motion. liquids in the states of rest and motion.
Hydrostatics - is a branch of hydraulics which deals Hydrostatics - is a branch of hydraulics which deals on the study of fluids at rest.
on the study of fluids at rest.
Hydrokinetics - branch of hydraulics which deals with Hydrokinetics - branch of hydraulics which deals with the study of pure motion in liquids.
the study of pure motion in liquids.
Hydrodynamics - branch of hydraulics which deals with Hydrodynamics - branch of hydraulics which deals with the study of forces exerted by or upon liquids in the study of forces exerted by or upon liquids in motion.
motion.
Cohesion - is a fluid property which refers to the Cohesion - is a fluid property which refers to the intermolecular attraction by which the separate intermolecular attraction by which the separate particles of the fluid are held together.
particles of the fluid are held together.
Adhesion - is a fluid property which refers to the Adhesion - is a fluid property which refers to the attractive force between the molecules and any solid attractive force between the molecules and any solid substance with which they are in contact.
substance with which they are in contact.
Surface tension - is the force per unit length that Surface tension - is the force per unit length that
an “imaginary film” formed on the surface of a liquid an “imaginary film” formed on the surface of a liquid
due to intermolecular attraction is capable of due to intermolecular attraction is capable of exerting.
exerting.
Fluid Mechanics - is a branch of science which deals Fluid Mechanics - is a branch of science which deals with the study of water and other fluids that are at with the study of water and other fluids that are at rest or in motion.
rest or in motion. Reservoir
Reservoir - stores the water coming from the opper- stores the water coming from the opper river or waterfalls.
river or waterfalls.
Spillway - a weir in the reservoir which discharges Spillway - a weir in the reservoir which discharges excess water so that the head of the plant will be excess water so that the head of the plant will be maintained.
Dam - a concrete structure that encloses the Dam - a concrete structure that encloses the reservoir.
reservoir.
Silt sluice - a chamber which collects the mud and Silt sluice - a chamber which collects the mud and through which the mud is discharged.
through which the mud is discharged.
Trash rack - a screen which prevents the leaves, Trash rack - a screen which prevents the leaves, branches and other water contaminants to enter into branches and other water contaminants to enter into the penstock.
the penstock.
Surge chamber - a standpipe connected to the Surge chamber - a standpipe connected to the
atmosphere and attached to the penstock so that the atmosphere and attached to the penstock so that the water will be at atmospheric pressure.
water will be at atmospheric pressure.
Penstock - the channel that leads the water from the Penstock - the channel that leads the water from the reservoir to the turbine.
reservoir to the turbine.
Turbine - converts the energy of the water into Turbine - converts the energy of the water into mechanical energy.
mechanical energy.
Generator - converts the mechanical energy of the Generator - converts the mechanical energy of the turbine into electrical energy output.
turbine into electrical energy output.
Draft tube - connects the turbine outlet to the Draft tube - connects the turbine outlet to the tailwater so that the turbine can be set above the tailwater so that the turbine can be set above the tailwater level. Used to keep the turbine up to 15 tailwater level. Used to keep the turbine up to 15 ft. above the tail water surface.
ft. above the tail water surface.
Tailrace - a channel which leads the water from the Tailrace - a channel which leads the water from the turbine to the tailwater.
turbine to the tailwater.
Tailwater - the water is discharged from the turbine. Tailwater - the water is discharged from the turbine. Peripheral coefficient - ratio of the peripheral Peripheral coefficient - ratio of the peripheral velocity of the runner over the velocity of the jet. velocity of the runner over the velocity of the jet. Water hammer - caused because of sudden stoppage of Water hammer - caused because of sudden stoppage of water flow in a pipe.
water flow in a pipe.
Surge tank - artificial reservoir used to relieve the Surge tank - artificial reservoir used to relieve the pipe line of excessive pressure.
pipe line of excessive pressure.
Wicket gates - control the power and speed of turbine Wicket gates - control the power and speed of turbine
Cavitation - occurs then the pressure at any point Cavitation - occurs then the pressure at any point in the flowing water drops below the vapor
in the flowing water drops below the vapor pressure of the water which varies with pressure of the water which varies with temperature.
temperature.
Weir - any obstruction of a stream flow over which Weir - any obstruction of a stream flow over which water flows.
water flows. Types of turbine: Types of turbine:
1. Propeller turbine (for small capacity)
1. Propeller turbine (for small capacity) - axial - axial
flow turbines have low heads up to 110 ft., high flow turbines have low heads up to 110 ft., high rotational speeds and large flow rates. This rotational speeds and large flow rates. This
turbine operates with specific speeds in the range turbine operates with specific speeds in the range of 80 and 200 rpm range. But best efficiencies is of 80 and 200 rpm range. But best efficiencies is between 120 and 160 rpm.
between 120 and 160 rpm.
2. Reaction turbines or francis turbine (for 2. Reaction turbines or francis turbine (for medium capacity)
medium capacity) - the specific speed varies from - the specific speed varies from 10 to 100. Best efficiencies are found in the 40 10 to 100. Best efficiencies are found in the 40 to 60 range. Heads between 110 to 800 ft.
to 60 range. Heads between 110 to 800 ft. 3. Impulse turbine (for large capacity)
3. Impulse turbine (for large capacity) - radial - radial flow or Pelton Wheel turbines have the lowest flow or Pelton Wheel turbines have the lowest specific speeds but are used when heads are high specific speeds but are used when heads are high (800 ft to 1,600 ft.). These turbines have
(800 ft to 1,600 ft.). These turbines have
specific speeds below 5. The kinetic energy of the specific speeds below 5. The kinetic energy of the jet is converted into rotating kinetic energy. jet is converted into rotating kinetic energy.
Figure 2.1: Hydro-electric Power Plant Figure 2.1: Hydro-electric Power Plant
Formulas: Formulas:
A. Gross head, h A. Gross head, hgg
h
hgg = head water elevation - tail water elevation = head water elevation - tail water elevation
B. Friction head loss, h
B. Friction head loss, hff
Using Morse Equation: Using Morse Equation:
h
hff = =
Using Darcy’s Equation: Using Darcy’s Equation:
h
hff = =
Where, h
Where, hff = friction head loss = friction head loss
f = coefficient of friction or friction f = coefficient of friction or friction factor factor L = length of penstock L = length of penstock g = 9.81 g = 9.81
= 32.2 = 32.2
D = inside diameter D = inside diameter C. Net head, h C. Net head, h h = h h = hgg - h - hff D. Penstock efficiency, e D. Penstock efficiency, e e = e =
E. Volume flow of water, Q E. Volume flow of water, Q
Q = Av Q = Av F. Water Power, P F. Water Power, PWW P PWW = =
ɣ
ɣ
wwQhQh Where,Where,
ɣ
ɣ
ww = specific weight of water = specific weight of water= 9.81 = 9.81
= = 62.462.4
G. Turbine efficiency, e G. Turbine efficiency, eTT e eTT = =
Where, PWhere, PBB = Brake power or turbine output = Brake power or turbine output
H. Generator efficiency, e H. Generator efficiency, eGG e eGG = =
I. Turbine output, P I. Turbine output, PBB P PBB = P = PWW
e eTT J. Generator output, P J. Generator output, PgengenP
Pgengen = P = PBB
e eGG = (P = (PWW
e eTT))
e eGGK. Generator speed, N K. Generator speed, N N = N =
Where, N = speed Where, N = speed f = frequency f = frequencyp = no. of poles (must be even no.) p = no. of poles (must be even no.) L. Utilized head, h
L. Utilized head, hww
h
hww = h = h
e ehhWhere, e
Exercise #1:
Exercise #1: In a hydroelectric power plant the tail In a hydroelectric power plant the tail water elevation is at 500 m. What is the head water water elevation is at 500 m. What is the head water elevation if the net head is 30 m and the head loss elevation if the net head is 30 m and the head loss is 5% of gross head?
is 5% of gross head?
Exercise #2:
Exercise #2: The tailwater and the headwater of a The tailwater and the headwater of a hydro-electric plant are 150 m and 200 m
hydro-electric plant are 150 m and 200 m
respectively. What is the water power if the flow is respectively. What is the water power if the flow is 15 m³/s and a head loss of 10% of the gross head? 15 m³/s and a head loss of 10% of the gross head?
M. Head of Pelton (Impulse) turbine: M. Head of Pelton (Impulse) turbine:
h = h =
+
+
Where, ρ = density of water = 1,000
Where, ρ = density of water = 1,000
Figure 2.2: Pelton Type Turbine Figure 2.2: Pelton Type Turbine Exercise #3:
Exercise #3: An impulse wheel at best produces 125 An impulse wheel at best produces 125 hp under a head of 210 ft. By what percent should hp under a head of 210 ft. By what percent should the speed be increased for 290 ft. head?
Exercise #4:
Exercise #4: In a double-overhung impulse-turbineIn a double-overhung impulse-turbine installation is to develop 20,000 hp at 275 rpm installation is to develop 20,000 hp at 275 rpm under a net head of 1,100 ft. Determine the under a net head of 1,100 ft. Determine the specific speed.
specific speed.
N. Head of Reaction (Francis and Kaplan) turbines: N. Head of Reaction (Francis and Kaplan) turbines:
h = h =
+ +
+ z + zFigure 2.3: Francis Turbine Figure 2.3: Francis Turbine O. Peripheral coefficient, O. Peripheral coefficient, ΦΦ Φ Φ = =
= =
Where, D = diameter of runner, m Where, D = diameter of runner, m N = speed of runner, rps N = speed of runner, rps
P. Specific speed of hydraulic turbine P. Specific speed of hydraulic turbine
N
NSS = =
√ √
, rpm, rpm NNSS = =√ √
,
,
rpmrpm*h
*h in in feet feet *h *h in in metersmeters *N in rpm *N in rpm Q. Total efficiency, e Q. Total efficiency, ett e ett = e = ehheemmeevv Where, e
Where, evv = volumetric efficiency = volumetric efficiency
e
emm = mechanical efficiency = mechanical efficiency
R. Turbine type selection based on head, ft. R. Turbine type selection based on head, ft.
NET HEAD
NET HEAD
TYPE OF TURBIN
TYPE OF TURBINE
E
Up
Up to to 70 70 feet feet Propeller Propeller TypeType 70
70 - - 110 110 ft. ft. Propeller Propeller or or FrancisFrancis 110
110 –– 800 800 ft. ft. Francis Francis TurbineTurbine 800
800 –– 1,300 1,300 ft. ft. Francis Francis or or ImpulseImpulse 1,300
1,300 ft. ft. and and above above Impulse Impulse TurbineTurbine
For small capacity, use Propeller Turbine. For small capacity, use Propeller Turbine. For medium capacity, use Francis Turbine. For medium capacity, use Francis Turbine. For high capacity, use Impulse Turbine. For high capacity, use Impulse Turbine.
Exercise #5:
Exercise #5: A pelton type of turbine has a gross A pelton type of turbine has a gross head of 40 m and a friction head loss of 6 m. What is head of 40 m and a friction head loss of 6 m. What is the penstock diameter if the penstock length is 90 m the penstock diameter if the penstock length is 90 m and the coefficient of friction head loss is 0.001 and the coefficient of friction head loss is 0.001 Morse?
Morse?
Exercise #6:
Exercise #6: A Pelton type turbine has 25 m head A Pelton type turbine has 25 m head friction loss of 4.5 m. The coefficient of friction loss of 4.5 m. The coefficient of friction head loss (from Morse) is 0.00093 and friction head loss (from Morse) is 0.00093 and penstock length of 80 m. What is the penstock penstock length of 80 m. What is the penstock diameter?
“
“
You cannot bri
You cannot bri ng about pros
ng about prospe
peri
ri ty by dis
ty by discouraging th
couraging th ri
ri ft.
ft.
You cann
You cann ot strengthen the we
ot strengthen the weak by we
ak by weakenin
akenin g the s
g the stron
tron g.
g.
You cann
You cann ot help th
ot help th e wag
e wage e
e earn
arn er by
er by
pul
pul lili ng down the wage
ng down the wage paye
payer.
r.
You cannot fur
You cannot fur ther the brothe
ther the brotherhood of man by
rhood of man by
encouragi
encouragi ng class hatred.
ng class hatred.
You cannot h
You cannot h elp the po
elp the poor by de
or by des
str
tr oying th
oying th e
e ri
ri ch.
ch.
You cannot k
You cannot k ee
eep out of tr
p out of tr oubl
oubl e
e by
by
sp
spending mor
ending mor e
e than
than you e
you earn
arn ..
You cannot bui
You cannot bui ld char
ld char acte
acter
r and courage by ta
and courage by takin
kin g
g
away man's ini
away man's ini ti
ti ative and indepe
ative and independence
ndence..
You cannot help men permane
You cannot help men permanently
ntly by do
by doin
in g for
g for them what
them what
they co
they coul
ul d and should do f
d and should do f or th
or th ems
emselve
elves
s
.”
.”
- Rev. William J. H. Boetcker
- Rev. William J. H. Boetcker
CHAPTER 3 CHAPTER 3
Air Compressor
Air Compressor
Air Compressor
Air Compressor - a machine which is used to increase - a machine which is used to increase the pressure of a gas by decreasing its volume. the pressure of a gas by decreasing its volume. The work input to a compressor is minimized when the The work input to a compressor is minimized when the compression process is executed in an internally compression process is executed in an internally reversible manner.
reversible manner.
Isentropic process in compression process involves no Isentropic process in compression process involves no cooling. (n = k). For most steady-flow devices, this cooling. (n = k). For most steady-flow devices, this is the ideal process that can be served as a suitable is the ideal process that can be served as a suitable model.
model.
Polytropic process in compression process involves Polytropic process in compression process involves some cooling. (1
some cooling. (1
n n
k) k)Isothermal process in compression process involves Isothermal process in compression process involves maximum cooling. (n = 1)
maximum cooling. (n = 1)
Adiabatic compression requires maximum work of Adiabatic compression requires maximum work of compression.
compression.
Isothermal process requires minimum work of Isothermal process requires minimum work of compression.
compression.
Practically, all compressors are powered by electric Practically, all compressors are powered by electric motors.
motors.
The ratio of mechanical power required to the The ratio of mechanical power required to the
electrical power consumed during operation is called electrical power consumed during operation is called the motor efficiency.
the motor efficiency.
W Wee = =
Where, W
Where, Wee = electric power/work, W = electric power/work, Wcc = compressor = compressor
power/work, e
power/work, emm = motor efficiency = motor efficiency
Adiabatic efficiency is a measure of the deviation of Adiabatic efficiency is a measure of the deviation of actual process from corresponding idealized zone. actual process from corresponding idealized zone.
Isentropic efficiency of turbine is the ratio of the Isentropic efficiency of turbine is the ratio of the actual work output of the turbine to the work output actual work output of the turbine to the work output that would be achieved of the process between the that would be achieved of the process between the inlet state and the exit pressure were isentropic. inlet state and the exit pressure were isentropic.
e eTT = =
Where, e
Where, eTT - isentropic efficiency, W - isentropic efficiency, Waa - actual turbine - actual turbine
work, W
work, Wii - ideal turbine work - ideal turbine work
Isentropic efficiency of compressor is the ratio of Isentropic efficiency of compressor is the ratio of the work input required to raise the pressure of a the work input required to raise the pressure of a gas to a specified value in an isentropic manner to gas to a specified value in an isentropic manner to the actual work input.
the actual work input.
e eTT = =
Where, e
Where, eTT - isentropic efficiency, W - isentropic efficiency, Waa - actual - actual
compressor work, W
compressor work, Wii - ideal compressor work - ideal compressor work
Uses of compressor: Uses of compressor:
- to drive pneumatic tools - to drive pneumatic tools - sand blasting - sand blasting - industrial cleaning - industrial cleaning - spray painting - spray painting
- starting a diesel engine - starting a diesel engine - to supply air in mine tunnels - to supply air in mine tunnels
- manufacture of plastic and industrial products - manufacture of plastic and industrial products Classification of air compressor:
Classification of air compressor: 1. Reciprocating compressor 1. Reciprocating compressor 2. Centrifugal compressor 2. Centrifugal compressor 3. Rotary compressor 3. Rotary compressor
Single-stage reciprocating compressor: Single-stage reciprocating compressor:
Figure 3.1 Figure 3.1 Formulas: Formulas: A. Compression process 1 to 2: A. Compression process 1 to 2: Figure 3.2 Figure 3.2 P P11VV11nn = P = P22VV22nn
= =((
))
= =((
))
B. Piston displacement, V
B. Piston displacement, VDD
For singe-acting compressor: For singe-acting compressor:
V
VDD = =
BB22SN,SN,
For double-acting compressor: For double-acting compressor:
Figure 3.3 Figure 3.3
Figure 3.4 Figure 3.4 Piston rod neglected:
Piston rod neglected:
V
VDD = 2 = 2
((
))
,,
Piston rod neglected: Piston rod neglected:
V
VDD = =
((
))
+ +**
((
)+
)+
,,
Where, B = D = piston rod diameter or bore Where, B = D = piston rod diameter or bore
S = stroke or piston length S = stroke or piston length C. Capacity of compressor, V
C. Capacity of compressor, V11
V
V11 = volume flow at suction = = volume flow at suction =
D. Volumetric efficiency, e D. Volumetric efficiency, evv e evv = =
= 1 + c - c= 1 + c - c((
))
E. Compressor power, W E. Compressor power, Wcc W Wcc = =
[([(
))
]]
Where, PWhere, P11 = suction pressure = suction pressure
P
P22 = discharge pressure = discharge pressure
F. Compressor efficiency, e F. Compressor efficiency, ecc e ecc = =
Where, PWhere, PBB = Brake power = Brake power
G. Piston speed = 2SN G. Piston speed = 2SN
Exercise #1:
Exercise #1: The discharge pressure of an airThe discharge pressure of an air compressor is 5 times the suction pressure. If volume compressor is 5 times the suction pressure. If volume flow at suction is 0.1 m³/sec, what is the suction flow at suction is 0.1 m³/sec, what is the suction pressure if compressor work is 19.57 KW? (Use n = pressure if compressor work is 19.57 KW? (Use n = 1.35).
1.35).
Exercise #2:
Exercise #2: The initial condition of air in an air The initial condition of air in an air compressor is 98 KPa and 27°C and discharges air at compressor is 98 KPa and 27°C and discharges air at 450 KPa. The bore and stroke are 355 mm and 381 mm, 450 KPa. The bore and stroke are 355 mm and 381 mm, respectively with percent clearance of 8% running at respectively with percent clearance of 8% running at 300 rpm. Find the volume of air at suction.
300 rpm. Find the volume of air at suction.
Two-stage reciprocating compressor: Two-stage reciprocating compressor:
Figure 3.5 Figure 3.5 Formulas: Formulas: A. Compressor work, W A. Compressor work, Wcc W Wcc = =
[([(
))
]]
B. Intercooler pressure, P B. Intercooler pressure, Pxx P Pxx = =
Figure 3.6 Figure 3.6C. Heat rejected in the intercooler, Q C. Heat rejected in the intercooler, Q
Q = mc
Where, c Where, cpp = 1 = 1
m =
m =
= =((
))
TTxx = intercooler temperature = intercooler temperature
D. Adiabatic compressor efficiency D. Adiabatic compressor efficiency
e
ecc = =
E. Ideal indicated power, IP E. Ideal indicated power, IP
IP = IP =
P
P
mimiV
V
DDExercise #3:
Exercise #3: A two stage air compressor has anA two stage air compressor has an intercooler pressure of 4 kg/cm². What is the intercooler pressure of 4 kg/cm². What is the discharge pressure if suction pressure is 1 discharge pressure if suction pressure is 1 kg/cm²?
kg/cm²?
3. Three-stage air compressor 3. Three-stage air compressor
Figure 3.7 Figure 3.7 Figure 3.8 Figure 3.8 Formulas: Formulas: A. Intercooler pressure, P A. Intercooler pressure, Pxx P Pxx = =
B. Compressor power, W B. Compressor power, Wcc W Wcc = =
[([(
))
]]
C. Heat rejected in the intercooler, Q C. Heat rejected in the intercooler, Q
Q = 2mc Q = 2mcpp(T(Txx - T - T11)) Where, c Where, cpp = 1 = 1
m =
m =
= =((
))
“The test of a first
“The test of a first
-rate intelli
-rate intelli ge
gence is the a
nce is the abili
bili ty to
ty to
hol
hol d two oppose
d two opposed ideas in th
d ideas in th e min
e min d at th
d at th e s
e same
ame
time, and s
time, and stil
til ll
retain the ability to function.”
retain the ability to function.”
–
–
F. Scott Fitzgerald
F. Scott Fitzgerald
“Al
“Al
l
l coins
coins
have haveth
th ree s
ree sides: h
ides: h eads
eads, tai
, tai ll s, and th
s, and th e e
e edge.
dge.
Th
Th e mos
e most in
t in telli
telli gent pe
gent people li
ople li ve o
ve on th
n th e e
e edge
dge,,
abl
abl e to se
e to see both
e both sides
sides..
II n sc
n school th
hool th ere
ere is only one righ
is only one righ t answe
t answer.
r.
II n r
n r e
eal l
al lif
if e the
e there is more than one right
re is more than one right ans
answe
wer, a
r, a wav
wave of
e of
choices
choices fr
fr om dif
om dif ferent perspe
ferent perspectives
ctives and poin
and poin ts of view.
ts of view.
Here‟s an
Here‟s an example. Wh
example. When I asked my
en I asked my poor dad
poor dad what 1+1
what 1+1
equaled,
equaled,
his answer was “2.” Rich dad‟s answer to that same
his answer was “2.” Rich dad‟s answer to that same
ques
question
tion was
was dif
dif ferent.
ferent.
His answer wa
His answer was “11.”
s “11.”
Thi
Thi s
s is why one
is why one man was p
man was poor and th
oor and th e
e other r
other r ich.
ich.
II n other words, the ide
n other words, the idea of r
a of r ight vs. wrong,
ight vs. wrong,
which i
which i s
s taught in
taught in s
school, is unintelli
chool, is unintelli ge
gent.
nt.
II n
n
fact it is ignora
fact it is ignorant, since „rig
nt, since „right vs. wrong‟ ig
ht vs. wrong‟ ignores,
nores,
rath
rath er than
er than explores
explores, the other side
, the other side..
II n my opini
n my opini on, the ide
on, the idea of r
a of r ight
ight ve
versus w
rsus wrong i
rong is the
s the bas
basis of all
is of all
disagree
disagreements, ar
ments, ar guments, divor
guments, divor ce
ce,
, un
un happin
happin es
ess
s,,
aggres
aggression, viol
sion, viol ence
ence, and war
, and war ..
”
”
- RTK
- RTK
CHAPTER 4 CHAPTER 4
Fans and Blowers
Fans and Blowers
Fan - a machine which is used to apply power to a Fan - a machine which is used to apply power to a gas in order to cause movement of the gas.
gas in order to cause movement of the gas.
Blower - a fan which is used to force air under Blower - a fan which is used to force air under suction, that is, the resistance to gas flow is suction, that is, the resistance to gas flow is imposed primarily upon the discharge.
imposed primarily upon the discharge.
Exhauster - a fan which is used to withdraw air Exhauster - a fan which is used to withdraw air under suction, that is, the resistance to gas flow under suction, that is, the resistance to gas flow is imposed primarily upon the inlet.
is imposed primarily upon the inlet.
Capacity of fan - volume flow rate measured at the Capacity of fan - volume flow rate measured at the outlet. outlet. Types of fans: Types of fans: 1. Propeller fan 1. Propeller fan 2. Tubeaxial fan 2. Tubeaxial fan 3. Vaneaxial fan 3. Vaneaxial fan 4. Centrifugal fan 4. Centrifugal fan Figure 4.1 Figure 4.1
Formulas: Formulas: A. Static head, h A. Static head, hss h hss = =
Where, hWhere, hww = manometer reading, meters of water = manometer reading, meters of water
ɣ
ɣ
ww = specific weight of water = 9.81 = specific weight of water = 9.81
ɣ
ɣ
aa = specific weight of air = 1.2 = specific weight of air = 1.2
If both static head at suction and discharge are If both static head at suction and discharge are given, given, h hss = =
B. Velocity head, h B. Velocity head, hvv h hvv = =
Where, vWhere, voo = outlet velocity, = outlet velocity,
g = 9.81
g = 9.81
= 32.2 = 32.2
If both velocity at suction and discharge are If both velocity at suction and discharge are given, given, h hvv = =
C. Total head, h C. Total head, h h = h h = hss + h + hvv D. Air power, D. Air power,P
P
aa P Paa = =ɣ
ɣ
aaQh
Qh
, KW, KWWhere, Q = fan capacity,
Where, Q = fan capacity,
E. Fan efficiency, e E. Fan efficiency, eff e eff = =
F. Static power, P F. Static power, Pss P Pss = =ɣ
ɣ
aaQh
Qh
ss G. Static efficiency, e G. Static efficiency, ess e ess = =
H. Fan laws H. Fan lawsVariable speed (constant fan size and density) Variable speed (constant fan size and density)
= =
= =((
))
= =((
))
Variable density (constant fan size and density) Variable density (constant fan size and density)
Q
Q11 = Q = Q22
= =
= =
Where,
Where, ρρ = density of air = density of air P = power P = power h = head h = head N = speed N = speed
Exercise #1:
Exercise #1: A fan draws 1.42 m³ per second of air at A fan draws 1.42 m³ per second of air at a static pressure of 2.54 cm of water through a duct a static pressure of 2.54 cm of water through a duct 300 mm diameter and discharges it through a duct of 300 mm diameter and discharges it through a duct of 275 mm diameter. Determine the static fan efficiency 275 mm diameter. Determine the static fan efficiency if total fan mechanical is 75% and air is measured at if total fan mechanical is 75% and air is measured at 25°C and 760 mmHg.
25°C and 760 mmHg.
Exercise #2:
Exercise #2: Calculate the air power of a fan that Calculate the air power of a fan that delivers 1,200 m³/min of air through a 1 m by 1.5 delivers 1,200 m³/min of air through a 1 m by 1.5 m oulet. Static pressure is 120 mmHg and density m oulet. Static pressure is 120 mmHg and density of air is 1.18 kg/m
of air is 1.18 kg/m33..
Exercise #3:
Exercise #3: The fan has a total head of 190 m andThe fan has a total head of 190 m and a static pressure of 20 cmHg. If the air density a static pressure of 20 cmHg. If the air density is 1.2 kg/m³, what is the velocity of air flowing? is 1.2 kg/m³, what is the velocity of air flowing?
“Give, and you will receive.
“Give, and you will receive.
Your gif
Your gif t wil
t wil l r
l r e
etur
tur n to you in
n to you in fu
fu ll
ll - pres
- press
se
ed dow
d down, shake
n, shaken
n
toge
together to make room for
ther to make room for more, runn
more, runn ing over,
ing over,
and poured into your
and poured into your lap.
lap.
The amount you
The amount you give w
give wilil l
l de
dete
termi
rmi ne the
ne the
amount you get back.”
amount you get back.”
- Luke 6:38 (NLT)
- Luke 6:38 (NLT)
“A man‟s true worth is the good he does in this world.”
“A man‟s true worth is the good he does in this world.”
- Mohammad
- Mohammad
“
“
The tru
The tru e p
e pri
ri nciple of capitalism is,
nciple of capitalism is,
„
„
Th e more pe
Th
e more people I
ople I s
serve
erve, the
, the
more effective I become.‟
more effective I become.‟
You mu
You mu st be g
st be gene
enerou
rou s if
s if you want
you want to se
to serve as many
rve as many
people as poss
people as possibl
ibl e.
e.
Un
Un for
for tun
tun ately, many pe
ately, many people want to be
ople want to be paid more,
paid more,
do les
do less, and retir
s, and retir e e
e earl
arl y.
y.
Doesn‟t this v
Doesn‟t this violate the prin
iolate the principle of gen
ciple of generosity?”
erosity?”
- RTK
- RTK
CHAPTER 5 CHAPTER 5Pumps
Pumps
PumpPump - a machine which is used to add energy to a- a machine which is used to add energy to a liquid in order to transfer the liquid from one point liquid in order to transfer the liquid from one point to another point of higher energy level.
to another point of higher energy level. Aquifers - deep ground water deposits where Aquifers - deep ground water deposits where
underground water are available for water supply and underground water are available for water supply and irrigation.
irrigation.
Hydraulic gradient - the locus of the elevation which Hydraulic gradient - the locus of the elevation which water will rise in a piezometer tube.
water will rise in a piezometer tube.
Figure 5.1: Pump System Figure 5.1: Pump System Types of pumps:
Types of pumps:
1. Reciprocating pump 1. Reciprocating pump
Low discharge, high head, self-priming, up to 5 ft. Low discharge, high head, self-priming, up to 5 ft. suction lift, positive displacement pumps:
suction lift, positive displacement pumps: 1. Piston type
1. Piston type 2. Plunger type 2. Plunger type
3. Bellows or diaphragm 3. Bellows or diaphragm
Figure 5.2 Figure 5.2
This is commonly used as Boiler Feed Pump for steam. This is commonly used as Boiler Feed Pump for steam. Reciprocating pumps can be single-acting or Reciprocating pumps can be single-acting or double-acting.
acting.
They can be simplex, duplex, triplex, etc. They can be simplex, duplex, triplex, etc. Air chamber - is to smoothen the flow due to the Air chamber - is to smoothen the flow due to the nature of flow of liquid. This can be placed on the nature of flow of liquid. This can be placed on the suction side or discharge side of piping
suction side or discharge side of piping installation.
installation.
Relief valve - this should be installed on the Relief valve - this should be installed on the discharge side between pump and any other valve. discharge side between pump and any other valve. Foot valve - should be installed at the end of the Foot valve - should be installed at the end of the suction pipe.
suction pipe.
All losses of capacity given in percentage of the All losses of capacity given in percentage of the displacement are referred to as slip: (1 - e
displacement are referred to as slip: (1 - evv).).
In new pumps, the slippage is within 2%. In new pumps, the slippage is within 2%.
2. Centrifugal pump 2. Centrifugal pump
Figure 5.3 Figure 5.3
High discharge, low head, not self-priming: High discharge, low head, not self-priming: 1. Radial flow - used for single and souble 1. Radial flow - used for single and souble suction
suction
2. Axial flow - acting like compressors 2. Axial flow - acting like compressors 3. Mixed flow
3. Mixed flow
Centrifugal pump is used to convert kinetic energy Centrifugal pump is used to convert kinetic energy into pressure energy through diffuser vanes.
into pressure energy through diffuser vanes. Specific speed - is defined as that speed in rpm Specific speed - is defined as that speed in rpm at which a given impeller would operate to deliver at which a given impeller would operate to deliver 1 GPM against a total dynamic head of 1 foot. 1 GPM against a total dynamic head of 1 foot. Specific speed is constant and is given by the Specific speed is constant and is given by the manufacturer.
manufacturer.
Impellers for higher heads usually have low Impellers for higher heads usually have low
specific speeds. Impellers for lower heads usually specific speeds. Impellers for lower heads usually have higher specific speeds.
have higher specific speeds.
For double suction pumps, the Q value is For double suction pumps, the Q value is
determined by dividing the given capacity by 2. determined by dividing the given capacity by 2.
3. Rotary pump 3. Rotary pump
Figure 5.4 Figure 5.4
Positive displacement pumps, low discharge, low Positive displacement pumps, low discharge, low head: head: 1. vanes 1. vanes 2. screws 2. screws 3. lobes 3. lobes 4. gear 4. gear
5. cam and piston 5. cam and piston 6. shuttle block type 6. shuttle block type 4. Kinetic pump
4. Kinetic pump - transform fluid kinetic energy- transform fluid kinetic energy to fluid static ppressure energy.
to fluid static ppressure energy. 1. jet pumps 1. jet pumps 2. ejector pumps 2. ejector pumps Figure 5.5 Figure 5.5
5. Deep well pump 5. Deep well pump
1. Turbine pumps - high suction lift up to 305 m. 1. Turbine pumps - high suction lift up to 305 m. 2. Plunger pumps - are refinement of the old hand 2. Plunger pumps - are refinement of the old hand pumps. This is best suited where the lifts are 7.6 m pumps. This is best suited where the lifts are 7.6 m or over and capacities up to 190 liters per minute. or over and capacities up to 190 liters per minute. 3. Ejector - a centrifugal pump used for small 3. Ejector - a centrifugal pump used for small capacities combines a single-stage centrifugal pump capacities combines a single-stage centrifugal pump at the top of the well and an ejector or jet located at the top of the well and an ejector or jet located down in the water.
down in the water.
4. Air lifts - another method of pumping wells is by 4. Air lifts - another method of pumping wells is by compressed air being admitted to the well to lift the compressed air being admitted to the well to lift the water to the surface.
water to the surface.
Classification of pumps based on suction lift Classification of pumps based on suction lift 1. Shallow well pump - suction lift up to 25 ft. 1. Shallow well pump - suction lift up to 25 ft. 2. Deep well pump - sution lift up to 120 ft. 2. Deep well pump - sution lift up to 120 ft. 3. Turbine pump - up to 300 ft.
3. Turbine pump - up to 300 ft. 4. Submersible pump
4. Submersible pump - for high head- for high head Cavitation
Cavitation - is the spontaneous vaporization of the- is the spontaneous vaporization of the fluid, resulting in a degradation of pump
fluid, resulting in a degradation of pump performance.
performance.
Causes of cavitation: Causes of cavitation:
1. Discharge head far below the pump head at peak 1. Discharge head far below the pump head at peak efficiency.
efficiency.
2. High suction lift or low suction head 2. High suction lift or low suction head 3. Excessive pump speed
3. Excessive pump speed 4. High liquid temperature 4. High liquid temperature
Bad effects of cavitation: Bad effects of cavitation:
1. Drop in capacity and efficiency 1. Drop in capacity and efficiency 2. Noise and vibration
2. Noise and vibration 3. Corrosion and pitting 3. Corrosion and pitting
NPSH (Net Positive Suction Head)
NPSH (Net Positive Suction Head) - is the difference- is the difference between actual suction pressure and saturation vapor between actual suction pressure and saturation vapor pressure of the liquid.
pressure of the liquid. NPSH
NPSHR R (Net Positive Suction Head Required) (Net Positive Suction Head Required) - is a- is a
function of the pump, and will be given by the pump function of the pump, and will be given by the pump manufacturer as part of the pump available at the manufacturer as part of the pump available at the name plate.
name plate. NPSH
NPSH A A (Net Positive Suction Head Available) (Net Positive Suction Head Available) - is the- is the
actual fluid energy at the inlet. actual fluid energy at the inlet.
If NPSHA is less than NPSHR, the fluid will cavitate. If NPSHA is less than NPSHR, the fluid will cavitate. Preventing cavitation:
Preventing cavitation:
1. Increasing the height of the fluid source. 1. Increasing the height of the fluid source.
2. Reducing friction and minor losses by shortening 2. Reducing friction and minor losses by shortening the suction line or using larger pipe size.
the suction line or using larger pipe size.
3. Reducing the temperature of the fluid at the pump 3. Reducing the temperature of the fluid at the pump entrance.
entrance.
4. Pressurizing the fluid supply tank. 4. Pressurizing the fluid supply tank. 5. Reducing the flow rate or velocity. 5. Reducing the flow rate or velocity.
Pump head: Pump head:
1. Friction head - head required to overcome 1. Friction head - head required to overcome resistance to flow in the pipe, fittings and resistance to flow in the pipe, fittings and valves.
valves.
2. Velocity or dynamic head - specific kinetic 2. Velocity or dynamic head - specific kinetic energy of the fluid.
energy of the fluid.
3. Static suction head - the vertical distance 3. Static suction head - the vertical distance above the centerline of the pump inlet to the free above the centerline of the pump inlet to the free level of water source.
level of water source.
4. Static suction lift - the vertical distance 4. Static suction lift - the vertical distance from pump certerline to the free level of water from pump certerline to the free level of water source below the pump inlet.
source below the pump inlet.
5. Static discharge head - is the vertical 5. Static discharge head - is the vertical distance from pump centerline to the free level of distance from pump centerline to the free level of the fluid in the discharge tank.
the fluid in the discharge tank.
6. Total suction head - is the head that includes 6. Total suction head - is the head that includes static head, velocity head and friction head at static head, velocity head and friction head at the suction side.
the suction side.
7. Total discharge head - is the head that 7. Total discharge head - is the head that includes static head, velocity head and friction includes static head, velocity head and friction head at the discharge side.
head at the discharge side.
8. Head - refers to all the head both at suction 8. Head - refers to all the head both at suction and discharge.
and discharge.
9. Drawdown - is the difference between static 9. Drawdown - is the difference between static water level and operating water level.
water level and operating water level. 10. For duplex pumps:
10. For duplex pumps: Pump dimensions: D
Pump dimensions: Dss x D x Dww X L X L
D
Dss = steam diameter = steam diameter
D
Dww = water diameter = water diameter
L = length of stroke L = length of stroke
11. Pump slip 11. Pump slip
For positive slip, the coefficient of discharge For positive slip, the coefficient of discharge (C
(Cdd) is less than 1 (decreases).) is less than 1 (decreases).
For negative slip, the coefficient of discharge For negative slip, the coefficient of discharge (C
(Cdd) is more than 1 (decreases).) is more than 1 (decreases).
12. Series pump 12. Series pump
To increase the head, connect the pump in series. To increase the head, connect the pump in series. The head of pump in series is h
The head of pump in series is h11 + h + h22..
The volume flow is Q
The volume flow is Q11 = Q = Q22..
Figure 5.6 Figure 5.6
13. Parallel pump 13. Parallel pump
To increase the discharge, connect the pump in To increase the discharge, connect the pump in parallel.
parallel.
The discharge of pump in parallel is Q
The discharge of pump in parallel is Q11 + Q + Q22..
The heads, h
The heads, h11 = h = h22..
Figure 5.7 Figure 5.7
14. To increase the head of submersible pump, 14. To increase the head of submersible pump, increase the number of stages of number of impeller. increase the number of stages of number of impeller.
Formulas: Formulas:
Figure 5.8 Figure 5.8 A. Volume flow rate of water, Q A. Volume flow rate of water, Q Q = Av Q = Av B. Pressure head, h B. Pressure head, hpp h hpp = =
C. Velocity head, h C. Velocity head, hvv h hvv = =
D. Total head of pump, h D. Total head of pump, h
h = (h
h = (hp2p2 - h - hp1p1) + (h) + (hv2v2 - h - hv1v1) + (z) + (z22 - z - z11) + (h) + (hf1f1 + h + hf2f2))
Where, z
Where, z11 is negative if source is below pump center is negative if source is below pump center
line. line.
P
Pss is negative if it is a vacuum. is negative if it is a vacuum.
E. Water power, P
E. Water power, PWW
P
PWW = =
ɣ
ɣ
wwQh, KWQh, KWWhere,
Where,
ɣ
ɣ
ww = specific weight of water = specific weight of waterF. Pump efficiency, e
F. Pump efficiency, epp
e epp = =
G. Head as determined from two pressure readings: G. Head as determined from two pressure readings:
h = h =
+ +
+ z + z Where, PWhere, P11 is negative if vacuum is negative if vacuum
Figure 5.9 Figure 5.9 H. Friction head, h
H. Friction head, hff
Darcy’s
Darcy’s Equation: h Equation: hff = =
Morse Equation: h Morse Equation: hff = =
I. Specific speed, N I. Specific speed, Nss N Nss = =
Where, N = speed, rpm Where, N = speed, rpm Q = discharge, gpm Q = discharge, gpm h = head, ft h = head, ftJ. Similar pumps: J. Similar pumps:
= =
= =
K. For the same pump:K. For the same pump:
Constant impeller diameter, variable speed: Constant impeller diameter, variable speed:
= =
= =((
))
= =((
))
Constant speed, variable impeller diameter: Constant speed, variable impeller diameter:
= =((
))
= =((
))
= =((
))
Constant speed, variable fluid density: Constant speed, variable fluid density:
= =
= =
= =
L. Characteristics of Reciprocating pumps: L. Characteristics of Reciprocating pumps:
Figure 5.9.1 Figure 5.9.1 1. Piston Displacement:
1. Piston Displacement:
Piston
Piston rod rod neglected: neglected: VVDD = 2 = 2
((
))
,,
Piston rod considered: V Piston rod considered: VDD = =
+ +
,,
2. Slip = V 2. Slip = VDD - Q - Q 3. %slip = 3. %slip =
x 100%x 100% 4. volumetric efficiency, e 4. volumetric efficiency, evv = =
= 1 - Slip= 1 - SlipExercise #1:
Exercise #1: A 4 m³/hr pump delivers water to aA 4 m³/hr pump delivers water to a pressure tank. At the start, the gage reads 138 KPa pressure tank. At the start, the gage reads 138 KPa until it reads 276 KPa and then the pump was shut until it reads 276 KPa and then the pump was shut off. The volume of the tank is 180 liters. At 276 off. The volume of the tank is 180 liters. At 276 KPa, the water occupied 2/3 of the tank volume. KPa, the water occupied 2/3 of the tank volume. Determine the volume of water that can be taken out Determine the volume of water that can be taken out until the gage reads 138 KPa.
until the gage reads 138 KPa.
Exercise #2:
Exercise #2: If a 1/3 horsepower pump runs for 20If a 1/3 horsepower pump runs for 20 min, what is the energy used?
min, what is the energy used?
Exercise #3:
Exercise #3: A double suction centrifugal pumpA double suction centrifugal pump delivers 20 ft³/sec of water at a head of 12 m delivers 20 ft³/sec of water at a head of 12 m and running at 650 rpm. What is the specific and running at 650 rpm. What is the specific speed of the pump?
