Fluid Mach
Short Description
fluid machinery...
Description
“The school system has it‟s own definition of what a geni geni us is. I t may not be the same same defi defi ni tion of your geni geni us.
ME9 FLUID MACHINERY
Dif ferent genius comes comes out in diff erent environments. Steve Thomas Edison‟s genius came out in a labor atory an d Steve Jobs geni geni us came out in his family‟s garage where he started Appl e computers. M ark Z uckerberg created created Facebook in hi s college dorm dorm room as he created created a way for hi s fellow students to connect and communi cate. cate.”
- Robert T. Kiyosaki
2. Velocity head, h V - Torricelli’s Theorem:
CHAPTER 1
“The
Basic Energy Equations
velocity
of
a
liquid
which
discharges
under
a
head is equal to the velocity of a body which falls in the same head .”
1. Pressure head, hP
hv =
, v =
Where, hv = velocity head v = velocity of fluid g = 9.81
= 32.2
Exercise #2: Determine the velocity of the liquid in a tank at the bottom, given that surface h = 7m. Figure 1.1
P = ρf
hP, hP =
Where, P = gage pressure hP = pressure head
ɣ = weight density ɣf = weight density of fluid = (S.G.)( ɣwater) Where, ɣw = 9.81
=
Exercise #1: What column of water?
62.4
is
the
pressure
of
a
100
cm
3. Volume flow, Q
4. Power of a jet, P
Figure 1.2
Q = (A
v) =
Figure 1.3
Where, A = cross-sectional area
P = ɣ
Q
h
Where, P = Power
ɣ = Weight density = ρg
v = velocity Q = volume flow rate
5. For bubbles
Flow through nozzle:
Q = Cd Where, v =
A
v
Cd = coefficient of discharge Exercise #3: Water is flowing through a cast iron pipe at the rate of 3500 GPM. The inside diameter of pipe is 6 in. Find the flow velocity.
Figure 1.4
A. T = c (Isothermal) if T is not given: P1V1 = P2V2 B. Use any process if T is given:
= Where, P1 = ɣh + Patm
*absolute P
P2 = 101.325 KPa or 14.7 psi (if not given)
neglecting friction, the total head or total amount of energy per unit weight, is the same at every point in the path of flow. 6.
Bernoulli’s
Theorem
Energy
8. Reynold’s Number, NR
NR =
(dimensionless) (dimensionless)
Where, NR < 2000 - Laminar Flow NR > 4000 - Turbulent Flow v = velocity of fluid D = internal diameter of pipe Exercise #4: Water is flowing in a pipe with radius of 30 cm at a velocity of 5 m/s. The viscosity of water is 1.17 Pa-s. What is the Reynolds Number? Figure 1.5
hT = hP + h v + z Where, z = elevation head Using continuity flow equation: Q1 = Q2 or A1v1 = A 2v2
+ + z = + + z 1
2
– resistance to flow 7. Viscosity, property to resist shear deformation.
or
the
A. Absolute or dynamic viscosity, – viscosity which is determined by direct measurement of shear resistance in B.
Kinematic
or . Viscosity,
divided the density in
.
9. Friction head loss, hL
A. Using Morse Equation: – absolute
viscosity hL = B. Using Darcy’s Equation: hL =
Where, hL = friction head loss
Venturi-meter - is used to measure the volume of flow.
f = coefficient of friction or friction factor Pitot tube - is used to measure the velocity of flow.
L = pipe length g = 9.81
= 32.2
C. Pressure drop in the pipe, Pd Pd = ɣhL Exercise #5: Water is flowing at a rate of 3,500 GPM. The inside radius is 8 cm and coefficient of friction is 0.0181. What is the pressure drop over a length of 50 m?
Q = A1v1 = A 2v2 For circular cross-section: A =
For rectangular cross-section: cross-section: A = bh Where, ρ =
in
A. If venturi-meter is horizontal:
Figure 1.6
=
Bouyancy - Archimedes Principle: A body partly or wholly submerged in a liquid is buoyed up by a force equal to the weight of the liquid displaced.
B. If venturi-meter is vertical
A. Weight of object in air
Figure 1.7
Figure 1.8
= - (z - z ) 1
Wo =
2
Where, P1 = inlet pressure P2 = throat pressure A perfect venturi with throat Exercise #6: diameter of 2 in. is placed horizontally in a pipe with 2 inches is placed horizontally in a pipe with 6 inches inside diameter. What is the difference between the pipe and venturi throat static pressure if the mass flow rate of water is 100 lb/sec?
Where,
o =
oVo
weight density of object = SG o
Vo = total volume of object
B. If the object is floating
Figure 1.9
BF = bouyant force = W o = ɣfVd = ɣoVo Where, ρf = density of fluid = SG f Vd = volume displaced Ve = volume exposed to air
ρw
w
Exercise #7: A 2 meter rod floats vertically in water. It has a 7 cm2 cross sectional and a specific gravity of 0.6. What length, L, is submerged?
C. If the object is submerged
Figure 1.9.1
BF = ɣfVo Wo = ɣoVo R + BF = Wo Where, R = weight of object in water Vo = Vd
Exercise #8: What is the buoyant force of a body that weighs 100 kg in air and 70 kg in water?
CHAPTER 2
Hydro-electric Power Hydraulics - branch of mechanics which deals with the laws governing the behavior of water and other liquids in the states of rest and motion. Hydrostatics - is a branch of hydraulics which deals on the study of fluids at rest.
L ao Tzu, Tzu, the Chin ese ese fou nder of Taoi sm
Hydrokinetics - branch of hydraulics which deals with the study of pure motion in liquids.
in t he 5th Centu Centu ry BC, stated: stated:
“If you give a man a fish, you feed him for a day. If you teach teach a man to fish you you feed him him for a lifetime.” “ Ar Ar e our schools fail in g to teach teach people people to fi sh? Or ar e our our schools teachi teachi ng students that th ey are entitl ed to their daily f ish? I s this why th ere are more and more people people are depe dependent ndent upon th e govern govern ment for li fe support support ? ”
Hydrodynamics - branch of hydraulics which deals with the study of forces exerted by or upon liquids in motion. Cohesion - is a fluid property which refers to the intermolecular attraction by which the separate particles of the fluid are held together. Adhesion - is a fluid property which refers to the attractive force between the molecules and any solid substance with which they are in contact.
- RTK Surface tension - is the force per unit length that “
Ask not what your country can do for you Ask what you can do do for your country.” country.”
- President John Kennedy
an “imaginary film” formed on the surface of a liquid
due to intermolecular attraction is capable of exerting. Fluid Mechanics - is a branch of science which deals with the study of water and other fluids that are at rest or in motion. Reservoir - stores the water coming from the opper river or waterfalls. Spillway - a weir in the reservoir which discharges excess water so that the head of the plant will be maintained.
Dam - a concrete structure that encloses the reservoir. Silt sluice - a chamber which collects the mud and through which the mud is discharged. Trash rack - a screen which prevents the leaves, branches and other water contaminants to enter into the penstock. Surge chamber - a standpipe connected to the atmosphere and attached to the penstock so that the water will be at atmospheric pressure. Penstock - the channel that leads the water from the reservoir to the turbine. Turbine - converts the energy of the water into mechanical energy. Generator - converts the mechanical energy of the turbine into electrical energy output. Draft tube - connects the turbine outlet to the tailwater so that the turbine can be set above the tailwater level. Used to keep the turbine up to 15 ft. above the tail water surface. Tailrace - a channel which leads the water from the turbine to the tailwater.
Cavitation - occurs then the pressure at any point in the flowing water drops below the vapor pressure of the water which varies with temperature. Weir - any obstruction of a stream flow over which water flows. Types of turbine: 1. Propeller turbine (for small capacity) - axial flow turbines have low heads up to 110 ft., high rotational speeds and large flow rates. This turbine operates with specific speeds in the range of 80 and 200 rpm range. But best efficiencies is between 120 and 160 rpm. 2. Reaction turbines or francis turbine (for medium capacity) - the specific speed varies from 10 to 100. Best efficiencies are found in the 40 to 60 range. Heads between 110 to 800 ft. 3. Impulse turbine (for large capacity) - radial flow or Pelton Wheel turbines have the lowest specific speeds but are used when heads are high (800 ft to 1,600 ft.). These turbines have specific speeds below 5. The kinetic energy of the jet is converted into rotating kinetic energy.
Tailwater - the water is discharged from the turbine. Peripheral coefficient - ratio of the peripheral velocity of the runner over the velocity of the jet. Water hammer - caused because of sudden stoppage of water flow in a pipe. Surge tank - artificial reservoir used to relieve the pipe line of excessive pressure. Wicket gates - control the power and speed of turbine Figure 2.1: Hydro-electric Power Plant
Formulas:
F. Water Power, PW
A. Gross head, hg
PW = ɣwQh
hg = head water elevation - tail water elevation B. Friction head loss, hf
Where, ɣw = specific weight of water = 9.81
Using Morse Equation:
62.4
G. Turbine efficiency, eT
hf =
=
eT =
Using Darcy’s Equation:
Where, PB = Brake power or turbine output
hf =
H. Generator efficiency, eG eG =
PB = PW
Where, hf = friction head loss f
=
coefficient
of
friction
or
friction I. Turbine output, PB
factor L = length of penstock g = 9.81
= 32.2
eT
J. Generator output, Pgen Pgen = PB
D = inside diameter
eG = (PW
eT)
eG
K. Generator speed, N
C. Net head, h
N =
h = hg - hf D. Penstock efficiency, e e =
Where, N = speed
f = frequency p = no. of poles (must be even no.)
E. Volume flow of water, Q Q = Av
L. Utilized head, hw hw = h
eh
Where, eh = hydraulic efficiency
Exercise #1: In a hydroelectric power plant the tail water elevation is at 500 m. What is the head water elevation if the net head is 30 m and the head loss is 5% of gross head?
M. Head of Pelton (Impulse) turbine: h =
+
Where, ρ = density of water = 1,000
Figure 2.2: Pelton Type Turbine Exercise #2: The tailwater and the headwater of a hydro-electric plant are 150 m and 200 m respectively. What is the water power if the flow is 15 m³/s and a head loss of 10% of the gross head?
Exercise #3: An impulse wheel at best produces 125 hp under a head of 210 ft. By what percent should the speed be increased for 290 ft. head?
Exercise #4: In a double-overhung impulse-turbine installation is to develop 20,000 hp at 275 rpm under a net head of 1,100 ft. Determine the specific speed.
Where, D = diameter of runner, m N = speed of runner, rps P. Specific speed of hydraulic turbine NS =
√ , rpm
NS =
*h in feet
√ √ ,
rpm
*h in meters *N in rpm
Q. Total efficiency, et et = ehemev Where, ev = volumetric efficiency em = mechanical efficiency R. Turbine type selection based on head, ft. N. Head of Reaction (Francis and Kaplan) turbines:
+ z h = +
NET HEAD Up to 70 feet
TYPE OF TURBINE TURBINE Propeller Type
70 - 110 ft.
Propeller or Francis
110 – 800 ft.
Francis Turbine
800 – 1,300 ft.
Francis or Impulse
1,300 ft. and above
Impulse Turbine
For small capacity, use Propeller Turbine. For medium capacity, use Francis Turbine. For high capacity, use Impulse Turbine. Figure 2.3: Francis Turbine
O. Peripheral coefficient, Φ Φ =
=
Exercise #5: A pelton type of turbine has a gross head of 40 m and a friction head loss of 6 m. What is the penstock diameter if the penstock length is 90 m and the coefficient of friction head loss is 0.001 Morse?
Exercise #6: A Pelton type turbine has 25 m head friction loss of 4.5 m. The coefficient of friction head loss (from Morse) is 0.00093 and penstock length of 80 m. What is the penstock diameter?
CHAPTER 3
Air Compressor Air Compressor - a machine which is used to increase the pressure of a gas by decreasing its volume.
Y ou cannot bri ng about prospe prosperi ri ty by discouraging discouraging th ri ft. “ You You cann ot strengthen the weak weak by weakenin weakenin g the stron stron g. You cann ot help th e wage wage earn earn er by
The work input to a compressor is minimized when the compression process is executed in an internally reversible manner. Isentropic process in compression process involves no cooling. (n = k). For most steady-flow devices, this is the ideal process that can be served as a suitable model.
pul li ng down the wage payer. payer. Polytropic process in compression process involves
You cannot fur ther the brotherhood brotherhood of man by encouragi ng class hatred. You cannot h elp the poor poor by des destr oying th e ri ch. You cannot k eep eep out of tr oubl e by
some cooling. (1
n
k)
Isothermal process in compression process involves maximum cooling. (n = 1) Adiabatic compression requires maximum work of compression.
spending spending mor e than you earn earn . You cannot bui ld char acter acter and courage by ta takin kin g away man's ini ti ative and independence independence.. You cannot help men permanently permanently by doin doin g for them what they coul coul d and should do f or th emselve emselves s .”
- Rev. William J. H. Boetcker
Isothermal process requires minimum work of compression. Practically, all compressors are powered by electric motors. The ratio of mechanical power required to the electrical power consumed during operation is called the motor efficiency. We =
Where, We = electric power/work, Wc = compressor power/work, em = motor efficiency Adiabatic efficiency is a measure of the deviation of actual process from corresponding idealized zone.
Isentropic efficiency of turbine is the ratio of the actual work output of the turbine to the work output that would be achieved of the process between the inlet state and the exit pressure were isentropic. eT =
Single-stage reciprocating compressor:
Where, eT - isentropic efficiency, Wa - actual turbine work, Wi - ideal turbine work Isentropic efficiency of compressor is the ratio of the work input required to raise the pressure of a gas to a specified value in an isentropic manner to the actual work input. eT =
Where, eT - isentropic efficiency, Wa - actual compressor work, Wi - ideal compressor work
Figure 3.1
Formulas: A. Compression process 1 to 2:
Uses of compressor:
- to drive pneumatic tools - sand blasting - industrial cleaning - spray painting - starting a diesel engine - to supply air in mine tunnels - manufacture of plastic and industrial products Figure 3.2
Classification of air compressor: 1. Reciprocating compressor 2. Centrifugal compressor 3. Rotary compressor
P1V1n = P2V2n
= ()
= ()
B. Piston displacement, VD
Where, B = D = piston rod diameter or bore
For singe-acting compressor:
S = stroke or piston length
B SN,
C. Capacity of compressor, V1
2
VD =
V1 = volume flow at suction =
For double-acting compressor:
D. Volumetric efficiency, e v
e = v
= 1 + c - c( )
E. Compressor power, Wc
Wc =
[() ]
Where, P1 = suction pressure
Figure 3.3
P2 = discharge pressure F. Compressor efficiency, e c ec = Where, PB = Brake power G. Piston speed = 2SN Figure 3.4
Piston rod neglected: VD = 2
( ) ,
Piston rod neglected: VD =
( ) * ( )+ +
,
The discharge pressure of an air Exercise #1: compressor is 5 times the suction pressure. If volume flow at suction is 0.1 m³/sec, what is the suction pressure if compressor work is 19.57 KW? (Use n = 1.35).
Two-stage reciprocating compressor:
Figure 3.5
Formulas: A. Compressor work, Wc
W = [() ] c
Exercise #2: The initial condition of air in an air compressor is 98 KPa and 27°C and discharges air at 450 KPa. The bore and stroke are 355 mm and 381 mm, respectively with percent clearance of 8% running at 300 rpm. Find the volume of air at suction.
B. Intercooler pressure, P x Px =
Figure 3.6
C. Heat rejected in the intercooler, Q Q = mcp(Tx - T 1)
m = = ()
3. Three-stage air compressor
Where, cp = 1
Tx = intercooler temperature D. Adiabatic compressor efficiency Figure 3.7
e = c
E. Ideal indicated power, IP IP = PmiVD Exercise #3: A two stage air compressor has an intercooler pressure of 4 kg/cm². What is the discharge pressure if suction pressure is 1 kg/cm²? Figure 3.8
Formulas: A. Intercooler pressure, Px Px =
B. Compressor power, Wc
Wc =
[() ]
C. Heat rejected in the intercooler, Q Q = 2mcp(Tx - T 1)
Where, cp = 1
m =
=
()
CHAPTER 4
Fans and Blowers Fan - a machine which is used to apply power to a gas in order to cause movement of the gas.
“The test of a first -rate - rate intelli gence gence is the abili abili ty to hol d two opposed opposed ideas in th e min d at th e same same time, and stil stil l retain the ability to function.”
F. Scott Fitzgerald – F. “Al l coins have th ree sides: sides: h eads, eads, tai l s, and th e edge. edge. Th e most most in telli gent people people li ve on on th e edge edge,, abl e to see see both sides. sides.
Blower - a fan which is used to force air under suction, that is, the resistance to gas flow is imposed primarily upon the discharge. Exhauster - a fan which is used to withdraw air under suction, that is, the resistance to gas flow is imposed primarily upon the inlet. Capacity of fan - volume flow rate measured at the outlet.
I n school school th ere is only one righ t answer. answer. I n r eal l if e there there is more than one right answe answer, r, a wave wave of choices fr om dif ferent perspectives perspectives and poin ts of view.
Here‟s an example. When When I asked my poor dad what 1+1 equaled, his answer was “2.” Rich dad‟s answer to that same question question was dif ferent. His answer was was “11.”
Types of fans: 1. Propeller fan 2. Tubeaxial fan 3. Vaneaxial fan
Thi s is why one man was poor poor and th e other r ich.
4. Centrifugal fan
I n other words, the idea idea of r ight vs. wrong, which i s taught in school, is unintelli gent. gent. I n fact it is ignorant, ignorant, since „right „right vs. wrong‟ ignores, ignores, rath er than explores, explores, the other side. side. I n my opini on, the idea idea of r ight versus versus wrong wrong i s the basis basis of all disagreements, disagreements, ar guments, divor ce, ce, un happin ess ess, aggression, aggression, viol ence, ence, and war .”
- RTK
Figure 4.1
Formulas:
D. Air power, Pa
A. Static head, hs hs =
Pa =
Where, Q = fan capacity,
Where, hw = manometer reading, meters of water
ɣw = specific weight of water = 9.81 ɣa = specific weight of air = 1.2
Ps =
es =
Variable speed (constant fan size and density)
=
o
hv =
suction
C. Total head, h
= ()
= ()
Variable density (constant fan size and density) and
discharge
are
Q1 = Q2
=
Where, ρ = density of air P = power h = head
h = hs + hv
H. Fan laws
v
at
ɣaQhs
G. Static efficiency, es
h = v = outlet velocity, g = 9.81 = 32.2 velocity
F. Static power, Ps
B. Velocity head, hv
If both given,
ef =
h =
Where,
KW
E. Fan efficiency, ef
If both static head at suction and discharge are given,
s
ɣaQh,
N = speed
=
Exercise #1: A fan draws 1.42 m³ per second of air at a static pressure of 2.54 cm of water through a duct 300 mm diameter and discharges it through a duct of 275 mm diameter. Determine the static fan efficiency if total fan mechanical is 75% and air is measured at 25°C and 760 mmHg.
Exercise #2: Calculate the air power of a fan that delivers 1,200 m³/min of air through a 1 m by 1.5 m oulet. Static pressure is 120 mmHg and density of air is 1.18 kg/m 3.
Exercise #3: The fan has a total head of 190 m and a static pressure of 20 cmHg. If the air density is 1.2 kg/m³, what is the velocity of air flowing?
CHAPTER 5
Pumps Pump - a machine which is used to add energy to a liquid in order to transfer the liquid from one point to another point of higher energy level.
“Give, and you will receive. Your gif t wil l r etur n to you in fu ll - press pressed down, down, shaken shaken
Aquifers - deep ground water deposits where underground water are available for water supply and irrigation. Hydraulic gradient - the locus of the elevation which water will rise in a piezometer tube.
together together to make room for more, runn ing over, and poured into your lap. The amount you give wil wil l dete determi rmi ne the
amount you get back.”
- Luke 6:38 (NLT) “A man‟s true worth is the good he does in this world.” - Mohammad “ The T he tru e pri pri nciple of capitalism is, „ Th Th e more people people I serve, erve, the more effective I become.‟ You mu st be gene generou rou s if you want to serve serve as many people as possibl possibl e. Un for tun ately, many people people want to be paid more, do less, less, and retir e earl earl y.
Doesn‟t this violate violate the principle principle of generosity?” generosity?”
Figure 5.1: Pump System
- RTK Types of pumps: 1. Reciprocating pump
Low discharge, high head, self-priming, up to 5 ft. suction lift, positive displacement pumps: 1. Piston type 2. Plunger type
3. Bellows or diaphragm
2. Centrifugal pump
Figure 5.3
High discharge, low head, not self-priming: Figure 5.2
1. Radial flow - used for single and souble suction
This is commonly used as Boiler Feed Pump for steam. 2. Axial flow - acting like compressors Reciprocating pumps can be single-acting or doubleacting. They can be simplex, duplex, triplex, etc. Air chamber - is to smoothen the flow due to the nature of flow of liquid. This can be placed on the suction side or discharge side of piping installation. Relief valve - this should be installed on the discharge side between pump and any other valve.
3. Mixed flow Centrifugal pump is used to convert kinetic energy into pressure energy through diffuser vanes. Specific speed - is defined as that speed in rpm at which a given impeller would operate to deliver 1 GPM against a total dynamic head of 1 foot. Specific speed is constant and is given by the manufacturer.
Foot valve - should be installed at the end of the suction pipe.
Impellers for higher heads usually have low specific speeds. Impellers for lower heads usually have higher specific speeds.
All losses of capacity given in percentage of the displacement are referred to as slip: (1 - e v).
For double suction pumps, the Q value is determined by dividing the given capacity by 2.
In new pumps, the slippage is within 2%.
3. Rotary pump
5. Deep well pump
1. Turbine pumps - high suction lift up to 305 m. 2. Plunger pumps - are refinement of the old hand pumps. This is best suited where the lifts are 7.6 m or over and capacities up to 190 liters per minute. 3. Ejector - a centrifugal pump used for small capacities combines a single-stage centrifugal pump at the top of the well and an ejector or jet located down in the water. Figure 5.4
Positive head:
displacement
pumps,
low
discharge,
low
4. Air lifts - another method of pumping wells is by compressed air being admitted to the well to lift the water to the surface. Classification of pumps based on suction lift
1. vanes
1. Shallow well pump - suction lift up to 25 ft.
2. screws
2. Deep well pump - sution lift up to 120 ft.
3. lobes
3. Turbine pump - up to 300 ft.
4. gear
4. Submersible pump - for high head
5. cam and piston
Cavitation - is the spontaneous vaporization of the fluid, resulting in a degradation of pump performance.
6. shuttle block type 4. Kinetic pump - transform fluid kinetic energy to fluid static ppressure energy.
Causes of cavitation: 1. Discharge head far below the pump head at peak efficiency.
1. jet pumps 2. ejector pumps
2. High suction lift or low suction head 3. Excessive pump speed 4. High liquid temperature
Figure 5.5
Bad effects of cavitation:
Pump head:
1. Drop in capacity and efficiency
1. Friction head - head required to overcome resistance to flow in the pipe, fittings and valves.
2. Noise and vibration 3. Corrosion and pitting NPSH (Net Positive Suction Head) - is the difference between actual suction pressure and saturation vapor pressure of the liquid. NPSHR (Net Positive Suction Head Required) - is a function of the pump, and will be given by the pump manufacturer as part of the pump available at the name plate. NPSH A (Net Positive Suction Head Available) - is the actual fluid energy at the inlet.
If NPSHA is less than NPSHR, the fluid will cavitate. Preventing cavitation:
1. Increasing the height of the fluid source. 2. Reducing friction and minor losses by shortening the suction line or using larger pipe size. 3. Reducing the temperature of the fluid at the pump entrance. 4. Pressurizing the fluid supply tank. 5. Reducing the flow rate or velocity.
2. Velocity or dynamic head - specific kinetic energy of the fluid. 3. Static suction head - the vertical distance above the centerline of the pump inlet to the free level of water source. 4. Static suction lift - the vertical distance from pump certerline to the free level of water source below the pump inlet. 5. Static discharge head is the vertical distance from pump centerline to the free level of the fluid in the discharge tank. 6. Total suction head - is the head that includes static head, velocity head and friction head at the suction side. 7. Total discharge head - is the head that includes static head, velocity head and friction head at the discharge side. 8. Head - refers to all the head both at suction and discharge. 9. Drawdown - is the difference between water level and operating water level. 10. For duplex pumps: Pump dimensions: D s x D w X L Ds = steam diameter Dw = water diameter L = length of stroke
static
11. Pump slip
13. Parallel pump
For positive slip, the coefficient (Cd) is less than 1 (decreases).
of
discharge
To increase parallel.
the
discharge,
connect
the
For negative slip, the coefficient (Cd) is more than 1 (decreases).
of
discharge
The discharge of pump in parallel is Q 1 + Q 2.
pump
in
The heads, h1 = h2.
12. Series pump To increase the head, connect the pump in series. The head of pump in series is h 1 + h2. The volume flow is Q 1 = Q2.
Figure 5.7
14. To increase the head of submersible pump, increase the number of stages of number of impeller.
Figure 5.6
Formulas:
F. Pump efficiency, ep ep =
G. Head as determined from two pressure readings: h =
+ + z
Where, P1 is negative if vacuum
Figure 5.8
A. Volume flow rate of water, Q Q = Av B. Pressure head, hp hp =
Figure 5.9
C. Velocity head, hv hv =
H. Friction head, hf
Darcy’s Equation: h f =
D. Total head of pump, h h = (hp2 - hp1) + (hv2 - hv1) + (z 2 - z1) + (hf1 + hf2) Where, z1 is negative if source is below pump center line.
Morse Equation: hf =
I. Specific speed, Ns Ns =
Ps is negative if it is a vacuum. E. Water power, P W
Where, N = speed, rpm PW =
Where,
ɣw =
ɣwQh,
KW
specific weight of water
Q = discharge, gpm h = head, ft
J. Similar pumps:
L. Characteristics of Reciprocating pumps:
= = K. For the same pump: Constant impeller diameter, variable speed:
=
=
()
= ()
Figure 5.9.1
1. Piston Displacement:
Constant speed, variable impeller diameter:
= ()
= ()
= ()
Piston rod neglected:
Piston rod considered: VD =
Constant speed, variable fluid density:
=
=
=
VD = 2
( ),
+ ,
2. Slip = V D - Q 3. %slip =
x
100%
4. volumetric efficiency, e v =
= 1 - Slip
Exercise #1: A 4 m³/hr pump delivers water to a pressure tank. At the start, the gage reads 138 KPa until it reads 276 KPa and then the pump was shut off. The volume of the tank is 180 liters. At 276 KPa, the water occupied 2/3 of the tank volume. Determine the volume of water that can be taken out until the gage reads 138 KPa.
Exercise #2: If a 1/3 horsepower pump runs for 20 min, what is the energy used?
Exercise #3: A double suction centrifugal pump delivers 20 ft³/sec of water at a head of 12 m and running at 650 rpm. What is the specific speed of the pump?
“Generosity is the key to succes. What are our schools teaching teaching our chil dren? Are they giving giving th em f ish to eat, eat, keepin keepin g th em needy needy and, of ten, greedy? greedy? Or do they teach teach ki ds to fi sh, to be self self -r eliant , in novative, and responsible responsible enou enou gh to f eed eed th emselves emselves? ? N eedy eedy people become gr eedy eedy people. Gr eedy eedy people become desperate desperate people. A nd desperate desperate people do desperate desperate th in gs.
I believe genius genius is found found at Maslow‟s fifth fifth level. At that level level are found powerf powerf ul and beautif beautif ul words, words, values, values, and abili ties
essential for today‟s world. The words are: 1. M orality: you don‟t have have to cheat cheat people to be be rich 2. Creativity: Creativity: tap into your geniu geniu s 3. Spontaneity: Spontaneity: li ve without the fear of making mistakes mistakes 4. Problem solvin solvin g: f ocus on solu solu tion s 5. Lack of prejudi ce: ce: h aving a wider wider context on lif e 6. Acceptance Acceptance of fact: not afraid to face the truth”
- RTK
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