CENTRIFUGAL PUMPS
CENTRIFUGAL PUMPS
e-notes: Dr.N.Balasubramanya e-notes: Dr.N.BalasubramanyaProfessor, Department of Civil Engineering Professor, Department of Civil Engineering
M.S.Ramaiah Institute of Technology, Bangalore-560054 M.S.Ramaiah Institute of Technology, Bangalore-560054
A pump is a hydraulic machine which converts mechanical energy into hydraulic energy A pump is a hydraulic machine which converts mechanical energy into hydraulic energy or pressure energy.
or pressure energy.
A centrifugal pump is also known as a Rotod
A centrifugal pump is also known as a Rotodynamic pump or dynamic pressure pump. Itynamic pump or dynamic pressure pump. It works on the pri
works on the principlnciple of centrife of centrifugal forceugal force. In this. In this type of pump the liqutype of pump the liquid is subjecteid is subjected tod to whirling motion by the rotating impeller which is made of a numbe
whirling motion by the rotating impeller which is made of a numbe r of backward curvedr of backward curved vanes. The liquid enters this impeller at its center or the e
vanes. The liquid enters this impeller at its center or the e ye and gets discharged into theye and gets discharged into the casing enclosing the outer
casing enclosing the outer edge of the impeller. The redge of the impeller. The rise in theise in the pressure head at anypressure head at any point/outlet of
point/outlet of the impeller the impeller isis Proportional to Proportional to the square the square of the tangential of the tangential velocity of tvelocity of thehe liquid at that point
liquid at that point )) 2g 2g 2 2 u u α α (i.e,
(i.e, .. Hence at the outlet of Hence at the outlet of the impeller where the radius the impeller where the radius isis more the rise I
more the rise In pressure head willn pressure head will be more and the liquid wibe more and the liquid will be discharged at the ll be discharged at the outletoutlet with a high pressure head. Due to this
with a high pressure head. Due to this high pressure head, the liquid can be high pressure head, the liquid can be lifted to alifted to a highe
higher level.r level. GeneraGenerally centrlly centrifugaifugal pumps are made of tl pumps are made of the radial fhe radial flow type onlylow type only. But. But there are also axial
there are also axial flowflow or propeller pumps or propeller pumps which are particularly adopted for which are particularly adopted for low heads.low heads. Advantages of centrifugal
Advantages of centrifugal pumps:-1.
1. ItIts is ininititial al cocost st is is loloww 2.
2. EfEffificicienency icy is his highgh..
3. Discharge is uniform and continuous 3. Discharge is uniform and continuous 4. Installation and maintenance is easy. 4. Installation and maintenance is easy. 5. It can run at high
5. It can run at high speeds,without the risk of separation of flowspeeds,without the risk of separation of flow Classification of centrifugal pumps
Classification of centrifugal pumps Centrifugal pumps may be
Centrifugal pumps may be classifiedclassified Into the following types
Into the following types 1.According to casing design 1.According to casing design
a)
a) VolVolute ute pump pump b) b) difdiffusfuser er or or turturbinbine pe pumpump 2. According to number of impellers
2. According to number of impellers a)
a) SinglSingle stage stage pump e pump b) mulb) multistatistage or ge or multi multi impelimpeller puler pumpmp 3. According to number of entrances
3. According to number of entrances to the impeller:
to the impeller: a)
a) SiSingngle le susuctctioion n pupumpmp (FOR FIGURES DOWNLOAD PRESENTATION)(FOR FIGURES DOWNLOAD PRESENTATION) b)
b) DoDoububle le susuctctioion pn pumumpp
4. According to disposition of shaft 4. According to disposition of shaft
a)
a) VeVertrticical al shshafaft t pupumpmp b)
b) HoHoririzonzontatal shl shafaft put pumpmp 5. According to liquid handled 5. According to liquid handled
a)
a) SeSemi omi opepen imn impepellllerer b)
6.According to specific speed 6.According to specific speed
a)
a) Low Low specifspecific sic speed or peed or radiaradial fll flow imow impellepeller pumr pumpp b)
b) ShShroroududed ed imimpepellllerer c)
c) Medium Medium specispecific fic speed speed or mior mixed fxed flow ilow impellmpeller per pumpump c) High s
c) High specific speedpecific speed or axial flow or axial flow type or prtype or propeller pump.opeller pump. 7. According to head (H)
7. According to head (H) •• Low head if H<15mLow head if H<15m
•• Medium head if 15<H<40mMedium head if 15<H<40m •• High head if H>40mHigh head if H>40m
In the ca
In the case of ase of a volute pvolute pumpump a spira spiral casial casing is provng is provided arided aroundound the impeller. The water
the impeller. The water which leaves the vanes is which leaves the vanes is directed to flowdirected to flow in the volute chamberin the volute chamber circumferentially. The area of the volute chamber graduall
circumferentially. The area of the volute chamber graduall y increases in the directiony increases in the direction flow. Thereby the velocity reduces and hen
flow. Thereby the velocity reduces and hence the pressure increases. As the water reachesce the pressure increases. As the water reaches the delive
the delivery pipe a considerablry pipe a considerable part of kinetice part of kinetic energyenergy is converis converted into pressurted into pressure energy.e energy. However, the eddies are not completely avoided
However, the eddies are not completely avoided , therefore some loss of energy takes, therefore some loss of energy takes place due to the continually increasing quantity o
place due to the continually increasing quantity o f water through the volute chamber.f water through the volute chamber. In the case of a diffuser pump the guide
In the case of a diffuser pump the guide wheel containing a series of guide wheel containing a series of guide vanes orvanes or diff
diffuser is theuser is the additiadditional componeonal component. The diffusent. The diffuser blades which provr blades which provides graduaides graduallylly enlarging passages surround the impeller periphery. They serve to au
enlarging passages surround the impeller periphery. They serve to au gment the process of gment the process of pressure built
pressure built up that is up that is normally achieved inormally achieved inn the volute casing. the volute casing. Diffuser pumps Diffuser pumps are alsoare also called turbine pumps in view of their resemblance to
called turbine pumps in view of their resemblance to a reaction turbine.a reaction turbine.
Multistage pumps and vertical shaft deep-well pumps fall under this category. Multistage pumps and vertical shaft deep-well pumps fall under this category. Centrifugal pumps can normally develop pressures upto 1000kp
Centrifugal pumps can normally develop pressures upto 1000kp a (100m). If highera (100m). If higher pressures are requir
pressures are required there are three options.a)ed there are three options.a) Increase of impeller Increase of impeller diameter.diameter. b)Increase of Rpm.
b)Increase of Rpm. c)Use of two or c)Use of two or more impellers in sermore impellers in series.ies.
The pump looks clumsy in option (a). The impeller material is heavily stressed in option The pump looks clumsy in option (a). The impeller material is heavily stressed in option (b)
(b) The thirThe third choice is d choice is the best the best and is genand is generally aerally adopted, tdopted, the impehe impellersllers which arwhich are usuallye usually of the same size are mounted on
of the same size are mounted on the same shaft. The unit is called a multistage pump. the same shaft. The unit is called a multistage pump. ItIt discharges the same quantity of fluid as a single stage pump
discharges the same quantity of fluid as a single stage pump but the head develobut the head develo ped isped is high. There are centrifugal pumps upto 54
high. There are centrifugal pumps upto 54 stages. However, generally not more than 10stages. However, generally not more than 10 stages are required.
stages are required. In the case of the In the case of the double suction impeller, two double suction impeller, two impellers are seimpellers are set back t back to back. The two suction eyes together reduce the intake. The two suction eyes together to back. The two suction eyes together reduce the intake. The two suction eyes together reduce the intake velocity reduce the
reduce the intake velocity reduce the risk of cavitations. Mixed flow type double suctionrisk of cavitations. Mixed flow type double suction axial flow pumps
axial flow pumps besides are besides are capable of developing higher capable of developing higher heads.heads. For convenience of For convenience of operation and maintenance, horizontal shaft settings are the pref
operation and maintenance, horizontal shaft settings are the pref erred setups forerred setups for centrifugal pumps. The exceptions are deep-well turbine pu
centrifugal pumps. The exceptions are deep-well turbine pu mps and axial flow pumps,mps and axial flow pumps, these have vertical shafts. Restricted space conditions usually require a vertical shaft these have vertical shafts. Restricted space conditions usually require a vertical shaft setti
setting.ng. CentrCentrifugal iifugal impellempellers usualrs usually have vanes fily have vanes fitted bettted betweenween the shrthe shroudes or plaoudes or plate.te. The crown plate has the suction
The crown plate has the suction eye and the base plate is mounted eye and the base plate is mounted on a sleeve whichon a sleeve which is keyed to the shaft. An impeller without the crown
is keyed to the shaft. An impeller without the crown plate is called the nonplate is called the non-clog or semi--clog or semi-open impeller. In an
open impeller. In an open impeller both crown plateopen impeller both crown plate and the base plate are absent.and the base plate are absent. Only clear liquids, can be safely pumped by a shrouded impeller pump. The semi-open Only clear liquids, can be safely pumped by a shrouded impeller pump. The semi-open impeller is useful for pumping liquids containing suspended solids, such as sewage, impeller is useful for pumping liquids containing suspended solids, such as sewage, molasses or paper pulp. The open-vane
molasses or paper pulp. The open-vane impeller pump is employed for dredgingimpeller pump is employed for dredging operations in harbours and rivers. Shrouded and semi open
iron
iron Or cast Or cast steel. Open vane impelsteel. Open vane impellers are uslers are usually made of ually made of forged steel. Iforged steel. If the liquidf the liquid pumped are corrosive, brass, bronze or gun metal
pumped are corrosive, brass, bronze or gun metal are the best materials for making theare the best materials for making the impellers.
impellers.
A radial flow impeller has small specific speeds (300 to 1000) & is suitable for A radial flow impeller has small specific speeds (300 to 1000) & is suitable for discharging relatively s
discharging relatively small quantities of flmall quantities of flow against highow against high heads. The direction of flowheads. The direction of flow at exit of the impell
at exit of the impeller is radial. er is radial. The mixedThe mixed flow type of impellflow type of impellers has a high specifers has a high specificic speed (2500 to 5000), has large inlet d
speed (2500 to 5000), has large inlet diameter D and impeller width B to handle iameter D and impeller width B to handle relativelyrelatively large discharges against medium heads. The axial flow type or
large discharges against medium heads. The axial flow type or propeller impellers havepropeller impellers have the highest speed range (5000 to 10,000). They are capable of pumping large discharges the highest speed range (5000 to 10,000). They are capable of pumping large discharges against small heads. The specific speed of radial pump
against small heads. The specific speed of radial pump will be 10<Ns<80, Axial pumpwill be 10<Ns<80, Axial pump 100<Ns<450, Mixed flow pump 80<Ns<160.
100<Ns<450, Mixed flow pump 80<Ns<160. Components of a centrifugal pump
Components of a centrifugal pump
The main components of a centrifugal pump The main components of a centrifugal pump are:are:
i) Impeller ii) Casing iii) Suction pipe iv) Foot valve with strainer, v) Delivery pipe vi) i) Impeller ii) Casing iii) Suction pipe iv) Foot valve with strainer, v) Delivery pipe vi) Delivery valve.
Delivery valve. Impeller
Impeller is the rotating component of the pump. is the rotating component of the pump. It is made up of a series of curvedIt is made up of a series of curved vanes. The impeller is mounted on the shaft conn
vanes. The impeller is mounted on the shaft conn ecting an electric motor.ecting an electric motor. Casing
Casing is an air tight chamber surrounding the impeller. The shape of is an air tight chamber surrounding the impeller. The shape of the casing isthe casing is designed in such a way that the
designed in such a way that the kinetic energy of the impeller is gradually changed kinetic energy of the impeller is gradually changed toto potential energy. This is achieved by graduall
potential energy. This is achieved by gradually increasing the area of cross y increasing the area of cross section in thesection in the direction of flow.
direction of flow. Suction pipe
Suction pipe It is the pipe connecting the pump to It is the pipe connecting the pump to the sump, from where the liquid has tothe sump, from where the liquid has to be lifted up.
be lifted up.
Foot valve with strainer
Foot valve with strainer the foot valve is a non-return valve which permits the flow of the foot valve is a non-return valve which permits the flow of the liquid from t
the liquid from the sumphe sump towards the pump. In towards the pump. In other words the foot valve other words the foot valve opens only inopens only in the upward direction.
the upward direction.
The strainer is a mesh surrounding the valve, it prevents the entry of debris and silt into The strainer is a mesh surrounding the valve, it prevents the entry of debris and silt into the pump.
the pump. Delivery pipe
Delivery pipeis a pipe connected to the pump to the overhead tank.is a pipe connected to the pump to the overhead tank. Delivery valve
Delivery valve is a valve which can reis a valve which can regulate the flow of liquid from the pump.gulate the flow of liquid from the pump. Priming of a centrifugal pump
Priming of a centrifugal pump
Priming is the process of filling the suction pipe, casing of the pump and
Priming is the process of filling the suction pipe, casing of the pump and the deliverythe delivery pipe upto the delivery valve with the liquid to be pumped.
pipe upto the delivery valve with the liquid to be pumped. If priming is not done the pump cannot deliv
If priming is not done the pump cannot deliver the liquid due to the fact that theer the liquid due to the fact that the head generated by the
head generated by the Impeller will be in terms of meters of air which will be very smallImpeller will be in terms of meters of air which will be very small (because specific weight of air is very much smaller than that of
(because specific weight of air is very much smaller than that of water).water). Priming of a centrifugal pump can be done b
Priming of a centrifugal pump can be done b y any one of the following my any one of the following methods:ethods: i)
i) PrPrimimining wg witith sh sucuctitionon/v/vacacuuuum pm pumump.p. iiii)) PPrriimmiinng wg wiitth a h a jjeet t pupummpp..
ii
iii)i) PrPriimiming ng wwitith h ssepepararatatoror.. iv
iv)) AuAutotomamattic ic or or sesellf f prprimimiingng.. Heads on a centrifugal pump: Heads on a centrifugal pump: Suction head (hs):
Suction head (hs):it is it is the verticalthe vertical distance between the distance between the liquid levelliquid level in the sump and the centre line
in the sump and the centre line of the pump. It is expressed as meters.of the pump. It is expressed as meters. Delivery head (hd):
Delivery head (hd):It is the vertical distance between the centre line oIt is the vertical distance between the centre line o f the pump andf the pump and the liquid level in t
Static head (Hs):
Static head (Hs): It is the vertical difference between the liquid levelsIt is the vertical difference between the liquid levels In the overhead tank and
In the overhead tank and the sump, when the pump is nthe sump, when the pump is not working. It is expressed asot working. It is expressed as meters.
meters. Therefore,
Therefore,HS= (hs+ hd)HS= (hs+ hd) Friction head (hf):
Friction head (hf): It is the It is the sum of thesum of the head loss due to the fhead loss due to the friction in the suction andriction in the suction and delivery pipes. The friction loss in both the
delivery pipes. The friction loss in both the pipes is calculated using the Darcy’spipes is calculated using the Darcy’s equation,
equation,hf=(fLV2/2gD)hf=(fLV2/2gD).. Total head (H):
Total head (H): It is the sum of the static head Hs, friction head (hf) and thIt is the sum of the static head Hs, friction head (hf) and th e velocitye velocity head in
head in the delivery pipe (Vd 2/2g). the delivery pipe (Vd 2/2g). Where, Vd=velocity in the delivery Where, Vd=velocity in the delivery pipe.pipe. )) 1 1 ((
2 2 gg V V dd h h h h h h H H 2 2 f f d d s s m m Manometric head(Hm):Manometric head(Hm): It is the total head developed by the pump. This head is slightlyIt is the total head developed by the pump. This head is slightly less than the head generated b
less than the head generated by the impeller due to some losses in the pumpy the impeller due to some losses in the pump 2 2gg V V dd 2 2 gg V V ss H H H H 2 2 2 2 m m
Working ofWorking of a a centrifugal pump:centrifugal pump:
A centrifugal pump works on the principal that when
A centrifugal pump works on the principal that when a certain mass of fluid is rotated bya certain mass of fluid is rotated by an external source, it is thrown away from the
an external source, it is thrown away from the central axis of rotation and a centrifugalcentral axis of rotation and a centrifugal head is impressed
head is impressed which enables it to rwhich enables it to rise to a higher level.ise to a higher level. Working operation of a centrifugal pump is explained in
Working operation of a centrifugal pump is explained in the following steps.the following steps. 1)
1) Close Close the the delivedelivery vry valve aalve and prnd prime ime the pthe pump.ump. 2)
2) StarStart the motot the motor conner connected to the pcted to the pump shafump shaft, this ct, this causes aauses an increasn increase in thee in the impeller pressure.
impeller pressure. 3)
3) Open the delOpen the delivery valivery valve gradualve gradually, so that thly, so that the liquid ste liquid starts flarts flowing inowing into the delivto the deliverer pipe.
pipe. 4)
4) A partiA partial vacuual vacuum is cream is created at the eyted at the eye of the cente of the centrifugarifugal actiol action, the liqn, the liquid rusuid rushedhed from the sump to
from the sump to the pump due to pressthe pump due to pressure difference at the twure difference at the twoo ends fo the suction pipe.ends fo the suction pipe. 5) As the impeller continues to run, move & more liquid is made available to the
5) As the impeller continues to run, move & more liquid is made available to the pump at its eye. Therefore impeller increases the energy of the
pump at its eye. Therefore impeller increases the energy of the liquid and delivers it toliquid and delivers it to the reservoir.
the reservoir.
6) While stopping the pump, the deliver
6) While stopping the pump, the delivery valve should be closed first, otherwise therey valve should be closed first, otherwise there may be back flow from the reservoir.
may be back flow from the reservoir. It may be noted that a uniform velocit
It may be noted that a uniform velocity of flow is maintained in the delivery pipe. This isy of flow is maintained in the delivery pipe. This is due to the special design of the casing.
due to the special design of the casing. As the flow proceeds from the tonAs the flow proceeds from the tongue of thegue of the casing to the delivery pipe, the area of the casing increases. There is a corresponding casing to the delivery pipe, the area of the casing increases. There is a corresponding change in the quantity of the
change in the quantity of the liquid from the impeller. Thus a uniform flow occurs in theliquid from the impeller. Thus a uniform flow occurs in the delivery pipe.
delivery pipe.
Operation difficulties in centrifugal pumps Operation difficulties in centrifugal pumps
a)
C
Caauussee RReemmeeddiiaal l MMeeaassuurreess 1) Improper priming due to leakage of
1) Improper priming due to leakage of foot valve or incomplete filling.
foot valve or incomplete filling.
Repair or replace the foot valve, Repair or replace the foot valve, prime completely.
prime completely.
2
2) ) HHeeaad d mmoorre e tthhaan n ddeessiiggn n hheeaadd RReedduucce e tthhe e hheeaad od or r cchhaanngge e tthhee pump
pump 3) Clogging of impeller, suction pipe or
3) Clogging of impeller, suction pipe or strainer
strainer
Clean the suspected part Clean the suspected part
4
4) ) SSuuccttiioon n lliifft t mmaay y bbe e eexxcceessssiivvee RReedduucce e tthhe e hheeiigghht t oof f ppuummp p aabboovvee the sump
the sump 5
5) S) Sppeeeed md moorre te thhaan dn deessiiggn sn sppeeeedd CCoonnnneecct at annootthheer pr prriimme me moovveer or of f higher speed
higher speed 6) Direction of rotation of impeller is
6) Direction of rotation of impeller is wrong
wrong
Change the direction. Change the direction.
B) Pump does not give the required capacit B) Pump does not give the required capacityy a) Leakage of air through the suction
a) Leakage of air through the suction pipepipe or through the gland packing
or through the gland packing
Stop the leakage Stop the leakage
b) Damage to some parts of the pump by b) Damage to some parts of the pump by wear & tear
wear & tear
Replace the damaged parts Replace the damaged parts
cc) ) CCllooggggiinng g oof f iimmppeelllleer r ppaassssaaggeess CClleeaan n tthhe e iimmppeelllleerr
C) Pump has poor efficiency C) Pump has poor efficiency a
b
b) L) Loow hw heeaad & d & hhiigghheer dr diisscchhaarrggee RReedduucce te thhe de diisscchhaarrggee
c) Impeller touching, the casing or c) Impeller touching, the casing or improper alignment of shaft
improper alignment of shaft
Carryout the necessary repair. Carryout the necessary repair.
D) Pump stops working D) Pump stops working
aa) ) AAiir r eennttrry y iinntto o ssuuccttiioon n ppiippee SSttoop p tthhe e ppuummpp, , pplluug g tthhe e lleeaakkaaggee,, reprime and start
reprime and start
b
b) ) SSuuccttiioon n lliifft t iis s hhiigghh RReedduucce e tthhe e ssuuccttiioon n lliifftt..
Efficiencies of centrifugal pump Efficiencies of centrifugal pump Manome
Manometric etric efficifficiencyency ((ηη): it is the ): it is the ratio ofratio of the manometric head to the the manometric head to the head actuallyhead actually generated by the impeller
generated by the impeller
2 2 2 2 2 2 VwVw uu gHm gHm u2/g u2/g Vw Vw Hm Hm n nmanomano Mechanical efficiency(Mechanical efficiency(ηηmechmech): It is the ratio of the impeller power to the p): It is the ratio of the impeller power to the p ower of theower of the motor or the prime mover.
motor or the prime mover.
power power motor motor power power impeller impeller mech mech n n Overall efficiency(Overall efficiency(ηηo): It is the ratio of the work done o): It is the ratio of the work done by the pump in lifting waterby the pump in lifting water against gravity and friction in the pipes to the energ
against gravity and friction in the pipes to the energ y supplied by the motor.y supplied by the motor.
motor motor or or mover mover prime prime the the of of power power friction friction gravity gravity against against done done work work n nooVelocity Triangles of a Centrifugal Pump Velocity Triangles of a Centrifugal Pump
Figure shows the inlet and outlet velocity triangles for a centrifugal pump.It ma
Figure shows the inlet and outlet velocity triangles for a centrifugal pump.It ma y be notedy be noted that the inlet velocity triangle is radial,(velocity of whirl is zero at inlet or VW1 =0
that the inlet velocity triangle is radial,(velocity of whirl is zero at inlet or VW1 =0 Depending on the geometry of the blade at outlet it can be:
Depending on the geometry of the blade at outlet it can be: Forward:if the blade angle
Forward:if the blade angle<90<9000 ,,Radial if Radial if ΦΦ=90=9000 ,, c) Bc) Bacackwkwarard id if f φφ
909000 Work done by the impeller of a centrifugal pump:Work done by the impeller of a centrifugal pump:
Figure shows the velocity triangles at the inlet and outlet tips of a
Figure shows the velocity triangles at the inlet and outlet tips of a vane fixed to thevane fixed to the impeller.
impeller.
Let N=speed of the impeller in RPM Let N=speed of the impeller in RPM
D= Diame
D=Diameter of the impeller at outlet D=Diameter of the impeller at outlet U
U11 = Tangential velocity of the impeller at inlet= Tangential velocity of the impeller at inlet πDπD N/6011N/60
U
U22= tangential velocity of the impeller at outlet= tangential velocity of the impeller at outlet πDπD 22N/60N/60
V
V11=absolute velocity of the liquid at inlet=absolute velocity of the liquid at inlet
V
V22= absolute velocity of the liquid at outlet.= absolute velocity of the liquid at outlet.
2 2 1
1&& Vf Vf Vf
Vf are the velocities of flow at inlet and outlet.are the velocities of flow at inlet and outlet. 2
2 1
1&& Vr Vr Vr
Vr Relative velocities at inlet and outletRelative velocities at inlet and outlet 2
2 Vw
Vw whirl velocity at outletwhirl velocity at outlet
α
α angle made byangle made by V V 11 with respect to the motion of the vanewith respect to the motion of the vane
θ
θ blade angle at inletblade angle at inlet
φ
φ= blade angle at outlet= blade angle at outlet For a series
For a series of curved vanes the force exerted of curved vanes the force exerted can be determined usingcan be determined using the impulsethe impulse momentum equation Work=force x distance.
momentum equation Work=force x distance.
similarly the work done/sec/unit weight of the liquid striking the similarly the work done/sec/unit weight of the liquid striking the vane= vane= (Vw(Vw uu VwVw uu )) g g 1 1 1 1 1 1 2 2 2 2
But for a centrifugal pump
But for a centrifugal pump VωVω11
00 Work done/sec/unit weightWork done/sec/unit weight g g u u Vw Vw22 22 And
And the wthe work ork done/sdone/secec VwVw22uu22
((44)) g g Q Q γ γWhere Q=volume of liquid flowing per second =
Where Q=volume of liquid flowing per second = Area x velocity of Area x velocity of fflloowwQQ
πDπD22BB22Vf Vf 22
((55))In eq (5),
In eq (5), BB is the width of the impeller at the outlet.22 is the width of the impeller at the outlet. Design factors of c
Design factors of c entrifugal pumps:entrifugal pumps: aa)) RRiimm ddiiaammeetteerr DD22
Rim velocity or impeller velocity Rim velocity or impeller velocity
60 60 N N πD πD u u 22 2 2
KKuu 2gHm2gHm Rim diameterRim diameter 2gKu2gKu HmHm πN πN 60 60 D D22
== KK HmHm N N 85 85 u uWhere N= speed in RPM Hm= manometric head, Where N= speed in RPM Hm= manometric head, mm
ratio ratio speed speed 2gHm 2gHm / / U U K Kuu
22
ValueValue of of varies varies from from 0.95 0.95 to to 1.8 1.8 depending depending on on the the specific specific speed.speed. b)
b) PipelPipeline diine diameteameter:r:
The diameter of section and delivery pipes are designed
The diameter of section and delivery pipes are designed to give velocities not exceedingto give velocities not exceeding 1.5 to 3 m/s on section and delivery sides.
1.5 to 3 m/s on section and delivery sides. c) Discharge (Q): the discharge or capacity of
c) Discharge (Q): the discharge or capacity of a centrifugal pump is given bya centrifugal pump is given by Where k =factor which accounts the reduction in
Where k =factor which accounts the reduction in flow area due toflow area due to To thickness of impeller vanes,
To thickness of impeller vanes, D2 =Rim diameter,B2 =Rim width, D2 =Rim diameter,B2 =Rim width,
Vf2=Constant velocity of flow through the impeller. Generally k=1 is con
Vf2=Constant velocity of flow through the impeller. Generally k=1 is con sidered.sidered.
PROBLEMS PROBLEMS
1.A centrifugal pump running at 800 Rpm is
1.A centrifugal pump running at 800 Rpm is working against a total head of 20.2 working against a total head of 20.2 m. them. the external diameter of the impeller is 480mm and outlet width 60mm.
external diameter of the impeller is 480mm and outlet width 60mm. If the valve angle atIf the valve angle at outlet is 40 and manometric efficiency is 70% determine
outlet is 40 and manometric efficiency is 70% determine a)Absolute velocity of water leaving
a)Absolute velocity of water leaving b)
b) Flow Flow velocivelocity aty at outt outletlet The vThe valve.alve. c) Angle made by the absolute
c) Angle made by the absolute velocity at outlet with the direction of motion at outlet.velocity at outlet with the direction of motion at outlet. d) Rate of flow through the pump.
d) Rate of flow through the pump. Soln: velocity of valve at outlet Soln: velocity of valve at outlet
60 60 2 2 2 2 N N D D u u
ππ x x x x 2020..11mm / / ss 60 60 800 800 48 48 .. 0 0
π π 2 2 2 2uu Vw Vw gHm gHm n n efficiency efficiency manometricmanometric manomano
,,1 1 .. 20 20 2 2 .. 20 20 81 81 .. 9 9 70 70 .. 0 0 2 2 x x Vw Vw x x
,, VwVw22
1414..0808mm / / ssFrom the outlet velocity triangle From the outlet velocity triangle
2 2 2 2 2 2 tan tan Vw Vw u u Vf Vf
φ φ ss m m x x Vf Vf 22
tantan404000 ((2020..11
1414..0808))
55..0505 / /
Absolute velocity of water leaving the valve
Absolute velocity of water leaving the valve V V 22 is given byis given by ss m m Vw Vw Vf Vf V V 22
2222
2222
55..050522
1414..080822
1414..9696 / / Angle made by the absolute velocity atAngle made by the absolute velocity at outlet with the direction of motion is given byoutlet with the direction of motion is given by 3586 3586 .. 0 0 08 08 .. 14 14 05 05 .. 5 5 tan tan 2 2 2 2
Vw Vw Vf Vf β β 00 7 7 .. 19 19
ββ RRaatte e oof f fflloow w tthhrroouuggh h tthhe e ppuummpp QQ
ππ D D22 B B22Vf Vf 22
ππ x x00..4848 x x00..0606xx55..0055
00..457457mm33 / / ss2.
2. A centrA centrifugal pifugal pump impeump impeller haller having exteving external and irnal and internanternal diametl diameter 480mm aer 480mm andnd 240mm respectively is running at 100 Rpm. The rate of flow through the pump is 0.0576 240mm respectively is running at 100 Rpm. The rate of flow through the pump is 0.0576 m3/s an
m3/s and velocid velocity of flty of flowow is consis constant and etant and equal to 2.4qual to 2.4m/s. thm/s. the diamee diameter ofter of the secthe section andtion and delivery pipes are 180mm and 120mm respectively and section and delivery heads are delivery pipes are 180mm and 120mm respectively and section and delivery heads are 6.2m(abs) and 30.2m(abs) of water respectively. If the power required to drive
6.2m(abs) and 30.2m(abs) of water respectively. If the power required to drive the pumpthe pump is 23.3KW and the outlet
is 23.3KW and the outlet vane angle is 45 determine. a) vane angle is 45 determine. a) inlet vane angleinlet vane angle b) Overallb) Overall efficiency c) manometric efficiency of the pump
efficiency c) manometric efficiency of the pump Soln: tangential velocity or impeller velocity at inlet Soln: tangential velocity or impeller velocity at inlet
ss m m x x x x N N D D u u 1212..5656 / / 60 60 1000 1000 24 24 .. 0 0 60 60 1 1 1 1
π π π π FFrroom m tthhe e iinnlleet t vveelloocciitty y ttrriiaannggllee 00..119911 56 56 .. 12 12 41 41 .. 2 2 tan tan 1 1 1 1
u u Vf Vf φ φ )) (( 8 8 .. 1010 00 inlet inlet vanevaneangleangle
θθOverall efficiency Overall efficiency 3 3 .. 23 23 05 05 .. 0 0 81 81 .. 9 9 0 0 xHm xHm x x P P rQHm rQHm n n
nn00
00..0238702387HmHm ((11))
g g V V r r p p Z Z g g V V r r p p Z Z Hm Hm but but 2 2 2 2 ,, 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 2 ss m m x x x x d d Q Q V V V V where where d d d d 55..0101 / / 12 12 .. 0 0 0567 0567 .. 0 0 4 4 4 4 ,, 22
22
22
π π π π ss m m x x x x d d Q Q V V V V where where ss ss 22..2323 / / 18 18 .. 0 0 0567 0567 .. 0 0 4 4 4 4 ,, 22
22
22
π π π π 2 2 1 1 Z Z Z Z letlet
i.e pump inlet and outlet are at same level.i.e pump inlet and outlet are at same level. )) (( 2 2 .. 6 6 1 1 hh mm absabs r r p p ss
22 hh 3030..22mm((absabs)) r r p p d d
m m x x x x Hm Hm 2525..0303 81 81 .. 9 9 2 2 23 23 .. 2 2 2 2 .. 6 6 81 81 .. 9 9 2 2 01 01 .. 5 5 2 2 .. 30 30 2 2 2 2
0 0 nn ,, overaloverall efficl efficiency of piency of pumpump =0.02387x25.03=0.597=59.7% =0.02387x25.03=0.597=59.7% Velocity of the impeller at outlet
Velocity of the impeller at outlet uu D D N N x x x x 2525..1313mm / / ss 60 60 1000 1000 48 48 .. 0 0 60 60 2 2 2 2
π π π πFrom the outlet velocity triangle From the outlet velocity triangle
2 2 2 2 2 2 tan tan Vw Vw u u Vf Vf
φ φ ,, 2 2 0 0 13 13 .. 25 25 4 4 .. 2 2 45 45 tan tan Vw Vw
,, ss m m Vw Vw22
2222..7373 / / MMaannoommeettrriic c eeffffiicciieennccyy 00..4343 4343%% 13 13 .. 25 25 73 73 .. 22 22 03 03 .. 25 25 81 81 .. 9 9 2 2 2 2
x x x x u u Vw Vw gHm gHm n nmanomano 3.3. It is It is required to deliver 0.048m3/s of required to deliver 0.048m3/s of water to a height water to a height of 24m through a 150mmof 24m through a 150mm diame
diameter and 120m loter and 120m long pipe by a centrng pipe by a centrifugal pumifugal pump. If the overp. If the overallall EffiEfficiency of thciency of thee pump is 75% and co efficient of friction f=0.01
pump is 75% and co efficient of friction f=0.01 for the pipe line. Find the power requiredfor the pipe line. Find the power required to drive the pump.
to drive the pump.
Soln: velocity of water pipe
Soln: velocity of water pipe 44 22 d d Q Q V V V V V V ss d d π π
mm ss x x x x / / 7 7 .. 2 2 15 15 .. 0 0 048 048 .. 0 0 4 4 2 2
π π Overall efficiency Overall efficiency P P rQHm rQHm n n00
P P x x x x00..048048 2727..3737 81 81 .. 9 9 75 75 .. 0 0
,, PP
1717..22KW KW4. The impeller of a centrifugal pump is of 300mm
4. The impeller of a centrifugal pump is of 300mm diameter and 50mm width at thediameter and 50mm width at the periphery and has blades whose tip angle incline
periphery and has blades whose tip angle incline backwards 60 from the radius. Thebackwards 60 from the radius. The pump deliveries 17m3/min of water and the impeller rotates at 1000
pump deliveries 17m3/min of water and the impeller rotates at 1000 Rpm. Assuming that t
Rpm. Assuming that the pump is designhe pump is design to admit radically. cto admit radically. calculatealculate a)Speed and direc
a)Speed and direction oftion of water as it water as it leaves the impelleleaves the impeller,r, b)T
d)
d) LifLift of the t of the pump. Tpump. Takeake mechanmechanical=9ical=95% and hy5% and hydraulic draulic efficefficiency=7iency=75%5% Soln: tangential velocity of the impeller at the outlet
Soln: tangential velocity of the impeller at the outlet ss m m x x x x N N D D u u 1515..7171 / / 60 60 1000 1000 3 3 .. 0 0 60 60 2 2 2 2
π π π πFrom continuity equation
From continuity equation QQ
ππ D D22 B B22Vf Vf 22,, mm ss x x x x Vf Vf 66 / / 05 05 .. 0 0 3 3 .. 0 0 2833 2833 .. 0 0 2 2
π πFrom the outlet velocity triangle From the outlet velocity triangle
2 2 2 2 2 2 tan tan Vw Vw u u Vf Vf
φ φ ss m m Vf Vf u u Vw Vw 1212..2424 / / 60 60 tan tan 6 6 71 71 .. 15 15 tan tan 00 2 2 2 2 2 2
φ φ Absolute velocityAbsolute velocity of water at of water at thethe outlet tip of outlet tip of the impellerthe impeller
2 2 2 2 2 2 2 2 2 2 2 2 2 2
Vf Vf
VwVw
66
1212..2424 V V V V 22
1313..6363 mm / / ss((magnitudemagnitude)) 0 0 1 1 2 2 2 2 1 1 5 5 .. 26 26 24 24 .. 12 12 6 6 tan tan tan tan
Vw Vw Vf Vf β βTorque exerted by the impeller on water Torque exerted by the impeller on water
)) 2 2 3 3 .. 0 0 24 24 .. 12 12 (( 81 81 .. 9 9 2833 2833 .. 0 0 81 81 .. 9 9 )) (( 22 22 x x xx x x R R Vw Vw g g rQ rQ T T
00..5252KN KN mm Shaft power (P) impeller or rotor powerShaft power (P) impeller or rotor power NT NT x x x x 5454..4545KW KW 60 60 52 52 .. 0 0 1000 1000 2 2 60 60 2 2ππ
ππ
But, mechanical efficiency But, mechanical efficiency
power power shaft shaft power power impeller impeller n nmechmech
P P ee ii.. ,,00..9595
5454..4545 PP
5757..3131KW KW Lift of the pumpLift of the pump
Impeller power=r(Q+q)H Impeller power=r(Q+q)H
Where r=sp wt of water=9.81 KN/m3 Where r=sp wt of water=9.81 KN/m3
H =ideal head=(theoretical head-hyd losses) H =ideal head=(theoretical head-hyd losses) Q=leakage of water m3/s
Q=leakage of water m3/s Neglecting
Neglecting leakages q leakages q we havewe have 54.45=9.81x0.2833xH
54.45=9.81x0.2833xH Or
Or h h =19.59m=19.59m We know,
We know, hydrauhydraulic effilic efficiencyciency
head head ideal ideal lift lift or or head head Actual Actual n nhh
)) (( ii hh xideal xideal head head H H
n n hft hft Actual
Actual
00 ..7070 x x1919..5959
1313..7171mmof of water water5. The following data relate to a centrifugal pump. Diameter of the impeller at inlet & 5. The following data relate to a centrifugal pump. Diameter of the impeller at inlet & outlet =180mm and 360mm respectively. width of impeller at inlet and outlet=144mm & outlet =180mm and 360mm respectively. width of impeller at inlet and outlet=144mm & 72mm respectively. rate of flow through the pump=17.28lps. Speed
72mm respectively. rate of flow through the pump=17.28lps. Speed of the impeller =of the impeller = 1500 Rpm. Vane angle at
1500 Rpm. Vane angle at outlet=45 water enters the impeller radially at inlet neglectingoutlet=45 water enters the impeller radially at inlet neglecting losse
Soln: velocity of flow at inlet Soln: velocity of flow at inlet
0144 0144 .. 0 0 18 18 .. 0 0 01728 01728 .. 0 0 1 1 1 1 1 1 x x x x B B D D Q Q Vf Vf π π π π
Velocity of flow at outlet
Velocity of flow at outlet mm ss
x x x x B B D D Q Q Vf Vf 22..1212 / / 0072 0072 .. 0 0 36 36 .. 0 0 01728 01728 .. 0 0 2 2 2 2 2 2
π π π πTangential velocity of impeller at outlet
Tangential velocity of impeller at outlet uu D D N N x x x x 2828..2727mm / / ss 60 60 1500 1500 36 36 .. 0 0 60 60 2 2 2 2
π π π πPressure rise in the impeller is given by the equation
Pressure rise in the impeller is given by the equation
22 22φφ
2 2 2 2 2 2 2 2 1 1 coscos 2 2 1 1 ec ec Vf Vf u u Vf Vf g g
22 22 22 22 00
45 45 cos cos 12 12 .. 2 2 27 27 .. 28 28 12 12 .. 2 2 81 81 .. 9 9 2 2 1 1 ec ec x x x x
6. A centrifugal pump delivers water at the rate
6. A centrifugal pump delivers water at the rate of 1800 lpm,to a height of 2of 1800 lpm,to a height of 20m,0m, Throu
Through a 0.1m, dia, 80m. logh a 0.1m, dia, 80m. long pipe.ng pipe. Find the powFind the power requier required to drired to drive the pump, ifve the pump, if thethe overall efficiency is 65%, and Darcy’s friction factor=0.02.
overall efficiency is 65%, and Darcy’s friction factor=0.02. Soln.
Soln. Discharge Discharge Q=1800 lpm=0.03 Q=1800 lpm=0.03 cumecs.cumecs. Delivery head hd =20m
Delivery head hd =20m
Dia of delivery pipe dd=0.1m Dia of delivery pipe dd=0.1m Length of delivery pipe
Length of delivery pipe lld d
8080mm OOvveerraalll l eeffffiicciieennccyy nn00
00..6565 f f
00..0202 Total head Total head 2g 2g Vd Vd h h h h h h h h H H 2 2 fd fd fs fs d d s s
So this probSo this prob hhss
00hhfsfs
00(details are not given)(details are not given)2g 2g Vd Vd h h h h H H 2 2 fd fd d d
9.81x2 9.81x2 1 1 x x πx0.1 πx0.1 4x0.03 4x0.03 x0.1 x0.1 9.81xπ 9.81xπ 0.03 0.03 8x0.02x80x 8x0.02x80x 20 20 2 2 2 2 5 5 2 2 2 2 H=32.65m H=32.65m Output of the pump=Output of the pump=γ γ QH QH
99..8181 x x00..0303 x x3232..6565
99..66kwkw But overall efficienyBut overall efficieny
pump pump the the drive drive to to require require power power pump pump the the of of Output Output
0 0 η ηPower required to drive the pump = 9.6/0.65=14.8 Power required to drive the pump = 9.6/0.65=14.8 kwkw
7.
7. A centrA centrifugal pifugal pump is reump is required tquired to delivo deliver 280er 280 ltrs oltrs of water pf water per secoer second againsnd against a headt a head of 16m, when running at 800rpm.
of 16m, when running at 800rpm. If the blades of the impeller are radial at inlet andIf the blades of the impeller are radial at inlet and velocity of flow is constant and equal to
velocity of flow is constant and equal to 2m/sec, find the proportions of the pump.2m/sec, find the proportions of the pump. Assu
Assumeme overaoverall effill efficiency as ciency as 80%80% and ratiand ratio o of breaof breadth to diadth to diameter ameter at outlet at outlet as 0.1s 0.1 Soln: th
Soln: the inlet and oute inlet and outlet velolet velocity trcity triangleiangles will bes will be asas shownshown From continuity equation
)) (( 67 67 .. 0 0 2
2 mm diameter diameter of of thetheimpeller impeller at at outlet outlet
D D
cm cm m m x x BB22
00..11 00..6767
00..067067
66..77 (Width of the impeller at outlet).(Width of the impeller at outlet).2 2 2 2uu Vw Vw gHm gHm n nmanomano
2 2 2 2 16 16 81 81 .. 9 9 8 8 .. 0 0 u u Vw Vw x x
)) (( 2 2 .. 196 196 2 2 2 2uu ii Vw Vw
but but uu D D N N x x x x 2828..11mm / / ss 60 60 800 800 67 67 .. 0 0 60 60 2 2 2 2
π π π π From eq (i)From eq (i) VwVw22 x x22..8181
196196..22 or or VwVw22
66..9999mm / / ss FFrroom m tthhe e oouuttlleet t vveelloocciitty y ttrriiaannggllee 00..00994477 99 99 .. 6 6 1 1 .. 28 28 2 2 tan tan 2 2 2 2 2 2
Vw Vw u u Vf Vf φ φ 0 0 41 41 .. 5 5
φφ (Blade angle at outlet)(Blade angle at outlet) 00..28628699 99 .. 6 6 2 2 tan tan 2 2 2 2
Vw Vw Vf Vf β β 00 16 16
ββ 8.8. The following data refer The following data refer to a centrifugal pump statito a centrifugal pump static head = 40m, suction height c head = 40m, suction height 5m,5m, dia of suction and delivery pipes =
dia of suction and delivery pipes = 0.1m, loss of head in suction pipe = 2m, 0.1m, loss of head in suction pipe = 2m, loss of headloss of head in delivery pipe = 8m, impeller dia at outlet =0.4m,
in delivery pipe = 8m, impeller dia at outlet =0.4m, impeller breadth at outletimpeller breadth at outlet
25mm.blades occupy 10% of the outlet area, speed 1200rpm. Exit angle of blade = 1500 25mm.blades occupy 10% of the outlet area, speed 1200rpm. Exit angle of blade = 1500 with the
with the tangent, Manometric efficiency = 80%, overtangent, Manometric efficiency = 80%, overall efficiency = 70%. Fiall efficiency = 70%. Find thend the power required to drive the pump and what pressures will be indicated by the gauges power required to drive the pump and what pressures will be indicated by the gauges mounted on the suction and delivery sides.
mounted on the suction and delivery sides. Soln: Outlet vane angle
Soln: Outlet vane angle
φφ
180180
150150
303000 Delivery headDelivery head hhd d
H H ss
hhss
4040
55
3535mm Head on the pump H=40+2+8=50mHead on the pump H=40+2+8=50m From the outlet velocity triangle From the outlet velocity triangle
2 2 2 2 2 2 tan tan Vw Vw u u Vf Vf φ φ ss m m x x x x N N D D u u where where 2525..1313 / / 60 60 1200 1200 4 4 .. 0 0 60 60 ,, 22 2 2
π π π πAlso from the equation Also from the equation
2 2 2 2uu Vw Vw gHm gHm n nmanomano
mm ss x x x x Vw Vw 2424..44 / / 8 8 .. 0 0 13 13 .. 25 25 50 50 81 81 .. 9 9 2 2
0 0 2 2 2 2 22
((uu
VwVw ))tantanφφ
((2525..1313
2424..44))tantan3030Vf Vf Vf Vf 22
00..422422mm / / ss 2 2 2 2 2 2 ,, arg argee QQ K K D D B BVf Vf disch disch
ππ
00..99 x xππ x x00..44 x x00..025025xx00..422422
00..01190119m / m33 / ss Power given to the liquid P=rQHPower given to the liquid P=rQH
99..8181 x x00..01190119 x x5050
55..8585KW KW Power required to drive the pumpPower required to drive the pump PP 88..3636kwkw 7 7 .. 0 0 85 85 .. 5 5 0 0
η ηPressure gauge reading on the suction side = hs+hfs
Pressure gauge reading on the suction side = hs+hfs
55
22
77mmof of water water Pressure gauge reading on the delivery side =Pressure gauge reading on the delivery side =hhd d
hh fd fd
3535
88
4343mm 9. Following data were obtained from a centrifugal p9. Following data were obtained from a centrifugal p ump in a laboratory. Pressure gaugeump in a laboratory. Pressure gauge reading on the suction side 15cm of mercur
reading on the suction side 15cm of mercury, pressure gauge reading on the dy, pressure gauge reading on the delivery sideelivery side 170kN/m2. quantity
between the gauges =500mm. Total input
between the gauges =500mm. Total input to the pump = 6.5kw.Find the efficiency of theto the pump = 6.5kw.Find the efficiency of the pump.
pump.
Soln: Suction head hs=0.15x13.5=2.04m of water Soln: Suction head hs=0.15x13.5=2.04m of water Delivery head hd=170/9.81=17.34m of
Delivery head hd=170/9.81=17.34m of water. Headwater. Head on the pump = on the pump = (hs+hd+x+Vd2/2g)(hs+hd+x+Vd2/2g) Since the dia of the delivery pipe is not
Since the dia of the delivery pipe is not given, velocity in the delivery pipe given, velocity in the delivery pipe is ignored.is ignored.
mm H H
22..0404
1717..3434
55))
1919..8888
DDiisscchhaarrgge e ffrroom m tthhe e ppuummpp 00..01270127 / / sseecc 81 81 .. 9 9 1 1 60 60 5 5 .. 7 7 33 m m x x
Output of the pump
Output of the pumpγ γ QH QH
99..8181 x x00..127127 x x1919..8888
22..4848kwkw Efficiency of the pump =2.48/6.5=0.382.=38.2% Efficiency of the pump =2.48/6.5=0.382.=38.2%10. The internal and external diameters of the
10. The internal and external diameters of the impeller of a centrifugal pump are 40cmsimpeller of a centrifugal pump are 40cms and 80cms respectively. The pump is running at
and 80cms respectively. The pump is running at 1200rpm. The vane an1200rpm. The vane angles at inlet andgles at inlet and outlet are 200 and 300 respect
outlet are 200 and 300 respectively. Water enters theively. Water enters the impeller radially and velocity impeller radially and velocity of of flow is constant. Determine the workdone by the impeller per kN of water.
flow is constant. Determine the workdone by the impeller per kN of water.
ss m m x x x x N N D D u u so so 2525..1313 / / 60 60 1200 1200 4 4 .. 0 0 60 60 :: ln ln 11 1 1
π π π π ss m m x x x x N N D D u u 5050..2626 / / 60 60 1200 1200 8 8 .. 0 0 60 60 1 1 2 2
π π π πFrom the inlet velocity triangle From the inlet velocity triangle
1 1 1 1 tan tan u u Vf Vf
θ θ ss m m Vf Vf Vf Vf 11
22
2525..1313tantan202000
99..1515 / /
From theFrom the outleoutlet velocity triat velocity trianglengle tanΦ=Vf2/(u2
tanΦ=Vf2/(u2-vw2)=9.15/(50.26-vw2)-vw2)=9.15/(50.26-vw2) or , Vw2=34.41m/s
or , Vw2=34.41m/s
Work done/sec=1/g(vw2 u2) =34.41*50.26/9.81=176.3kn-m/s/kn Work done/sec=1/g(vw2 u2) =34.41*50.26/9.81=176.3kn-m/s/kn 11. The impeller of a centrifugal pump runs at
11. The impeller of a centrifugal pump runs at 90 Rpm and has vaves 90 Rpm and has vaves inclined at 120 toinclined at 120 to the direction of mot
the direction of motion at exit. If ion at exit. If the manometric headthe manometric head is 20m and manometric efis 20m and manometric efficiencyficiency is 75%
is 75% Vane angleVane angles at inlets at inlet. Take the veloc. Take the velocity of flow aity of flow as 2.5m/ss 2.5m/s, throug, throughout and thehout and the diameter of the impeller at exit as twice that at inlet.
diameter of the impeller at exit as twice that at inlet. a)
a) DiaDiametmeter oer of thf the ime impelpeller ler at eat exit.xit.
Soln: From the definition of manometric efficiency
Soln: From the definition of manometric efficiency ηηmanomano
gHmgHm / / VwVw22uu22 )) (( 6 6 .. 261 261 75 75 .. 0 0 20 20 81 81 .. 9 9 2 2 2 2 ii x x u u Vw Vw
FFrroom m tthhe e oouuttlleet t veellov occiitty y ttrriiaannggllee 11..4444 60 60 tan tan 5 5 .. 2 2 60 60 tan tan )) (( 22 00 00 2 2 2 2
Vf Vf Vw Vw u u VwVw22
((uu22
11..4444)) Substituting the valueSubstituting the value VwVw22,,((uu22
11..4444))uu22
261261..66
1616..99mm / / ss60 60 2 2 2 2 N N D D u u but but
ππss m m x x x x D D 33..5959 / / 90 90 9 9 .. 16 16 60 60 2 2
π π further further uu uu 88..4545mm / / ss 2 2 9 9 .. 16 16 2 2 2 2 1 1
FFrroom m tthhe e iinnlleet t vveelloocciitty y ttrriiaannggllee 00..22995599 45 45 .. 8 8 5 5 .. 2 2 tan tan 1 1 1 1
u u Vf Vf θ θ )) (( 48 48 .. 1616 00 Inlet Inlet VaneVane Angle Angle
θθ12. A centrifugal pump delivers 250lps against a head of 20m. When the impeller rotates 12. A centrifugal pump delivers 250lps against a head of 20m. When the impeller rotates at 1500rpm. If the mano metric efficiency is 75%
at 1500rpm. If the mano metric efficiency is 75% and the loss of head in thand the loss of head in the pump ise pump is 0.033V22, where V2 is the absolute velocity at exit. The diameter of the impeller 0.033V22, where V2 is the absolute velocity at exit. The diameter of the impeller
a)
a) ThThe be blalade de angangle le at at exexitit
Take the width of the impeller at exit
Take the width of the impeller at exit as 0.4D where D is the diameter of the as 0.4D where D is the diameter of the impellerimpeller Soln: Soln: uu D D N N xDx xDx 7878..55DD 60 60 1500 1500 60 60 2 2 2 2
π π π π 2 2 1 1 199 199 .. 0 0 4 4 .. 0 0 25 25 .. 0 0 D D D D xDx xDx DB DB Q Q Vf Vf
π π π πFrom the definition of manometric efficiency From the definition of manometric efficiency
2 2 2 2uu Vw Vw gHm gHm n nmanomano
7 7 .. 26 26 75 75 .. 0 0 20 20 2 2 2 2
mano mano n n Hm Hm g g u u Vw VwBut, manometric head=(workdone the impeller
But, manometric head=(workdone the impeller – – losses in the pump)losses in the pump) 20 20 7 7 .. 26 26 033 033 .. 0 0 2222
V V V V 22
1414..2525mm / / ss FromFrom eq (i) eq (i) andand (ii)(ii)
D D Vw Vw or or D D x x Vw Vw 33..3434 7 7 .. 26 26 81 81 .. 9 9 5 5 .. 78 78 2 2 2 2
From the outlet velocity triangle
From the outlet velocity triangle Vf Vf 2222
VwVw2222
V V 11222 2 2 2 2 2 2 2 1414..22 34 34 .. 3 3 199 199 .. 0 0
D D D D SolSolvinving by g by tritrial aal and end errorrorr D=0D=0.24.242 m2 m ss m m x x D D u u22
7878..55
7878..55 00..242242
1919 / /
mm ss D D Vf Vf 33..44 / / 242 242 .. 0 0 199 199 .. 0 0 199 199 .. 0 0 2 2 2 2 2 2
ss m m D D Vw Vw 1313..88 / / 242 242 .. 0 0 34 34 .. 3 3 34 34 .. 3 3 2 2
00..654654 8 8 .. 13 13 19 19 4 4 .. 3 3 tan tan 2 2 2 2 2 2
Vw Vw u u Vf Vf φ φ )) (( 2 2 .. 3333 00 outlet outlet vanevane angleangle
φ φ
13. A centrifugal pump lifts water against a static head of 40
13. A centrifugal pump lifts water against a static head of 40 m. The section and deliverym. The section and delivery pipes are each 15cm in diameter. Th
pipes are each 15cm in diameter. The head loss in the section and de head loss in the section and delivery pipes areelivery pipes are respectively 2.20m and 7.5m. The impeller is 40cm in diameter and 2.5cm wide at the respectively 2.20m and 7.5m. The impeller is 40cm in diameter and 2.5cm wide at the month. It revolves at 1200Rpm and the
month. It revolves at 1200Rpm and the vane angle at exit is 3vane angle at exit is 30. if the manometric0. if the manometric efficiency is 80%. Calculate the discharge.
efficiency is 80%. Calculate the discharge.
Soln: Soln: x x00..151522 xV xV ss
QQ 4 4 π π ss V)) (( 6 6 .. 56 56 QQ ii V V ss
((ππ D D22 B B22))Vf Vf 22
QQ ((ππ x x00..44 x x00..025025))Vf Vf 22
QQ Vf Vf 22
3131..88QQ ((iiii)) FFrroom m eeq q ((aa) ) aannd d ((bb)) Vf Vf 22
00..5656V V ss ((iiiiii)) ss m m x x x x N N D D u u now now 2525..11 / / 60 60 1200 1200 4 4 .. 0 0 60 60 2 2 2 2
π π π π g g Vs Vs hf hf hf hf h h h h H H mm ss d d ss d d 2 2 )) (( 2 2
g g Vs Vs H H mm 2 2 5 5 .. 7 7 2 2 .. 2 2 40 40 2 2
(( )) 2 2 7 7 .. 49 49 2 2 iv iv g g Vs Vs H H mm
2 2 2 2uu Vw Vw gHm gHm n nmanomano
/ / 2525..11 00..5656 cotcot3030 2525..11 2 2 7 7 .. 49 49 81 81 .. 9 9 8 8 .. 0 0 00 2 2 x x x x V V g g Vs Vs x x ss V V ss22
3939V V ss
3333
00 )) sec sec (( / / 83 83 .. 00 mm ss velocityvelocity ininthethe tiontion pipepipe V V ss
)) arg arg (( / / 3 3 0147 0147 .. 0 0 6 6 .. 56 56 83 83 .. 0 0 &
mm ss Disch Disch ee14. A centrifugal pump has a total lift of 15m
14. A centrifugal pump has a total lift of 15m and is placed 2m above and is placed 2m above the water level inthe water level in the sump. The velocity of
the sump. The velocity of water in the delivery water in the delivery pipe is 2m/s.pipe is 2m/s. If the radiIf the radial velocity of flowal velocity of flow through the wheel is 3m/s and tangent to the
through the wheel is 3m/s and tangent to the vane at exit makes an vane at exit makes an angle of 60 find (a)angle of 60 find (a) the velocity of water at exit (b) the guide
the velocity of water at exit (b) the guide vane angle © the pressure at the vane angle © the pressure at the impeller exit.impeller exit. Neglect friction and other losses.
Neglect friction and other losses. Sol
Soln:n: tottotal headal head mm g g Vd Vd 20 20 .. 15 15 62 62 .. 19 19 2 2 15 15 2 2 15 15 2 2 2 2
From the outlet velocity triangle
From the outlet velocity triangle 22 00 2 2 2 2 60 60 tan tan Vf Vf u u Vw Vw
(( 11..7373)) 3 3 3 3 2 2 2 2
uu uu Hm Hm g g u u Vw Vw now now,, 22 22
1515..22 81 81 .. 9 9 )) 73 73 .. 1 1 (( ..ee uu22
uu22
ii uu22
1313..1212mm / / ss ss m m Vw Vw22
((1313..1212
11..7373))
1111..3939 / / 78 78 .. 11 11 3 3 39 39 .. 11 11 22 22 2 2 2 2 2 2 2 2 2 2
VwVw
Vf Vf
V V 00..263263 39 39 .. 11 11 3 3 tan tan 2 2 2 2
Vw Vw Vf Vf β β 0 0 75 75 .. 14 14
ββ (guide vane angle at exist)(guide vane angle at exist)
Applying bernoulli’s equation to points on the sump water surface and impeller exit, Applying bernoulli’s equation to points on the sump water surface and impeller exit, taking datum at the sump level.
taking datum at the sump level. HmHm g g V V r r p p
0 0 0 0 2 2 2 2 2 2 2 2 2 2
62 62 .. 19 19 78 78 .. 11 11 2 2 2 2 .. 15 15 2 2 2 2 r r p p =6.13m of water (gauge) =6.13m of water (gauge)15. The axis of a centrifugal pump is 2.5m above the water level in the sump and the 15. The axis of a centrifugal pump is 2.5m above the water level in the sump and the static lift from the pump centre is 35m. The friction losses in the section and
static lift from the pump centre is 35m. The friction losses in the section and deliverydelivery Pipes are of 15cm diameter. The impeller is 30cm diameter and 2
Pipes are of 15cm diameter. The impeller is 30cm diameter and 2 cm wide at outlet ancm wide at outlet and itsd its speed is 1800 Rpm. The blade
speed is 1800 Rpm. The blade angle at exit is 30. calculate the shangle at exit is 30. calculate the shaft power to be suppliedaft power to be supplied and the discharge delivered. Take n mano=75% and n o=70%. If the guages are
