CH-7 Hydraulic Machine Solved Examples.pdf

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1. Examples
CHAPTER-SEVEN
Hydraulic machines

2. Waterfromawellistobepumpedtoaheightof40mfromthesource.The
quantityofwatertobedeliveredis500L/s,througha480mmdiameterpipe.It
isalsodesiredtomaintaina100kPapressureatthesummit.Thefrictionalhead
lossesfromthesuctionanddischargeofthepumpareequivalentto2.0m.If
thepumpspeedis850rpm,determinethepowerneededbythepumpinhp.
PMP
2
1
Example7.1

3. Cont...
3

4. Itisrequiredtodeliver0.048m
3
/sofwatertoaheightof24mthrougha150
mmdiameterpipeand120mlong,byacentrifugalpump.Iftheoverall
efficiencyofthepumpis75percentandco-efficientoffriction,f=0.01fortheir
pipeline,findthepowerrequiredtodrivethepump
Example7.2

5. Cont...
5

6. Example 7.3 Centrifugal Pump
A centrifugal pump lifts water under a static head of 36 mof water of which 4 m
is suction lift. Suction and delivery pipes are both 150 mm in diameter. The head
loss in suction pipe is 1.8 mand in delivery pipe 7 m. The impeller is 380 mm in
diameter and 25 mm wide at mouth and revolves at 1200 r.p.m. Its exit blade
angle is 35°. If the manometricefficiency of the pump is 82 percent determine:
(i) The discharge through the pump, and
(ii) The pressure at the suction and delivery
branches of the pump
6

7. .
7

8. .
8

9. .
9

10. Example-7.4 Pumping head
Waterat15°Cistobedischargedfromareservoiratarateof18L/susingtwohorizontalcast
ironpipesconnectedinseriesandapumpbetweenthem.Thefirstpipeis20mlongandhasa
6-cmdiameter,whilethesecondpipeis35mlongandhasa3-cmdiameter.Thewaterlevelin
thereservoiris30mabovethecenterlineofthepipe.Thepipeentranceissharp-edged,and
lossesassociatedwiththeconnectionofthepumparenegligible.Neglectingtheeffectofthe
kineticenergycorrectionfactor,determinetherequiredpumpingheadandtheminimum
pumpingpowertomaintaintheindicatedflowrate.

11. Example-7.5 Pump Pressure
Thediagramshowsapumpdeliveringwaterthroughaspipe30mmboretoa
tank.Findthepressureatpoint(1)whentheflowrateis1.4dm
3
/s.Thedensity
ofwateris1000kg/m
3
.Thelossofpressureduetofrictionis50kPa.
11

12. Solution
12

13. Example 7.6 Specific Speed and Rational Speed
13

14. Example 7.7: Head and Power by a Pump
Waterisbeingpumpedfromthelowerreservoiratelevationof+100mto
theupperreservoiratelevationof+150mwithaflowrateof2m
3
/s.
And,thepipehasalengthof900manddiameterof60cm.Ifthe
efficiencyofthepumpis75%,
a)whatistheshaftpowerrequiredtodrivethepump?
TakeC=120(Newweldedsteelpipematerial)Haz.Weqn. Ans:2,859.314KW
b)Whatisthecostofelectricenergytofillareservoirvolumeof8000m
3
ifmotorefficiency=90%?
Takecostofenergy=1.5Birr/kwhr Ans:5,289.73Birr
14

15. Example 7.8
Water is required for a city with a population of 10,000and pumped from a well with the
following data:-
Rate of water supply =150litres/Person/day
Pumping hours per day = 16hours
Static lift from minimum water level =125m
of the well to FSL of reservoir
Length of rising pipe =1000m
Diameter of rising pipe =190mm
Minor loss =10% of friction loss
Friction factor of the pipe =0.03
Efficiency of motor =95% and Efficiency of Pump =70%
a)Determine the power supplied to the motor?
b)The cost of electrical energy to fill 10,000m
3
reservoir if the energy charge is
0.75Birr/kwhr?
15

16. Exercise
Awatersourcewithanelevationof10mistobepumpedbyacentrifugalpumptoanopen
reservoiratanelevationof80m.Thesuctionpipeanddischargepipediameteris255mmand
200mm,respectively.Thepumpcenterlineisat5m.Theheadlossatsuctionpipeis0.05m
and0.45atthedischargepipe.Thepumpdeliverswaterat15L/sandhasanefficiencyof75%
whiletheelectricmotoris80%.Determine
a)Water horsepower of the pump
b)Brake horsepower of the pump
c)Power input to drive the motor, in kW
16

17. Example 7.9 Power and Energy from turbine
AHydropowerdamhasthefollowingmainfeatures:
•Headwaterlevel=+500m,Tailwaterlevel=+464m,Totalheadloss=1.5m,
•TwoFrancisTurbinesofcapacities14,000KWhavebeeninstalled,
•Hydraulicefficiency=86%,Conveyanceefficiency=92%,
•Averagenumberofdaysinamonth=30days,Servicehourperday=10hr
a)Estimatetheflowrateavailableinthepenstocks?
b)Determinethemaximumenergygenerationpermonth?
c)Determinethespecificspeedoftheturbineiftherotationalspeedis150rpm?

18. Solution
a) Total installed Capacity = 2*14,000 = 28,000KW
•GrossHead,H
G=HWL-TWL=500-464=46m
•NetHead,H
net=H
G-h
f=46-1.5=44.5m
•Over all efficiency =Hydraulic efficiency*Conveyaneefficiency =
H*
C =
0.86*0.92 = 0.791
•Total installed Capacity , P= 
o*
w*Q*H
net, 28,000= 0.791*9.81* Q*44.50
•The flow rate , Q = 81.087m
3
/se Discharge per penstock=Q/4=20.27m
3
/s
•b) Energy, E=P*t = 28000KW*30days* 10hr/day = 8,400,000KWhr
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19. Reading Assignment
•Reciprocating Pump
•Net Positive Suction Head and Lift
•Pump and turbine Performance characteristics Curves
•Pumps in Series and Parallel
•Losses and efficiencies of pumps and turbines
•Cavitation in Pumps and turbines

20. THANK YOU!!!
The End 2016E.C