7/25/2019 Sheet 1 Pelton Wheel

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Faculty of Eng. Shoubra 3rdYear (Production)

Mechanical Dept. Sheet No. 1 urbine!

"ydraulic#$achine! %&1'#%&1

Pelton wheel

1# Pelton *heel *ith a needle + controlled no,,le de-elop! '& hp *hen

the total head i! %&&$ and the /et dia$eter i! 1& c$. the no,,le di!charge

coefficient 0- &.2. !!u$e that the total head and *heel efficiency

re$ain con!tant. deter$ine the percentage reduction in *hen the

hor!epo*er i! reduced to '&& hp by (a)needle regulation 4 (b) partial clo!ure

of throttle -al-e on pipeline4 al!o obtain the lo!! of head acro!! the -al-e in

ca!e (b).

%# four /et Pelton turbine i! !upplied by a re!er-oir *ho!e !urface i! at an

ele-ation of '&&$ abo-e the no,,le! of the turbine. he *ater flo*! through

a pipe &&$ long4&.5' $ dia$eter4 *ith a friction coefficient 6&.&5'.Eachno,,le pro-ide! a /et 5'$$ dia$eter and the no,,le -elocity coefficient

0-&.2. he /et! i$pinge on buc7et! of the *heel at a radiu! of &.' $ and

are deflected (relati-e to the *heel) through an angle of 1&8. Fluid friction

*ithin the buc7et! reduce! the relati-e -elocity by 1'9. he blade !peed to

/et !peed ratio&.:2 and the $echanical efficiency of the turbine i! 29

0alculate the lo!! of head in the pipeline and hence4 deter$ine for the

turbine;

a#the !peed of the turbine

b#the o-erall efficiency (ba!ed on the effecti-e head) c#the po*er output

3# generator i! dri-en by a !$all 4!ingle Pelton turbine de!igned to ha-e a

po*er !pecific !peed of %& .the effecti-e head at no,,le inlet i! 1%& $ and the

no,,le -elocity coefficient i! &.2'. he runner rotate! at 22& re-re!er-oir to no,,le i! %'& $. the turbine ha! t*o runner! *ith t*o /et! per

runner. ll the four /et! ha-e !a$e dia$eter!. he pipe line i! 3&&&$ long.

he efficiency of po*er tran!$i!!ion through pipe line and no,,le i! 19

and efficiency of each runner i! &9.the -elocity coefficient of each no,,le

i! &.5' and the coefficient of friction for the pipe i! &.&:' deter$ine;

a#the "P de-eloped by the turbine

b#the dia$eter of the /et

c#the dia$eter of pipe line

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7/25/2019 Sheet 1 Pelton Wheel

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'# he follo*ing data refer to a Pelton *heel; the buc7et angle = 1'84 the

coefficient of di!charge for the no,,le 0- &.24 the friction coefficient 7

&.%. !!u$e that the opti$u$ !peed ratio differ! fro$ &.' a! a re!ult of

lo!!e! due to *indage and bearing friction4 *hich are proportional to the

!>uare of the rotational !peed (ta7e the proportionality con!tant e>ual to

&.%)4 obtain a for$ula for the opti$u$ !peed ratio4 hence calculate it for the

abo-e gi-en data and al!o calculate the $a?i$u$ o-erall efficiency.

# For the follo*ing t*o#no,,le Pelton *heel4 calculate it! $a?i$u$

efficiency and output. Pitch circle dia$eter of runner i! %.' $4 no,,le

dia$eter i! &.1' $4 head on the no,,le i! 1&& $4 0- for no,,le i! &.24

buc7et angle at e?it i! 15384 hor!epo*er lo!t in di!7 friction i! . ? 1 N34

hor!epo*er lo!t in bearing friction i! %.1 ? 1 N%4 *here N i! the !peed of

*heel in rp$4 !peed ratio i! &.:'4 the relati-e -elocity i! reduced by 1& 9 of

it! $agnitude before lea-ing the buc7et! due to friction in buc7et!.

5# Pleton *heel i! !upplied *ith *ater in the no,,le bo? at a pre!!ure head

of '& $. the -elocity coefficient for the no,,le i! &.. he relati-e -elocity of

*ater *hile in contact *ith the buc7et! i! turned through 1'& 8and i! al!o

reduced by 1'9 o*ing to friction lo!!e! .the re>uired ratio of buc7et to /et

ratio !peed i! &.:54 and &.2 of energy i$parted to the *heel4 a! deter$ined

by the -elocity diagra$!4 i! con-erted to $echanical energy. @heel

dia$eter i! 1& ti$e! the /et dia$eter. Find the /et and *heel dia$eter! and

the !peed of rotation to de-elop %&& "P under the!e condition!.

2# $ulti /et Pelton turbine *ith a *heel 1.:5 $ dia$eter4 operate under

effecti-e head of %&&$ at no,,le inlet and u!e! : $3

pro-ed that the *heel efficiency i! 22 9and -elocity coefficient of each

no,,le i! &.4 !!u$ing that the turbine operate! at a blade !peed to /et

!peed ratio &.:5. Deter$ine;

a#the *heel rotational !peed

b#the po*er output and the po*er !pecific !peed

c#the buc7et friction coefficient gi-en that the relati-e flo* i! deflected

1'8

d#the re>uired nu$ber of no,,le! if the ratio of the /et dia$eter to $ean

dia$eter of the *heel i! li$ited to a $a?i$u$ -alue of &.113

Prof. Dr Moha$ed Moa*ed

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