reaction force in pelton turbines
TRANSCRIPT
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Reaction force on Pelton
turbines
Relative reaction force
Absolute reaction force
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Relative reaction force
acting on the Pelton runner
The relative reaction force is the force acting
from the jet on a bucket when the runner is
rotating.
This force can be found by the help of Newtons
2. law:
21RR
RRR
wwQF
dwQdt
dmdwdm
dt
dwdmadF
The relative flow rate is given by:
112
s111R uc4
ducAwAQ
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111 ucw 111222u2 ucwwcosww
Further we can find values for the relative velocities
1111RR ucucQF The relative reaction force becomes:
11RR ucQ2F
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If we use:2
cu
1
1
2
c
2
ccuc 11
111
Then:
The relative reaction force becomes:
422222
2
111
1 cA
cwA
cQF RR
pgHAF nR
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Absolute reaction force
acting on the Pelton runner
The absolute reaction force can be found by
calculating the impulse from the jet.
This force can be found by the help of Newtons
2. law:
221Au21AA wucQccQF
For a relative velocity, w2 = -(c-u)
The absolute reaction force becomes:
cu2wu 2
ucQ2F 1AA
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Exercise 1
Find FAand FRfor the runner velocity u = 0
For Hn= 500 m and ds= 0,10 m
sm99Hg2wc n11
N15395499
4
1,010002F
cw4
d2ucQ2F
2
2
R
11
2s
11RR
N153954994
1,010002F
c4
d2ucQ2F
22
A
2
1
2
s11AA
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Exercise 2
Find FAand FRfor the runner velocity u = 0,5 c
For Hn= 500 m and ds= 0,10 m
sm99Hg2c n1
N38489
4
99
4
1,010002F
2cw
4d2ucQ2F
22
R
11
2
s11RR
N769772
99
4
1,010002F
2
cc
4
d2ucQ2F
22
A
11
2
s11AA
sm5,49
2
cw 11
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