8/13/2019 Reaction Force in Pelton Turbines

1/8

Reaction force on Pelton

turbines

Relative reaction force

Absolute reaction force

8/13/2019 Reaction Force in Pelton Turbines

2/8

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

8/13/2019 Reaction Force in Pelton Turbines

3/8

111 ucw 111222u2 ucwwcosww

Further we can find values for the relative velocities

1111RR ucucQF The relative reaction force becomes:

11RR ucQ2F

8/13/2019 Reaction Force in Pelton Turbines

4/8

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

8/13/2019 Reaction Force in Pelton Turbines

5/8

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

8/13/2019 Reaction Force in Pelton Turbines

6/8

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

8/13/2019 Reaction Force in Pelton Turbines

7/8

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

8/13/2019 Reaction Force in Pelton Turbines

8/8