8/10/2019 Chute Performance and Design for Rapid Flow Conditions

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8/10/2019 Chute Performance and Design for Rapid Flow Conditions

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m g

m v.

v.

v

"s"

"n"

"x"

"y"

FD

m

Ho Ao

H Am v

R

R

2

FN

B

B

H

Hv Rectangular Cross

Section

Circular Cross Section

VelocityProfile

vo

Bo

pn

p

B

H

B

Ho

H

s

ds

= pn

v

vo

dF

8/10/2019 Chute Performance and Design for Rapid Flow Conditions

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0.4

0.45

0.5

0.55

0.6

0 10 20 30 40 50 60

ue for Ho/B = 0.2

ue for Ho/B = 0.6EQUIVALENT

FRICTION

ANGULAR POSITION (deg)

Vo = 4 m/s R = 2.0 m

CutOffAngle

3

3.5

4

4.5

5

0 10 20 30 40 50 60

Vel for Variable ue, Ho/B=0.2

Vel for Const. ue = 0.5

Vel for Variable ue, Ho/B =-0.6

Vel for Const. ue = 0.58

VELOCITY

(m/s)

ANGULAR POSITION (deg)

Vo = 4 m/s R = 2.0 m

Cut-OffAngle

a)

b)

4

4.5

5

5.5

6

0 10 20 30 40 50 60

Velocity for Lambda = 0 deg

Velocity for Lambda = 2.5 deg

Velocity for Lambda = 5 deg

ANGULAR POSITION (deg.)

STREAMVEL

OCITY

(m/s)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 10 20 30 40 50 60

B for Lambda = 0 deg

B for Lambda = 2.5 deg

B for Lambda = 5 deg

H/B for Lambda = 0 deg

H/B for Lambda = 2.5 deg

H/B for Lambda = 5 deg

ANGULAR POSITION (deg.)

STREAMT

HICKNESSH

(m)and

RATIO

H/B

a)

b)

m g

v

v

m v

m v

R

FD

m

"t"

"n"

.

.

2

R

CrossSectionB

FN

8/10/2019 Chute Performance and Design for Rapid Flow Conditions

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8/10/2019 Chute Performance and Design for Rapid Flow Conditions

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8/10/2019 Chute Performance and Design for Rapid Flow Conditions

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-0.5 0 0.5 1 1.5 2

0

1

2

3

4

5

R = 1 m

R = 2 m

R = 3 m

R = 4 m

VERTICALDISTANCE

(m)

HORIZONTAL DISTANCE (m)

5.5

6

6.5

7

7.5

8

8.5

9

9.5

0 10 20 30 40 50 60

R=1.0 m; h=4.18 m; Vo=9.06 m/s

R=2.0 m; h=3.36 m; Vo=8.12 m/s

R=3.0 m; h=2.54 m; Vo=7.06 m/s

R=4.0 m; h=1.73 m; Vo = 5.82 m/s

ANGULAR POSITION (deg)

VELOCITY

(m/s)

a)

b)

1

2

3

4

5

6

6.15

6.2

6.25

6.3

6.35

6.4

0.5 1 1.5 2 2.5 3 3.5 4 4.5

Wa (kPa m/s)

h (m)

Ve (m/s)WEARATFEEDPOINTWa(kPam/s)

INITIALDROPHEIG

HTh(m)

EXITVELOCITY

Ve(m/s)

CHUTE RADIUS OF CURVATURE R (m)

1

2

3

4

5

6

6.15

6.2

6.25

6.3

6.35

6.4

0.5 1 1.5 2 2.5 3 3.5 4 4.5

WEARATFEEDPOINTWa(kPam/s)

INITIALDROPHEIG

HTh(m)

EXITVELOCITY

Ve(m/s)

CHUTE RADIUS OF CURVATURE R (m)

c)

Wa (kPa m/s)

h (m)

Ve (m/s)

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

Const Radius Chute

Parabolic Chute

COORDINATE y (m)

COORDINATE

x(m)

5.5

6

6.5

7

0 0.5 1 1.5 2 2.5 3 3.5

v (m/s) for Parabolic Chutev (m/s) for Const Radius Chute

VERTICAL COORDINATE POSITION x (m)

STREAMVELOCITY

v(m/s)

a)

b)

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0.8

1

1.2

1.4

1.6

1.8

2

0 0.5 1 1.5 2 2.5 3 3.5

NWR for Parabolic Chute

NWR for Const. Radius Chute

VERTICAL COORDINATE POSITION x (m)

NON-DIMENSIONALWEAR

NWR

Initial Velocity = 5.82 m/s