Notches and Weirs in Fluid Measurement

(1)

8/17/2019 Mfh-04 Aliran Melalui Pelimpah

http://slidepdf.com/reader/full/mfh-04-aliran-melalui-pelimpah 1/27

NOTCHES WEIRS

(2)

DEFINITIONS

A notch may defined as an opening provided in the side of a tank (or vessel) such that the liquid surface in the tank is below the top edge of the opening. Notches made of metallic plates, and are provided in narrow channels (laboratory) to measure the rate of flow.

A weir is the name given to a concrete or massonry structure built across a river or stream in order to raise the level of the water on the upstream side and to allow the excess water to flow over its entire length to the downstream side. Weirs may also be used for measuring the rate of flow water in rivers or streams.

2

(3)

CLASSIFICATION OF NOTCHES

Based on the shape of the opening:

Rectangular notch Triangular (V-notch) Trapezoidal notch Parabolic notch, and Stepped notch.

According to the effect of the sides on the nappe emerging from notch:

Notch with and contraction

Notch without end contraction or suppressed notch.

3

(4)

CLASSIFICATION OF WEIRS (1/2)

Based on the shape of the opening of:

Rectangular notch, Triangular notch, and Trapezoidal notch

Based on the shape of the crest:

Sharp crested weirs, Narrow crested weirs, Broad crested weirs, and Ogee shaped weirs

4

(5)

CLASSIFICATION OF WEIRS (2/2)

According to the effect of the sides on the nappe emerging from notch:

Notch with and contraction

Notch without end contraction or suppressed notch.

According to the discharge conditions:

Freely discharging weirs, and Submerged (or downed) weirs

5

(6)

FLOW OVER A RECTANGULAR SHARP CRESTED WEIR OR NOTCH

Consider a rectangular sharp crested weir as

shown below: L crest length, and H is the height of the water surface above the crest.

6 Head above the crest, H

Height of the weir or notch, p

Nappe

(7)

CLASSIFICATION OF THE SHARP CRESTED WEIR

Sharp crested weir can be classified as follows:

1. Based on the shape of the weir 1) Rectangular

2) Triangular 3) Trapezoidal

7

rectangular triangular trapezoidal

2. Based on the elevation of tail water (down stream water):

1) Free flow weir, when the downstream water surface is below the crest of the weir.

2) Submerged weir, when the downstream water surface is above the crest of the weir.

Free flow weir submerged weir

(8)

RECTANGULAR SHARP CRESTED WEIR

Rectangular sharp crested weir: crest width b, overflow hight H, discharge coefficient Cd, and velocity approach can be neglected.

g 2 0 V z

0 0 z

2 2 2

1

gh 2 ) z z ( g 2

V

₂ ₁ ₂

8

Consider to water segment of dh at the depth h from water surface . Bernoulli equation between point 1 and 2 is,

g 2 V g

z p g

2 V g z p

2 2 2 2

1 2 1 1

dh h

b

V

₁

1

H

²

v

₂

As V 1

^≈

0, and both points are at atmospheric pressure, then the equation become:

or

(9)

H

0

H 0 d

H

0

12 12

3 h g 2 2 Cdb dh h b . g 2 C dq

Q C b 2 g . H

³²

3

Q 2

_d

9

Segment area : dA = b.dh

The discharge through the segment is : dq V 2 dA

dh . b . gh 2 dA

. V

dq 2

By considering the discharge coefficient Cd, then the discharge is :

dh . b . h . g 2 C

dq d 1 2

Integration of the equation produces:

(continued)

(10)

dA V

dq 2 )

g 2 h v ( g 2 dh . b . C dq

2a d

H

a d

H

g dh h v

b g C

dq Q

0

2

0

2

)

1

( 2 . 2

2 3 2 2 a

3 2 a

d

2 g

v g

2 h v

. g 2 b . 3 C Q 2

10

When the velocity approache is considered , V a , the energy head at the upstream of the weir is:

g 2 h v

a 2

Velocity through the segment of dh is then :

g ) 2 h v

( g 2 V

2 a 2

The discharge through the segment is :

Intergration of the equation produces :

(continued)

(11)

TRIANGULAR SHARP CRESTED WEIR

11

Discharge through the triangular sharp crested weir: water depth above crest H, discharge coefficient C d , and overflow angle α.

2 dh tg ) h H ( 2 dh . b da gh

2 v

Consider to segment dh at the water depth h from the water surface. Segment area is

Velocity through the segment is

The discharge through the segment is :

gh 2 . 2 dh tg ) h H ( 2 C gh

2 da C

dq d d

B

b

α

h dh

V

₁

1

H

²

v

₂

V² /2g

(12)

12

Integration the equation produces the discharge through the whole weir:

H

0 d

H

0

dh h ) h H ( g 2 2

tg C 2 dq

Q

²¹

H

d

tg 2 2 g

0

( Hh h ) dh

C 2 Q

2 3 21

H 5 0 2 3 2

3 d

2

25

23

h Hh

g 2 2

tg . C Q

) H H

( g 2 2

tg . C

Q 3 2 d 3 2

²⁵

5 2

²⁵

2 5

H g 2 2

tg . 15 C

Q 8 d

(continued)

(13)

13

When the velocity approache is considered, the the equation become:

2 / 2 5 2

/ 2 5

d 2 v g

g 2 v H

g 2 2

tg . 15 8 C

Q

(continued)

(14)

TRAPEZOIDAL SHARP CRESTED WEIR

14

2 5 2

3

H g 2 2

tg . 15 C

H 8 g 2 b 3 C

Q 2 d 1 d 2

where: C d1 = discharge coefficient of rectangular weir C d2 = discharge coefficient of triangular weir

As the trapezoidal is the combination of rectangular and triangular, so the discharge through the trapezoidal weir is the summation of discharge through the rectangular weir and triangular weir.

b

h dh

V

¹

1

H

²

v

₂

V² /2g

(15)

BROAD CRESTED WEIR

15

Weir is called wide crested weir when the crest width is

wider than 0.66 of the overflow depth ( t > 0,66H) , and the present of the straight flow-lines (horizontal) on the top of

the crest.

The pressure on the overflow above the wide crest is hydrostatic pressure. Application of Bernoulli equation on the points before and on the top of the weir crest can be used to find out the flow velocity above the crest.

By measuring the water depth at the upstream, H, the discharge over the weir can be determined.

When the water level at the downstream of the weir is above

the crest, the weir is called imperfect weir or submerged

weir.

(16)

g 2 V g z p

2 2 2

2 2

1 1

1

g 2 h V 0

0 H 0

2 2

g 2 V h

H

2 2

) h H ( g 2 v

16

Aplication of Bernoulli equation on wide crested weir results:

H h 1 2

BROAD CRESTED WEIR (continued)

V . A . C

Q d

2 1

) h Hh

( g 2 b C )

h H

( g 2 h . b C

Q d d 2 3

or

Discharge of the weir is then:

(17)

Maximum discharge is occurred when (Hh 2 -h 3 ) is maxsimum. The value of (Hh 2 -h 3 ) is maximum when the value of dQ/dh = 0

2

3

1

2

2 g ( Hh h ) b

dh C d dh

dQ

d

17

0 2 ( Hh

²

h

³

)

¹²

dh g d b

dh C dQ

d

0 2

3 2

2 1

3 2

2

) h Hh

(

h Hh

2 Hh – 3h 2 = 0 atau h

₃²

H

BROAD CRESTED WEIR (continued)

(18)

Substitute the value of h into the equation of Q, produces :

18

2

3

1

3 2 2

3

2 g H ( 2 H ) ( H ) b

C

Q d

3 27 3 4

27 3 8 9

4 2

2 g H H C b g H

b C

Q d d

2 3

3

2

3

2

C b g H

Q d

The discharge over the weir can be calculated by measuring the water lever at the upstream of the weir, H.

BROAD CRESTED WEIR (continued)

(19)

EXAMPLE

1. Air mengalir melalui ambang lebar dengan bentang 20 m. Perbedaan

tinggi air akibat ambang adalah 0,4 m. Hitung besarnya aliran maksimum melalui ambang dengan koefisien debit 0,8

19

Perbedaan tinggi muka air, H - h = 0,4 m Jadi, h = H – 0,4m

Aliran maksimum bila h 3 2 H

Maka, 3 2 H H 0 , 4 3H - 1,2 = 2H

H = 1,2 m

Debit maksimum melalui pelimpah,

2 3 2

3

2 384

0

3

2

32

C b g H . C b g H

Q d d

Untuk percepatan gravitasi g=9,81 m/det

(20)

EXAMPLE

20

2. Hitung besarnya debit melalui peluap terendam dengan panjang ambang, b dan koefisien debit Cd

23

bH C

7 1 , 1

Q

_d

det / m 95 , 35 2

, 1 . 20 . 8 , 0 . 71 , 1

Q

²³ ³

H

1

H

²

Debit aliran melalui peluap terendam adalah jumlah aliran setinggi luapan H1-H2 dengan aliran terendam setinggi H2

Q = Q1 + Q2

) H H

( g 2 bH C )

H H

( g 2 b C

Q 3 2 d 1 2

³²

d 2 1 2

(21)

RECTANGULAR CRESTED WEIR

21

(22)

CIPOLETTI WEIR

22

(23)

V-NOTCH WEIR

23

(24)

TIPE AMBANG

24

(25)

SLUICE GATE

25

Figure 9. Free outflow followed by a shooting tailwater flow

Figure 10. Free outflow followed by an undulating hydraulic jump in the

tailwater

figure 11. free outflow followed by a

perfect hydraulic jump with surface

roller in the tailwater

(26)

LABYRINTH WEIR

26

(27)

SPILLWAY

27