Venturimeter (Contd.)

17
Venturimeter (Contd.) CDEEP IIT Bombay CE 223 L ) S/Slide f 3 V 2 2g E. L . t A 11/6 " N 'Y d rek 14.GA.• ... -S1/4 .• S. ‘OkArtAIZAIZIAr ..................... b A V 2 2g zez ,,,p, 4. . , NN, Niernm t'T% w 20 °: Inlet Throat

Transcript of Venturimeter (Contd.)

Page 1: Venturimeter (Contd.)

Venturimeter (Contd.)

CDEEP IIT Bombay

CE 223 L ) S/Slide f 3

V 2 2g

E. L . •

t A 11/6" N 'Y

drek

14.GA.•

... -S1/4.• S. ‘OkArtAIZAIZIAr

.....................

• b A V 2

2g

zez,,,p, 4..,NN,Niernm

t'T% w 20 °: •

Inlet Throat

Page 2: Venturimeter (Contd.)

Venturimeter (Contd.)

CDEEP IIT Bombay

CE 223 LialSlide Pl 1 +—v

22 1 +

(

Pi

/ = —P2

V 22 +z 2

= OH

7

V2 2

ae?1

7 +

2g

P2 7

2g 2g 7 t_2,1 sa 2

• Using continuity equation for an incompressible fluid

V2 = 11 22 2

2g 2g 2g

A,\ 2

1 —( - A l

Page 3: Venturimeter (Contd.)

Venturimeter (Contd.)

• From the above two Eqs. CDEEP

IIT Bombay

CE 223

► , NA2gAH )

(AA: 2

A 1 -12 g A H

N (A —

A2 )

• The theoretical discharge

Qth = A2.v2 A l A rji NtAH =k-vAH

• Actual discharge

ac = Cella Cd <1.0 {0.95 to 0.98}

Page 4: Venturimeter (Contd.)

Venturimeter (Contd.)

CDEEP Ill Bombay

CE 223 L )a Slide

Values of D; Is for water at 72°F-(diarreter in inches x velocity in fps)

—NR + 8,000 (P-0.0000104 ft 2/sec)

23 5 7.5 1012.5 25 50 75100125 250

500 750 1000

094 106 2 3 4 5 6 78 106 2 3 4 5 6 7 8 106

2 3 4 5 6 7 8 10 7

V2 102 Reynolds number at throw NA—

D2 a2

Coefficient for venture tubes

1.00

0.99

0.98

Cd

0.97

O.

0.95

200* I [

x 1

100' I _anon I ba

Sri 1 il I I A I , 1 I

r

3°.1 1 15. I 8' x 42

..0.

o f 2 x 1

2 I ' X ' 1 CA7 Q.' I -r-7112E/Z4

[--

Di meat diameter, ft I D2 -throat diameter, ft

A a throat area,sq ft i rr -]

2

i I I 1 1 Iffi 1 I 1

Page 5: Venturimeter (Contd.)

in &flea VerEu,r4. 4.,

AR =

CDEEP IIT Bombay

CE 223 L 19) / Slide )7-

Page 6: Venturimeter (Contd.)

Inclined Venturimeter

p i + = + (z, + y„,x

CDEEP IIT Bombay

CE 223 I )23- Slide /

`-2— Zoitun at Lowe-6 TO 41 CSC() S

( \ Yu, P-) z + z2 = —x+—.x = x(s — 1) = AH

i f ) If ) Ij

• Precautions

i) Pipe must run full i.e. under pressure

ii) The pressure at the throat should not go below

vapour pressure to avoid cavitations damage

Page 7: Venturimeter (Contd.)

Advantages of Venturimeter

CDEEP IIT Bombay

CI 223 t 12uSlidelS b

• Advantages- Simple, reliable, suitable over a great range of pipe sizes, say from 5cm to 6m in dia.

• Without calibration the discharge may be predicted to within 1.5%

• Overall losses do not exceed 10 to 15% of the differential head

• Large discharges can be handled

• Q depends on the gauge difference x regardless of the orientation of venturimeter

Page 8: Venturimeter (Contd.)

Orificemeter CDEEP

IIT Bombay

CE 223 L_Lt/Slide

• Standard orifice is a sharp edge circular opening in

the wall of a tank containing fluid

• Out coming streamlines contract and then become

parallel at the vena-contracta

• Pressure throughout the vena-contracta section is considered as atmospheric

Page 9: Venturimeter (Contd.)

V2

h

V1/4 g°--

-ct

1)„ 02 A- -al /4—

It

Orificemeter(Contd.) CDEEP

IIT Bombay

CE 223 CL

• For a 2-D slot & irrotational flows, theoretically

C` (7 + 2) =

0.61

Cc = (area of jet at vena contracta)/area of opening)

Page 10: Venturimeter (Contd.)

Orificemeter(Contd.) CDEEP

IIT Bombay

CE 223 LIT/Slide_l

• Let, Cv = (actual velocity)/(theoretical velocity)

• Vth = (2gh) 1/2 and Vac = Cv(2gh) 1/2

Q„. = C,./10 C,,V2gh

Page 11: Venturimeter (Contd.)

Orificemeter(Contd.) C DEEP

IIT Bombay

CE 223 t_i9JSlide4_

• Orifice meters are used to measure flow in closed

Conduits

• A concentric square edged circular hole in a thin plate clamped between the flanges of a pipe

• Head losses are high though inexpensive to make

Page 12: Venturimeter (Contd.)

Orificemeter(Contd.)

CDEEP IIT Bombay

7 CF 223 LaSlide_51

• The minimum section of the stream tube occurs downstream from the orifice owing to the formation of the

vena contracta

• From Bernoulli eq. & continuity eq.

V h

Page 13: Venturimeter (Contd.)

Orificemeter(Contd.)

Q = Gym x A 2 = Ce C v rith A o CDEEP

IIT Bombay

or CE 223 La/SlicleaS

Cc C v A

V2gAH Q = i

JA, — C A:

where

C v .C c

Ao is the area of orifice.

• Cd depends on C,,C, & shape of installation as defined by

Ao/Ai

x A o = C d .A 0 V2gaH

Page 14: Venturimeter (Contd.)

Mouthpiece CDEEP

IIT Bombay

• Mouthpiece is a short tube not longer than 2 or 3

times the dia.

CE 223 LASlideS

• Attachment of the mouthpiece increases the Cd value as a

negative pressure is generated near the vena contracta

® paly=0

1

Page 15: Venturimeter (Contd.)

Time of Emptying a Tank

CDEEP IIT Bombay

CL 223 L IgiSlide

• As the reservoir surface drops slowly, Bernoulli's Eq. can be applied

• Equating the volume discharged from the orifice with the reduction in volume in the reservoir

Qc5t=— A R S y

• Both Q and AR should be expressed as a function of y prior to integration to find 't'

Page 16: Venturimeter (Contd.)

Time of Emptying a Tank (Contd.)

Example: CDEEP IIT Bombay

CL 223 Li9/Slide_Mir 9 • A tank shown in the figure has a 100 mm

diameter orifice, Cd = 0.65, fitted at the bottom

• Compute the time to lower the surface from 2.5 to 1.0 m

above the orifice

• Assume the plan area of the tank to vary linearly with depth

y

t 2.5m

Page 17: Venturimeter (Contd.)

Time of Emptying a Tank (Contd.)

CDEEP IIT Bombay

• Solution: time needed to lower from 2.5 to 1 m above orifice

CE 223 ISSlidede

11

a\12g ' 0.65(1. 0.1) 2 )V2*9.81 Is 3 , Ayihdy= (2 -z-)y-1/2dy

=73.8 sec