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

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

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}

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

in &flea VerEu,r4. 4.,

AR =

CDEEP IIT Bombay

CE 223 L 19) / Slide )7-

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

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

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

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)

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

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

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

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

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

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'

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

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