007b (PPT) Orificemeter.pdf

1. Flow measurement
Session 2
Orifice meter
Dr. Vijay G. S.
Professor
Dept. of Mech. & Ind. Engg.
MIT, Manipal
email: vijay.gs@manipal.edu
Mob.: 9980032104

2. • Orifice meter or Orifice plate is a device employed for measuring the
discharge of fluid through a pipe.
• It works on the same principle of the venturi meter.
• It is cheaper than a venturimeter as
it has the simplest design and occupies minimal space
2
Orifice meter
it consists of a flat circular plate with a concentric circular
sharp edge hole called orifice.
• This plate is inserted in the pipe such that the orifice
is concentric with the pipe cross section.
• The orifice diameter do
do  0.5 × d1 where, d1 = pipe diameter
Generally, 0.4d1 < do < 0.8d1
Orifice
Orifice plate
Dr. Vijay G S, Professor, MIT, Manipal

3. 3
Orifice meter – contd…
Dr. Vijay G S, Professor, MIT, Manipal

4. Orifice plate
4
Orifice meter – contd… • The sudden change in the
flow area in Orifice
meters causes
considerable swirl
(eddies) and thus
significant head loss or
permanent pressure loss
occurs
• The region at which the
jet of fluid assumes
minimum cross sectional
area is known as the
“Vena contracta”
Swirl (eddies)
Pressure tapping position:
• On upstream side l1 = 1.5 to 2 times d1
• On downstream side l2 = 0.5 d1
l1 l2
d1
do
d2
Dr. Vijay G S, Professor, MIT, Manipal

5. 5
Orifice meter – contd…
Vena Contracta
Dr. Vijay G S, Professor, MIT, Manipal

6. 6
Orifice meter – contd…
Eddies
Dr. Vijay G S, Professor, MIT, Manipal

7. 7
p1, V1, d1, a1 at section (1)
p2, V2, d2, a2 at section (2)
Applying Bernoulli’s equation at
sections 1 and 2 we get,
Expression for rate of flow through an Orificemeter
2 2
1 1 2 2
1 2
2 2
 
    
o o
p V p V
z z
g g g g
As pipe is horizontal, z1 = z2
2 2
1 1 2 2
2 2
 
  
o o
p V p V
g g g g
2 2
1 2 2 1
2 2
 
   
  
   
 
 
o o
p p V V
g g g g
 
1 2
o
p p
h
g



2 2
2 1
2 2
 
V V
h
g g Dr. Vijay G S, Professor, MIT, Manipal

8. Applying continuity equation at sections 1 and 2,
a1 V1 = a2 V2==> V1 = (a2 / a1) V2
2 2
2 1
2 2
 
V V
h
g g
2
2 1
2 2 2
1 2
1
2 2 2
1 2
2
2
a
V gh
a a
a gh
V
a a
 
  

 
 

2
2
2
2 2
1
2
2 2
2 2
2
1
2 2 2
2 1 2
2
1
2 2
1
2
2
 
 
 
 
 
 
 
 
 

   
 
a
V
a
V
h
g g
V a
a
g
V a a
h
g a
Expression for rate of flow through an Orifice meter – contd…
8
Dr. Vijay G S, Professor, MIT, Manipal

9. 9
1
2 2 2
1 2
2
a gh
V
a a



• But a2 is the area of cross section of the fluid jet at vena contracta and
cannot be generally measured.
• So a2 should be expressed in terms of ao the area of cross section of the fluid
at orifice, which is known.
The ‘Coefficient of Contraction’ Cc is defined as:
2
c
o
a Area of cross section of fluid jet at Vena Contracta
C
a Area of cross section of fluid at Orifice
 
 a2 = Cc× ao
 
1 1
2 2 2 2
2
1 2 1
2 2
c o
a gh a gh
V
a a a C a
  
 
Expression for rate of flow through an Orifice meter – contd…
Dr. Vijay G S, Professor, MIT, Manipal

10. Expression for rate of flow through an Orifice meter – contd…
10
The discharge through the Vena contracta is given as
Q = a2× V2
Q = (Cc× ao) × V2
 
1
2
2
1
2
th c o
c o
a gh
Q C a
a C a
 

This is the theoretical discharge through the Orifice meter is
1
2 2 2
1
2
c o
th
c o
C a a gh
Q
a C a


But the actual discharge Qact will be less than the theoretical discharge Qth
Dr. Vijay G S, Professor, MIT, Manipal

11. • i.e., Qact < Qth  Qact = Cd × Qth , where Cd = Coefficient of discharge
• Further, the equation for discharge must also be expressed in a form that is
similar to that of the venturimeter, for comparison purpose.
• Cd must also account for the significant head losses occurring due to the
eddies.
• Cd is defined such that:
11
Expression for rate of flow through an Orifice meter – contd…
2 2
1 0
2 2 2
1
d c
c o
a a
C C
a C a



2 2 2
1
2 2
1
c o
c d
o
a C a
C C
a a

 

1
2 2
1
2
d o
act
o
C a a gh
Q
a a
 

1 1
2 2 2 2 2
1 1
2 2 2 2 2
1 1
2 2
. .,
c o d o
c o o
c d
c o o
C a a gh C a a gh
a C a a a
C C
i e
a C a a a

 

 
Dr. Vijay G S, Professor, MIT, Manipal

12. 12
• The coefficient of discharge Cd for Orifice meter is much smaller than Cd for
a Venturi meter.
 For Venturi meter, Cd  0.95 to 0.98
 For Orifice meter, Cd  0.6 to 0.65
The actual discharge of venturi meter is
1 2
2 2
1 2
2


d
act
C a a gh
Q
a a
The actual discharge of orifice meter is
1
2 2
1
2
d o
act
o
C a a gh
Q
a a


a2 = area of c/s of throat ao = area of c/s of orifice
Expression for rate of flow through an Orifice meter – contd…
Dr. Vijay G S, Professor, MIT, Manipal

13. Case (i): Orifice meter is horizontal, manometer is upright, m > o
Case (ii): Orifice meter is inclined, manometer is upright, m > o
Case (iii): Orifice meter is horizontal, manometer is inverted, m < o
Case (iv): Orifice meter is inclined, manometer is inverted, m < o
1


 
 
 
 
m
o
h x
1


 
 
 
 
m
o
h x
Expression for h
13
Dr. Vijay G S, Professor, MIT, Manipal

14. 14
Comparison between Venturi meter and Orifice meter:
Venturi meter Orifice meter
Higher cost Lower cost
Larger size Smaller size
Low head loss High head loss
High coefficient of discharge
Cd  0.95 to 0.98
Low coefficient of discharge
Cd  0.65 to 0.70
Used for measuring the flow rates of
incompressible fluids (gases with low
pressure variations, as well as liquids)
Generally used for measuring the
flow rate of liquids
Dr. Vijay G S, Professor, MIT, Manipal

15. PROBLEMS ON ORIFICE METER
15
Dr. Vijay G S, Professor, MIT, Manipal

16. Problem 1: An orifice meter with orifice diameter 10 cm is inserted in a pipe of
20 cm diameter. The pressure gauges fitted upstream and downstream of the
orifice meter gives readings of 19.62 N/cm2 and 9.81 N/cm2 respectively.
Coefficient of discharge for the orifice meter is given as 0.6. Find the discharge
of water through pipe.
o = 1000 kg/m3 (Flowing water)
d1 = 20 cm = 0.2 m (Pipe dia)
do = 10 cm = 0.1 m (Orifice dia)
p1 = 19.62 N/cm2 = 19.62×104 N/m2
p2 = 9.81 N/cm2 = 9.81×104 N/m2
Cd = 0.6
2 2
2
1
1
0.2
0.03142
4 4
d
a m
  
  
2 2
2
2 0.1
0.00785
4 4
o
d
a m
  
  
3
1
2 2 2 2
1
2 0.6 0.03142 0.00785 2 9.81 10
0.06813 /
0.03142 0.00785
d o
act
o
C a a gh
Q m s
a a
    
  
 
Qact = 68.13 lps 16
    4
1 2 19.62 9.81 10
1000 9.81
10
o
p p
h
g
m of water

  
 


Dr. Vijay G S, Professor, MIT, Manipal

17. Problem 2: An orifice meter with orifice diameter 15 cm is inserted in a pipe of
30 cm diameter. The pressure difference measured by a mercury-oil differential
manometer on the two sides of the orifice meter gives a reading of 50 cm of
mercury. Find the rate of flow of oil of specific gravity 0.9 when the coefficient
of discharge of the orifice meter 0.64.
o = 900 kg/m3 (Flowing oil)
m = 13600 kg/m3 (Manometer fluid)
d1 = 30 cm = 0.3 m (Pipe dia)  a1 = d1
2/4 = 0.07069 m2
do = 15 cm = 0.15 m (Orifice dia)  ao = do
2/4 = 0.01767 m2
x = 50 cm = 0.5 m
Cd = 0.64 1
13600
0.5 1 7.056
900
m
o
h x
h m of oil


 
 
 
 
 
   
 
 
17
Dr. Vijay G S, Professor, MIT, Manipal

18. Problem 2 contd…
18
1
2 2
1
2 2
3
2
0.64 0.07069 0.01767 2 9.81 7.056
0.07069 0.01767
0.13742 /
d o
act
o
C a a gh
Q
a a
m s


    



Qact = 137.42 lps
Dr. Vijay G S, Professor, MIT, Manipal

19. Problem 3: An orifice meter is used to measure the air flow passing through a
pipe of 8 cm diameter. The diameter of orifice meter is 2 cm. The pipe is
horizontal. The head causing flow is measured by using a manometer containing
water. The measured head is 5.6 m of water. The density of air 1.193 kg/ m3.
Take Cd = 0.65
19
o = 1.193 kg/m3 (Flowing air)
m = 1000 kg/m3 (Manometer fluid water)
d1 = 8 cm = 0.08 m (Inlet dia)  a1 = d1
2/4 = 0.00502 m2
do = 2 cm = 0.02 m (Orifice dia)  ao = do
2/4 = 0.000314 m2
x = 5.6 m of water
Cd = 0.65 1
1000
5.6 1 4688.4
1.193
m
o
h x
h m of air


 
 
 
 
 
   
 
 
Dr. Vijay G S, Professor, MIT, Manipal

20. Problem 3 contd…
20
1
2 2
1
2 2
3
2
0.65 0.00502 0.000314 2 9.81 4688.4
0.00502 0.000314
0.06202 /
d o
act
o
C a a gh
Q
a a
m s


    



Qact = 62.02 lps
Dr. Vijay G S, Professor, MIT, Manipal