1. FLUID MECHANICS – 1
Semester 1 2011 - 2012
Week – 9
FLOW MEASUREMENT
CO4
Compiled and modified
by
Sharma, Adam
2. Chapters to cover
1. Properties of Fluid
2. Fluid Statics
3. Fluid in Motion
4. Friction in Piping System
5. Flow Measurement
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3. Chapters to cover
1. Properties of Fluid
2. Fluid Statics
3. Fluid in Motion
4. Friction in Piping System
5. Flow Measurement
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4. Flow Measurement
• Explain type of flow measuring
equipments
• Calculate fluid flow through
– Pitot tube,
– Orifice meter,
– Venturi meter
– Nozzle meter.
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5. Types of Flowmeters
F lo w m e t e r s
P re ssu re M e c h a n ic a l T h e rm a l O th e r
Types Types Types Types
O r ific e s T u r b in e H o t-w ir e V o rte x
flo w m e te r flo w m e te r flo w m e te r flo w m e te r
V e n tu ri T u b e R e c ip o c a te in g R e s is tiv e -b r id g e E le c tr o m a g n e tic
flo w m e te r P is to n flo w m e te r flo w m e te r flo w m e te r
F lo w T u b e O v a l-G e a r O th e rs U ltr a s o n ic
flo w m e te r flo w m e te r F lo w m e te r
F lo w N o z z le s O th e rs O th e rs
flo w m e te r
P ilo t T u b e s
flo w m e te r
O th e r s
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6. Pitot Tube
1
P2 2
P1,V1 Stagnation
Point V2=0
P1 is a Static pressure: It is measured by a device (static tube)
that causes no velocity change to the flow. This is usually
accomplished by drilling a small hole normal to a wall along
which the fluid is flowing.
P2 is a Stagnation pressure: It is the pressure measured by an
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open-ended tube facing the flow direction. Such a device is
7. Pitot Tube
The basic pitot tube simply consists of a tube pointing directly into the
fluid flow. The fluid is at rest or stagnant inside the tube. A pressure is
created in the stagnant tube that is greater than the pressure of the
fluid stream. The magnitude of this increased pressure is related to
the velocity of the moving fluid. The pressure of the moving fluid is
called the static pressure.
(a) A Pitot probe measures stagnation pressure at the nose of
the probe, while (b) a Pitot-static probe measures both
stagnation pressure and static pressure, from which the flow 7
speed is calculated.
8. Pitot-Static Tube
The static and Pitot tube are often combined into the one-piece Pitot-static
tube.
Examples
Used in
aircraft
nose
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10. Obstruction Flowmeters:
Orifice, Venturi, and
Nozzle Meters
Flowmeters based on this principle
are called obstruction flowmeters
and are widely used to measure flow
rates of gases and liquids.
Flow through a constriction in a pipe.
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11. The losses can be accounted for by incorporating a correction factor called the
discharge coefficient Cd whose value (which is less than 1) is determined
experimentally.
The value of Cd depends on both b and the Reynolds number, and
charts and curve-fit correlations for Cd are available for various types of
obstruction meters.
For flows with high Reynolds numbers (Re > 30,000), the value of
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Cd can be taken to be 0.96 for flow nozzles and 0.61 for orifices.
13. Pipe Flowrate Meters
Example 1: Flow through an orifice meter
The flow rate of water at 20°C (ρ = 998 kg/m3 and μ = 1.002x10-3 kg/m ·
s) through a 50-cm-diameter pipe is measured with an orifice meter
with a 30-cm-diameter opening to be 250 L/s. Determine the pressure
difference
indicated by the orifice meter and the head loss. The discharge
coefficient of the orifice meter is Cd = 0.61.
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14. Pipe Flowrate Meters
Assumptions 1 The flow is steady and incompressible. 2 The discharge
coefficient of the orifice meter is Cd = 0.61.
Properties The density and dynamic viscosity of water are given
to be ρ = 998 kg/m3 and μ = 1.002x10-4 kg/ms, respectively.
Analysis The diameter ratio and the throat area of the orifice are
β = d D = 30 50 = 0.60
A0 = πd 2 4 = π (0.3) 2 4 = 0.07069 m 2
For a pressure drop of across the orifice plate, the flow
rate is expressed as ∆P = P − P2
1
2( P − P2 )
Q = AoCd 1
(
ρ 1− β 4 )
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15. Pipe Flowrate Meters
Substituting,
2∆P
(
0.25m /s = 0.07069 m
3 2
)( 0.61) ( )(
998 kg/m 3 1 − 0.60 4 )
This gives a pressure drop
of,
∆p = 14600 kg.m/s = 14.6 kPa
2
We know,
∆P = ρgh
This is the head loss
then,
∆P 14600
h= = = 1.49 m
ρg (998)(9.81)
16. Pipe Flowrate Meters
Venturi Meter
This device consists of a conical contraction, a short cylindrical
throat and a conical expansion. The fluid is accelerated by being
passed through the converging cone. The velocity at the “throat”
is assumed to be constant and an average velocity is used. The
venturi tube is a reliable flow measuring device that causes little
pressure drop. It is used widely particularly for large liquid and gas
flows.
P1 P2
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18. Pipe Flowrate Meters
Venturi Meter
2( p1 − p2 )
Qactual = CVQideal = C V A T
ρ (1 − β 4 )
AT = π d 2 / 4 Area of the throat
CV = CV (β = d / D, Re = ρ VD / µ )
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19. Pipe Flowrate Meters
Venturi Meter
A Venturi meter equipped with a differential pressure gage is
used to measure the flow rate of water at 15°C (ρ = 999.1 kg/m3)
through a 5-cm-diameter horizontal pipe. The diameter of the
Venturi neck is 3 cm, and the measured pressure drop is 5 kPa.
Taking the discharge coefficient to be 0.98, determine the
volume flow rate of water and the average velocity through the
pipe.
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20. Pipe Flowrate Meters
Assumptions 1 The flow is steady and incompressible. 2 The discharge
coefficient of the venturi meter is Cd = 0.98.
Properties The density and dynamic viscosity of water are given
to be ρ = 999.1 kg/m3 and.
Analysis The diameter ratio and the throat area of the orifice are
β = d D = 3 5 = 0.60
A0 = πd 2 4 = π (0.03) 2 4 = 0.0007069 m 2
For a pressure drop of across the orifice plate, the flow
rate is expressed as ∆P = 5 kPa
2( P − P2 )
Q = AoCd 1
(
ρ 1− β 4 )
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21. Pipe Flowrate Meters
Substituting,
(
Q m /s = 7.069 ×10 m
3 -4 2
)( 0.98) ( 2(5000)
)(
999.1 kg/m 3 1 − 0.60 4 )
This gives a flow rate of,
Q = 0.00235 m /s = 2.35 liters/s
3
Average velocity in pipe is,
Q Q 0.00235 m 3 /s
V= = = = 1.20 m/s
A ρD / 4 π (0.05 m ) / 4
2 2
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22. Pipe Flowrate Meters
Nozzle Meter
2( p1 − p2 )
Qactual = C n Qideal = C n A n
ρ(1 − β4 )
A n = πd 2 / 4 Area of the hole
C n = C n (β = d / D, Re = ρVD / µ )
Nozzle meter discharge coefficient
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23. Pipe Flowrate Meters
Nozzle Meter
A flow nozzle equipped with a differential pressure gage is used to
measure the flow rate of water at 10°C (ρ= 999.7 kg/m3 and μ = 1.307
x 10-3 kg/m · s) through a 3-cm-diameter horizontal pipe. The nozzle
exit diameter is 1.5 cm, and the measured pressure drop is 3 kPa.
The nozzle has a discharge coefficient of Cd= 0.96.Determine the
volume flow rate of water, the average velocity through the pipe,
and the head loss.
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24. It’s the same!!!!!!!!!!!
All equations
2( p1 − p2 ) ORIFICE
Qactual = CoQideal = Co A o
ρ (1 − β 4 )
2( p1 − p2 ) VENTURI
Qactual = C VQideal = CV A T
ρ (1 − β 4 )
2( p1 − p 2 )
Qactual = C n Qideal = C n A n NOZZLE
ρ(1 − β4 )
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28. Pitot-Static Tube
An object is traveling at an elevation of 10,000
m in standard atmosphere. The pressure
difference indicated by the Pitot-static probe
attached to the roof is 2000 Pa. What is the
velocity of the object? (The density of air at
this altitude is 0.414 kg/m3)
Pitot-static
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