Short Notes: Flow Measurement | Short Notes for Mechanical Engineering PDF Download

 Page 1


Flow Measurement 
Flow measurement is the chapter in Fluid mechanics which deals with the 
application of Bernoulli equation applicable to many situations, not just the pipe 
flow. It consists of various measurement apparatus such as Venturimeter, Orifice 
meter, Pitot Tube, etc. and its application to flow measurement from tanks, within 
pipes as well as in open channels.
Flow measurement is the quantification of bulk fluid movement. Flow can be 
measured in a variety of ways. Positive displacement flow meters accumulate of a 
fixed volume of fluid and then count the number of times the volume is filled to 
measure flow.
Some flow measuring instruments are given as:
Pitot Tube
• The Pitot tube is a simple velocity measuring device.
• Uniform velocity flow hitting a solid blunt body, has streamlines similar to 
this: •
• Some move to the left and some to the right. The centre one hits the blunt 
body and stops.
• At this point (2) velocity is zero The fluid does not move at this one point. This 
point is known as the stagnation point.
Page 2


Flow Measurement 
Flow measurement is the chapter in Fluid mechanics which deals with the 
application of Bernoulli equation applicable to many situations, not just the pipe 
flow. It consists of various measurement apparatus such as Venturimeter, Orifice 
meter, Pitot Tube, etc. and its application to flow measurement from tanks, within 
pipes as well as in open channels.
Flow measurement is the quantification of bulk fluid movement. Flow can be 
measured in a variety of ways. Positive displacement flow meters accumulate of a 
fixed volume of fluid and then count the number of times the volume is filled to 
measure flow.
Some flow measuring instruments are given as:
Pitot Tube
• The Pitot tube is a simple velocity measuring device.
• Uniform velocity flow hitting a solid blunt body, has streamlines similar to 
this: •
• Some move to the left and some to the right. The centre one hits the blunt 
body and stops.
• At this point (2) velocity is zero The fluid does not move at this one point. This 
point is known as the stagnation point.
• Using the Bernoulli equation we can calculate the pressure at this point.
• Along the central streamline at 1: velocity ui, pressure pi
° At the stagnation point of: U 2 = 0. (Also z -i = z2 )
E l + ! ±
P i
PQ 2
P 9
1 2
P i = P i + ----- u \
1 1 2 9 1
Note Point: The blunt body does not have to be a solid. It could be a static column 
of fluid, this feature is used measure the flow velocity.
• Two piezometers, one as normal and one as a Pitot tube within the pipe can 
be used such as
r mz mm w m
h 1
w m m m A
L
h2
m m m f i
.
1|
I
¦
a :4 4 ;
pgh2 =pgh\ + ^P“l 
u = ^2g(h2 - h l)
• The above expression is for velocity from two pressure measurements and 
the application of the Bernoulli equation.
Pitot Static Tube
• The Pitot static tube combines the tubes and they can then be easily 
connected to a manometer:
Page 3


Flow Measurement 
Flow measurement is the chapter in Fluid mechanics which deals with the 
application of Bernoulli equation applicable to many situations, not just the pipe 
flow. It consists of various measurement apparatus such as Venturimeter, Orifice 
meter, Pitot Tube, etc. and its application to flow measurement from tanks, within 
pipes as well as in open channels.
Flow measurement is the quantification of bulk fluid movement. Flow can be 
measured in a variety of ways. Positive displacement flow meters accumulate of a 
fixed volume of fluid and then count the number of times the volume is filled to 
measure flow.
Some flow measuring instruments are given as:
Pitot Tube
• The Pitot tube is a simple velocity measuring device.
• Uniform velocity flow hitting a solid blunt body, has streamlines similar to 
this: •
• Some move to the left and some to the right. The centre one hits the blunt 
body and stops.
• At this point (2) velocity is zero The fluid does not move at this one point. This 
point is known as the stagnation point.
• Using the Bernoulli equation we can calculate the pressure at this point.
• Along the central streamline at 1: velocity ui, pressure pi
° At the stagnation point of: U 2 = 0. (Also z -i = z2 )
E l + ! ±
P i
PQ 2
P 9
1 2
P i = P i + ----- u \
1 1 2 9 1
Note Point: The blunt body does not have to be a solid. It could be a static column 
of fluid, this feature is used measure the flow velocity.
• Two piezometers, one as normal and one as a Pitot tube within the pipe can 
be used such as
r mz mm w m
h 1
w m m m A
L
h2
m m m f i
.
1|
I
¦
a :4 4 ;
pgh2 =pgh\ + ^P“l 
u = ^2g(h2 - h l)
• The above expression is for velocity from two pressure measurements and 
the application of the Bernoulli equation.
Pitot Static Tube
• The Pitot static tube combines the tubes and they can then be easily 
connected to a manometer:
• In reality, its diameter is very small and can be ignored i.e. points 1 and 2 are 
considered to be at the same level.
• The holes on the side connected to one side of a manometer, while the central 
hole connects to the other side of the manometer.
• Using the theory of the manometer
PA = P\ + P z(x - h) + PmanSh 
P B = P2 +PSX 
P a = P b
P i + P 8 X = P \ + p g ( x - h ) + P mang h
We know that,
1 2
P2 ~ P \ f 1
giving
P \ + hs ( P m a n - p ) = P \
m
W 1
\2gh(pm - p ) •
• Advantages of Pitot tube:
o Simple to use (and analyse) 
o Gives velocities (not discharge) 
o May block easily as the holes are small
Venturi Meter
• The Venturi meter is a device for measuring discharge in a pipe.
• It is a rapidly converging section which increases the velocity of flow and 
hence reduces the pressure.lt then returns to the original dimensions of the 
pipe by a gently diverging 'diffuser' section.
Page 4


Flow Measurement 
Flow measurement is the chapter in Fluid mechanics which deals with the 
application of Bernoulli equation applicable to many situations, not just the pipe 
flow. It consists of various measurement apparatus such as Venturimeter, Orifice 
meter, Pitot Tube, etc. and its application to flow measurement from tanks, within 
pipes as well as in open channels.
Flow measurement is the quantification of bulk fluid movement. Flow can be 
measured in a variety of ways. Positive displacement flow meters accumulate of a 
fixed volume of fluid and then count the number of times the volume is filled to 
measure flow.
Some flow measuring instruments are given as:
Pitot Tube
• The Pitot tube is a simple velocity measuring device.
• Uniform velocity flow hitting a solid blunt body, has streamlines similar to 
this: •
• Some move to the left and some to the right. The centre one hits the blunt 
body and stops.
• At this point (2) velocity is zero The fluid does not move at this one point. This 
point is known as the stagnation point.
• Using the Bernoulli equation we can calculate the pressure at this point.
• Along the central streamline at 1: velocity ui, pressure pi
° At the stagnation point of: U 2 = 0. (Also z -i = z2 )
E l + ! ±
P i
PQ 2
P 9
1 2
P i = P i + ----- u \
1 1 2 9 1
Note Point: The blunt body does not have to be a solid. It could be a static column 
of fluid, this feature is used measure the flow velocity.
• Two piezometers, one as normal and one as a Pitot tube within the pipe can 
be used such as
r mz mm w m
h 1
w m m m A
L
h2
m m m f i
.
1|
I
¦
a :4 4 ;
pgh2 =pgh\ + ^P“l 
u = ^2g(h2 - h l)
• The above expression is for velocity from two pressure measurements and 
the application of the Bernoulli equation.
Pitot Static Tube
• The Pitot static tube combines the tubes and they can then be easily 
connected to a manometer:
• In reality, its diameter is very small and can be ignored i.e. points 1 and 2 are 
considered to be at the same level.
• The holes on the side connected to one side of a manometer, while the central 
hole connects to the other side of the manometer.
• Using the theory of the manometer
PA = P\ + P z(x - h) + PmanSh 
P B = P2 +PSX 
P a = P b
P i + P 8 X = P \ + p g ( x - h ) + P mang h
We know that,
1 2
P2 ~ P \ f 1
giving
P \ + hs ( P m a n - p ) = P \
m
W 1
\2gh(pm - p ) •
• Advantages of Pitot tube:
o Simple to use (and analyse) 
o Gives velocities (not discharge) 
o May block easily as the holes are small
Venturi Meter
• The Venturi meter is a device for measuring discharge in a pipe.
• It is a rapidly converging section which increases the velocity of flow and 
hence reduces the pressure.lt then returns to the original dimensions of the 
pipe by a gently diverging 'diffuser' section.
about 6°
Using Bernoulli along the streamline from point 1 to point 2,
2 2 
P\ u\ P2 u2
— + — + Zi = — + — + z7
pg 2g Pg 2g
By continuity,
Q = U\A\ = u2A2
„ ul A l 
u 2 ~ —
Substituting and rearranging gives
P \~P 2
Pg
h z i - z 2 =-
u \
'Ig
" \
I
1
___ 1
2 g
----- 1
C M in
l
U ] = A
A] - A 2
Actual discharge takes into account the losses due to friction, we include a 
coefficient of discharge (Cd=0.9)
Page 5


Flow Measurement 
Flow measurement is the chapter in Fluid mechanics which deals with the 
application of Bernoulli equation applicable to many situations, not just the pipe 
flow. It consists of various measurement apparatus such as Venturimeter, Orifice 
meter, Pitot Tube, etc. and its application to flow measurement from tanks, within 
pipes as well as in open channels.
Flow measurement is the quantification of bulk fluid movement. Flow can be 
measured in a variety of ways. Positive displacement flow meters accumulate of a 
fixed volume of fluid and then count the number of times the volume is filled to 
measure flow.
Some flow measuring instruments are given as:
Pitot Tube
• The Pitot tube is a simple velocity measuring device.
• Uniform velocity flow hitting a solid blunt body, has streamlines similar to 
this: •
• Some move to the left and some to the right. The centre one hits the blunt 
body and stops.
• At this point (2) velocity is zero The fluid does not move at this one point. This 
point is known as the stagnation point.
• Using the Bernoulli equation we can calculate the pressure at this point.
• Along the central streamline at 1: velocity ui, pressure pi
° At the stagnation point of: U 2 = 0. (Also z -i = z2 )
E l + ! ±
P i
PQ 2
P 9
1 2
P i = P i + ----- u \
1 1 2 9 1
Note Point: The blunt body does not have to be a solid. It could be a static column 
of fluid, this feature is used measure the flow velocity.
• Two piezometers, one as normal and one as a Pitot tube within the pipe can 
be used such as
r mz mm w m
h 1
w m m m A
L
h2
m m m f i
.
1|
I
¦
a :4 4 ;
pgh2 =pgh\ + ^P“l 
u = ^2g(h2 - h l)
• The above expression is for velocity from two pressure measurements and 
the application of the Bernoulli equation.
Pitot Static Tube
• The Pitot static tube combines the tubes and they can then be easily 
connected to a manometer:
• In reality, its diameter is very small and can be ignored i.e. points 1 and 2 are 
considered to be at the same level.
• The holes on the side connected to one side of a manometer, while the central 
hole connects to the other side of the manometer.
• Using the theory of the manometer
PA = P\ + P z(x - h) + PmanSh 
P B = P2 +PSX 
P a = P b
P i + P 8 X = P \ + p g ( x - h ) + P mang h
We know that,
1 2
P2 ~ P \ f 1
giving
P \ + hs ( P m a n - p ) = P \
m
W 1
\2gh(pm - p ) •
• Advantages of Pitot tube:
o Simple to use (and analyse) 
o Gives velocities (not discharge) 
o May block easily as the holes are small
Venturi Meter
• The Venturi meter is a device for measuring discharge in a pipe.
• It is a rapidly converging section which increases the velocity of flow and 
hence reduces the pressure.lt then returns to the original dimensions of the 
pipe by a gently diverging 'diffuser' section.
about 6°
Using Bernoulli along the streamline from point 1 to point 2,
2 2 
P\ u\ P2 u2
— + — + Zi = — + — + z7
pg 2g Pg 2g
By continuity,
Q = U\A\ = u2A2
„ ul A l 
u 2 ~ —
Substituting and rearranging gives
P \~P 2
Pg
h z i - z 2 =-
u \
'Ig
" \
I
1
___ 1
2 g
----- 1
C M in
l
U ] = A
A] - A 2
Actual discharge takes into account the losses due to friction, we include a 
coefficient of discharge (Cd=0.9)
Qideal ~ u\^ \
Qactual ~ ^dQideal ~ ^ d u 1^1
Qactual = Cd A \ A2
1
• In terms of the manometer readings,
Pi + PgZ\ =P2+ Pmangh + Pg(z2 “ h)
Giving,
Qactual = Cd A 1A2
I 4-4
• This expression does not include any elevation terms, (zl or z2)
• When used with a manometer The Venturimeter can be used without knowing 
its angle
Venturimeter Design Note Point:
• The diffuser assures a gradual and steady deceleration after the throat. So 
that pressure rises to something near that before the meter.
• The angle of the diffuser is usually between 6 and 8 degrees.
• Wider and the flow might separate from the walls increasing energy loss.
• If the angle is less the meter becomes very long and pressure losses again 
become significant.
• The efficiency of the diffuser of increasing pressure back to the original is 
rarely greater than 80%.
• Care must be taken when connecting the manometer so that no burrs are 
present.
Orifice meter
• Orifice meter is a device used for measuring the rate of flow of a fluid flowing 
through a pipe which works on the same principle as that of venturimeter.
• Setup for Orifice meter consists of a flat circular plate which has a circular 
hole, in concentric with the pipe which is called orifice.
• The diameter of orifice is generally 0.5 times the diameter of the pipe (D), 
although it may vary from 0.4 to 0.8 times the pipe diameter.