Sub Module 2.13
Measurement of fluid velocity
Quadrant 2
List of animations/Videos:
1. Basics of pitot tube is
presented http://www.endress.com/eh/home.nsf/contentview/5DF333B975F4E0F7
C1257657004A832C?Open&popup
2. Orifice plate, nozzle and
venturi http://www.endress.com/eh/home.nsf/contentview/68B673520D6DEFCDC
12575D30035EF77?Open&popup
3. http://iom.invensys.com/EN/Pages/Foxboro_MandI_Flow_Coriolis.aspx (flow
measurement)
4. http://iom.invensys.com/EN/Pages/Foxboro_MandI_Flow_Vortex.aspx (vortex flow
meter)
5. Orifice plate basics are discussed in this video
http://www.youtube.com/watch?v=nW421UQa7as
6. Turbine flow meter Vs Oval gear flow meter
http://www.youtube.com/watch?v=EUWsNbOkK9I
7. How to build anemometer
http://www.youtube.com/watch?v=SZpXGPMvJNo
8. Hot wire anemometer
http://www.youtube.com/watch?v=xdQMpHKJKps
9. Working of area velocity sensor is shown
http://www.youtube.com/watch?v=p2t_kZOZvdY
10. Ultrasonic flow measuring principle is revealed
http://www.youtube.com/watch?v=Bx2RnrfLkQg&list=PLLSJ4QFrqwiJKIhi_x4CQkICOUCdxXb
6d&feature=player_detailpage
11. Ultrasonic Doppler velocimetry is demonstrated
http://www.youtube.com/watch?v=9uzavWHQVp8
12. Anemometer – a wiki article is read
http://www.youtube.com/watch?v=JE4kQqyTMVA
Flow meters:
13. Flow measurement by rotameter and turbine meter
http://www.youtube.com/watch?v=EBFAQsZmieU
14. Rotameter working is explained
http://www.youtube.com/watch?v=fbaRWTJ1aTw
15. Inside of a flow meter
http://www.youtube.com/watch?v=XGm9GBKHAnU
Page 1 of 16
16. http://www.youtube.com/watch?feature=player_embedded&v=En2oAhPxagU
(vortex flow meter)
17. Multi viscosity turbine meter animation is shown in this video
http://www.youtube.com/watch?v=S0P8oU9ykc8&list=TLkaCRLzSUNyA
Illustrations:
1. Venturimeter and manometer sketch is provided
http://www.ae.metu.edu.tr/~ae244/docs/FluidMechanics-byJamesFay/2003/Textbook/Nodes/chap04/node13.html
2. Schematic diagram of conventional hot wire anemometer is presented
http://urrg.eng.usm.my/index.php?option=com_content&view=article&id=191:curr
ent-development-of-mems-flow-sensor-&catid=31:articles&Itemid=70
List of questions(FAQ):
Pitot tube:
1. Define the term flow
2. Explain pitot and pitot static tube to measure fluid velocity
3. Explain the effect of compressibility with usual notations
4. Write a short note on pitot tube
5. Explain the operation of pitot tubes.
6. Describe the installation procedure of pitot tubes.
7. List the different methods of flow measurement.
Impact probe:
8. Explain impact probe in supersonic flow
9. Discuss a wedge probe
10. What are the orientation effects in probes
11. Discuss the working of a blunt nose impact probe.
12. Mention the different types of probes used to measure supersonic flow.
13. Discuss the effect of orientation in using probes for supersonic flow.
Hot wire anemometers/Doppler Velocimeter /Area flow meters:
14. Write a short note on hot wire anemometer
15. With a bridge circuit, explain constant temperature (CT) anemometer and explain
the linear representation of its output
16. Explain constant current operation mode of an anemometer
17. How is velocity fluctuations measured in turbulent flows?
18. List the typical specifications of a hot wire anemometer
Page 2 of 16
19. Explain velocity measurement using Doppler velocimeter.
20. Discuss the construction and working of laser Doppler anemometer.
21. What is Laser Doppler Velocity meter? What are the 2 possible ways of operating a
LDV? Explain.
22. Discuss the construction, working and applications of Ultrasonic Doppler Velocity
meter.
23. With the help of schematic diagrams explain the construction and working of
different types of obstruction meters
24. Discuss turbine meter
25. Discuss rotameter and electromagnetic flow meter, stating their construction,
working and limitations.
26. State different quantity meters used for flow measurement. Explain any one of
them.
27. What is orifice plate? What are its different types? What is the difference between
orifice and nozzle?
28. What do you mean by area flow measurement?
29. Describe the working principle of turbine flow meter with a schematic diagram.
30. Describe the working principle of magnetic flow meter with a schematic diagram.
31. Explain the working of ultrasonic flow meters with a suitable sketch.
32. What are flow visualization schemes? Explain them briefly.
Quadrant 3
Wiki links/reference links/web courses of other universities.
1. http://www.efunda.com/designstandards/sensors/hot_wires/hot_wires_intro.cfm
(hotwire anemometer basics)
2. http://www.efunda.com/designstandards/sensors/pitot_tubes/pitot_tubes_intro.cf
m (pitot static tube)
3. http://www.efunda.com/designstandards/sensors/laser_doppler/laser_doppler_intr
o.cfm (laser Doppler)
4. http://www.efunda.com/designstandards/sensors/flowmeters/flowmeter_intro.cfm
(common flow meters)
5. http://www.efunda.com/designstandards/sensors/flowmeters/flowmeter_va.cfm
(variable area flow meter)
6. http://en.wikipedia.org/wiki/Rotameter (rotameter)
7. www.omega.com/prodinfo/rotameters.html (rotameter)
8. http://www.brooksinstrument.com/flow-pressure-level-measurementtechnology/variable-area.html (VA Rotameter)
9. http://www.efunda.com/designstandards/sensors/flowmeters/flowmeter_tbn.cfm
(turbine flow meter)
Page 3 of 16
10. http://iom.invensys.com/EN/Pages/Foxboro_MandI_Flow.aspx (flow measurement)
11. Detailed technical information on different types of rotameters are presented
http://cdn2.us.yokogawa.com/product_TIRotameterEnged4.pdf
12. Different types of floats are presented
http://classes.engineering.wustl.edu/che473/files/rotameters/Rotameter%20lab%2
0manual.pdf
13. Technical information on rotameters
https://www.mathesongas.com/pdfs/products/flowmeter-product-lineoverview.pdf
Quadrant 4
Numerical problems:
Pitot tube:
1. A pitot static tube is used to measure the velocity of an airplane. If the air
temperature and pressure are 10oC and 100 kPa respectively, calculate the airplane
velocity in km/h, if the differential pressure is 300 mm water column.
Solution:
ρ m = density of water = 999.9 kg/m3
T = air temperature = 273 +10 = 283 oC
p = air pressure = 100 x 103 Pa
R g = gas constant = 287 J/kg . K
ρair = p/(R g x T) = 100 x 1000/(287 x 283) =1.231 kg/m3
The pressure difference in terms of head of water = h = 0.3 m
∆p = ρ m g h = 999.9 x 9.8 x 0.3 = 2939.7 Pa
Speed of airplane =V = �2∆p/ ρair = �2 𝑥
2939.7
1.231
= 69.11 m/s =
= 69.11 x 3.6 = 248.8 km/h
2. A pitot static tube is used to measure the velocity of an aircraft. If the air
temperature and pressure are 7 oC and 100 kPa respectively, calculate the
differential pressure in terms of head of water in m, if the aircraft velocity is 300
km/h.
Solution:
ρair = p/(Rg x T) = 100 x 1000/(287 x 280) =1.244 kg/m3
ρm = density of water = 999.8 kg/m3
Speed of airplane =V = �2∆p/ ρair =300 km/h = 83.33 m/s
∆p = V2 x ρ air /2 = ρ m g h
h = V2 x ρ air / (2 x ρ m g) = 83.332 x 1.244 / (2 x 999.8 x 9.8) = 0.44 m
Page 4 of 16
Problem on Orifice plate:
3. Calculate the flow rate of water through a 12 cm pipe with an orifice of 6 cm as
restriction. The orifice is arranged for flange taps and a mercury manometer reads
30 cm Hg at 27 o C. The temperature of flowing water is 33 o C. Assume µ = 0.00052
units.
Solution:
d = orifice diameter = 0.06 m
r = radius of orifice = 0.03 m
D = diameter of pipe = 12 cm
β = d/D = 6/12 = 0.5
A = area of orifice = π x r2 = π x 0.032 = 0.0028 m2
h = manometer reading =0.3 m
E=1
ρ w = density of water = 992 kg/ m3
ρ m = density of mercury = 13490 kg/ m3
Q = flow rate through orifice meter = KA 2 E �2𝑔ℎ(( ρ m / ρ w ) -1)
After substitution and simplification we get
Q = K x 0.024
Re = 4Q ρ w / (π d µ ) = 405.31 x 105 Q
To determine flow coefficient K, assume Re = 5 x 105. Flow coefficient K is
found from standard tables for β = 0.5 and the assumed Re values ie K = 0.626
Now, Q = 0.626 x 0.024 = 0.0148 m3 /s
And Re = 405.31 x 105 x 0.0148 = 5.998 x 105
The Re obtained above is nearer to the assumed value, hence Q = 0.0148 m3 /s
Problem on venturimeter:
4. A horizontal venturimeter with 20 cm inlet and 10 cm throat is used for measuring
the flow of water in a chemical process. The differential pressure between the inlet
and throat is 20 cm when measured using a U-tube manometer. Calculate the
water flow rate if the discharge coefficient for the venturimeter is 0.97. Density of
water is 1000 kg/m3 and specific gravity of mercury is 13.6. Thermal expansion
factor E = 1.
Solution:
r t = throat radius = 5 cm = 0.05 m
r 1 = inlet radius = 10 cm = 0.1 m
A 1 = inlet area = π x r 1 2 = π x 0.12 = 0.0314 m2
A 2 = throat area = π x r t 2 = π x 0.052 = 0.007852 m2
Cd = 0.97
( ρ m / ρ w ) = 13.6
h = 20 cm = 0.2 m
Page 5 of 16
M= A 1 x A 2 / �(𝐴1𝑥𝐴1 − 𝐴2𝑥𝐴2)
Flow rate of water = Q = Cd M �2𝑔ℎ(( ρ m / ρ w ) -1)
After substitution and simplification, Q = 0.056 m3 /s
5. Calculate the diameter of throat of a venturimeter to be used in a horizontal
section of a 10 cm diameter pipe so that reading on the differential U-tube
manometer is 50 cm when the discharge is 20 litres/sec. Assume the discharge
coefficient of the meter as 0.95.
Solution:
Q = flow rate is 20 litres/sec
r 1 = inlet radius = 5 cm =0.05 m
r t = throat radius = ?
h = 50 cm = 0.5 m
Cd = 0.95
Assme ( ρ m / ρ w ) = 13.6
A 1 = inlet area = π x r 1 2 = π x 0.052 m2
Use the procedure given in the previous problem and find A 2 = throat area, and then
throat diameter.
Problem on rotameter:
6. A tapered metering glass tube is used to measure the fluid flow rate. Its internal
diameter at the bottom is 20 mm. The float is made of aluminium with relative
density of 2.7. It has a volume of 500 mm3, an effective diameter of 12 mm and a
vertical range of movement of 210 mm. The included taper angle of tube is 6o and
Cd = 1. Calculate the range of flow of fluid with relative density of 0.8. Also
calculate the fluid flow rate when float is at mid height.
Solution:
Cd = coefficient of discharge = 1
Aann = annular area between float and tube
Suffix 1 indicates lowest position of float
Suffix 2 indicates top position of float
Vfl = volume of float = 500 mm3 =500 x 10-9 m3
ρfl = density of float material = 2.7 units
ρf = density of fluid = 0.8 units
A 1 = area of tube at bottom
rfl = radius of float = 6 mm
Q = flow rate of fluid through tube
Afl = cross sectional area of float = π x 62 mm2 = 36 π x 10-6 m2
Aann 1 = A 1 – Afl = 201 mm2 = 201 x 10-6 m2
Aann 2 = A 2 – Afl
Page 6 of 16
r 2 = radius of tube at top = 10 + 210 tan 3o = 21 mm
Ann 2 = π (r 2 2 –rfl2 ) = 1271.7 mm2 = 1271.7 x 10-6 m2
Q 1 = Cd x Ann 1 �(2𝑔𝑉𝑓𝑙 ( ρfl – ρf)/ (Afl x ρf)) = 9.125 x 10-5 m3 /s
Q 2 = Q 1 Ann 2 / Ann 1 = 57.73 x 10-5 m3 /s
Therefore the flow range is 9.125 x 10-5 m3 /s to 57.73 x 10-5 m3 /s
Flow at mid height = h = 105 mm
rh = radius at mid height = 10 + 105 tan 3o = 15.5 mm
Ann h = Annular area between float and tube at mid height
= π (15.52 – 62 ) = 641.35 x 10-6 m2
Q h = flow rate at mid height = 29.1 x 10-5 m3 /s
7. Suppose that a rotameter uses a cylindrical float 30 mm high and 20 mm in
diameter and of proper density to give density compensation. If the coefficient Cd
is 1 and the maximum inside diameter of the metering tube is 60 mm, what flow
rate can the rotameter accommodate?
Solution:
rfl = radius of float = 10 mm
hfl = height of float = 30 mm
r = radius of tube at the top position 30 mm
Page 7 of 16
Vfl = volume of float = π x 102 x 30 = 9420 mm3 = 9420 x 10-9 m3
Ann = annular area at the top between the float and tube
= π (r2 – rfl2) = π (302 – 102) = 2512 mm2 = 2512 x 10-6 m2
Afl = area of float = π rfl 2 = π x 102 = 314 mm2 = 314 x 10-6 m2
Q = flow rate = Cd x Ann �(2𝑔𝑉𝑓𝑙 ( ρfl – ρf)/ (Afl x ρf))
Assuming suitable values of densities and after substitution and simplification
Q = 2.96 x 10-3 m3 /s
Multiple choice questions (choose the correct answer)
1. The hot wire anemometer is used to measure
a. Gas pressure
b. Liquid flow
c. Velocity of gas
d. Wind pressure
2. A rotameter measures flow rate based on
a. Variable area
b. variable length
c. variable pressure
d. variable temperature
3. A magnetic flow meter functions on the principle of
a. Piezoelectric effect
b. pressure
c. Faradays law
4. Suggest a flow meter to measure flow rate of slurries
a. Magnetic flow meter b. Impeller flow meter c. rotameter
5. Suggest a flow meter to measure the flow rate of petroleum product
a. Magnetic flow meter b. Impeller flow meter c. rotameter
Page 8 of 16
d. Hall effect
6. A pitot static tube measures
a. Static pressure
b. dynamic pressure
d. Difference between total and static pressure
c. total pressure
7. A flow measuring device suitable to find total flow is
a. Turbine flow meter
b. rotameter c. venturimeter
8. An electromagnetic flow meter
a. Should be mounted vertically
c. should be rotated at constant speed
9. Rotameter is a
a. drag force flow meter
c. variable head flow meter
d. orifice plate
b. should be mounted horizontally
d. can be mounted in any position
b. variable area flow meter
d. propeller type flow meter
10. Name the flowmeter which is not an obstruction type
a. a venturimeter
b. a nutating disk flow meter
c. an orifice meter
d. pitot tube
11. Another name for a rotameter is
a. vortex meter
b. turbine flow meter
c. a variable area meter
d. electromagnetic flow meter
12. Which of the following device is a rate meter
a. venturimeter
b. hot wire anemometer
c. current meter
d. nutating disk
13. The local velocity at a point in a channel is measured by
a. current meter
b. vane anemometer
c. flow nozzle
d. pitot static tube
14. A tank having a capacity of 0.05 m3 is filled up with water in 2 seconds. The density of water
is 1000 kg/m3. What is the volume flow rate in m3/s?
a. 0.025
b. 0.05
c. 1.0
d. 1.5
15. A tank having a capacity of 0.05 m3 is filled up with water in 2 seconds. The density of water
is 1000 kg/m3. What is the mass flow rate in kg/s?
a. 25 b. 50 c.75
d. 100
Page 9 of 16
Answer table
1.
2.
3.
4.
5.
6.
7.
c
a
c
a
b
d
a
8. d
9. b
10. b
11. c
12. a
13. d
14. a
15. a
Say True / false
16. A flow meter can be used to measure pressure
17. A rotameter is used to measure fluid flow based on variable area
18. A rotameter needs a narrow tapered tube for flow measurement
19. A Magnetic flow meter functions on the principle of Faradays law
20. A Magnetic flow meter is bidirectional flow meter
21. A Magnetic flow meter can be used to measure flow of petroleum products
22. A impeller flow meter can be used to measure flow of petroleum crude oil
23. Electromagnetic flowmeter cannot be used for electrically non-conducting fluid
24. Anemometry and velocimetry are synonyms
Answer table
16. F
17. T
18. T
19. T
20. T
21. T
22. T
23. T
24. T
Complete the following statements with appropriate words:
25. Obstruction type instruments such as --------and------- are commonly used to measure
flow rate.
26. -------is a rate meter where as -----------is a quantity meter.
27. Pitot static tube senses both the -------- pressure and the ----------static pressure in a
single probe
28. Flow at higher rates is known as -------29. At low Reynolds numbers (below 2000), the flow is dominated by -------- forces.
30. At high Reynolds numbers (above 20000) the flow is dominated by ------- forces.
31. The conventional orifice is a ---------- plate
Page 10 of 16
32. To measure low flow rates ------ is the best choice.
33. Inlet pressure is measured at the --------, and ------------------is determined in the
throat section of the venturi meter.
34. The use of classical venture meter is limited to measure flow of -----------, ---------------liquids and gases
35. Flow nozzles are not recommended for ---------36. Nozzles can be installed in any position, however ------------------orientation is ideal.
37. In the case of variable area flowmeters, either the --------------------- or a ------------- is
used to return the flow element to its rest position when the flow lessens.
38. In rotameter, the float moves -----------------in proportion to the fluid flow rate and
the annular area between the float and the tube wall
Answer table
25. Pitot tube and venturimeter
26. Pitot tube, nutating disk
27. Stagnation, static
28. Turbulence
29. Viscous
30. Inertial
31. Thin circular
32. A differential pressure cell with an
integral orifice
33. Entrance, static pressure
34. Clean, noncorrosive
35. Slurries or dirty fluids
36. Horizontal
37. Gravity, spring
38. Up and down
Assignment questions and solutions
1. What is an orifice plate? Mention its different types
Ans : Orifice plate is a thin metallic plate circular in shape. It is thick enough to
withstand buckling forces due to pressure difference. The material normally used is
corrosion resistant steel.
Types: There are 3 types of orifice plates, namely concentric, eccentric and
segmental type. Concentric type of plate is very widely used. Eccentric and
segmental types are used for measuring flow of fluids containing solids.
2. Briefly describe hot wire anemometers.
Ans: Hot wire anemometers are hot wire resistance transducer wire filaments. These
are used for measurement of flow rates of non-conducting liquids and gases. By
suitably locating this device, in open channels and closed pipes, flow rate can be
measured. The hot wire filament is generally a fine wire of platinum or tungsten, and
is mounted in the flow channel by means of suitable supports. The transducer probe
Page 11 of 16
is located at the center of the pipe with the direction of wire perpendicular to the
direction of flow of fluid.
Hot wire anemometers are normally used in two different modes:
a. Constant current type
b. Constant temperature type.
A typical probe schematic diagram can be found in web resource: nptel.iitm.ac.in/IITMADRAS/Mechanical_Measurements, Sub-module 2.13 (Fig. 110, 111, 114)
3. Present the typical performance figures for an ultrasonic Doppler flow meter.
Ans:
1. Over the flow range 0 to 15 m/s a repeatability of +/- 1 % of full scale
2. For small pipes with well mixed slurries linearity of +/- 2 % for Re > 105
3. Measurements with clamp on meters is possible up to 120 deg C
Questions on flow rate measurement:
4. Explain the construction and working of a rotameter.
Ans: the construction and working of a rotameter are presented below:
Construction: A rotameter consists of a tapered glass tube whose internal diameter
is manufactured to very close limits. The tube is made of borosilicate which is highly
resistant to chemical action and thermal shocks. For high pressure rotameters, glass
window enclosure is provided.
The next important part is a float. It is heavier than the liquid it displaces. Generally
it is made of steel, lead or tantalum. Density of float must be several times greater
than the density of liquid, so that density compensation is automatically provided ie
rotameter reading is not affected by change in density.
Working: Rotameter is mounted vertically. The flow of fluid is allowed in upward
direction. The float floats in fluid. A variable area is formed between the float and
the internal surface of the tube. For a given flow rate, float will assume certain
position at equilibrium. Thus position of float determines flow rate.
As flow occurs upwards through the tube, four different forces act on float:
a. Downward gravitational force
b. Upward buoyant force
c. Pressure force
d. Viscous drag force
For a given flow rate, float assumes a certain position where total upward forces =
total downward forces. The fluid flow rate is proportional to position of float.
Page 12 of 16
5. What are the advantages and limitations of a rotameter?
Advantages:
a. Pressure loss in rotameter is almost constant and small.
b. It cannot be used for corrosive fluid
c. It is reasonably accurate especially at low flow rates.
d. It has a linear scale.
e. It can be compensated for changes in fluid density and viscosity.
f. The measurement range can be altered easily by changing float and tube.
g. Flow of liquid is visible.
Limitations:
a. It should be installed in vertical position only.
b. It is expensive if working pressure and temperature are high
c. Not suitable to measure flow of opaque fluid, since float is not visible
d. Not suitable, when fluid is carrying large percentage of solids in suspension.
e. Since glass tube is used, it is not strong, compared to venture, nozzle and
orifice.
Self answered questions and answers:
1. Illustrate the pitot tube arrangement to measure fluid velocity
Ans: Please refer web resource: nptel.iitm.ac.in/IITMADRAS/Mechanical_Measurements, Sub-module 2.13 (Fig. 98)
2. Discuss the working of a blunt nose impact probe.
Ans: Please refer web resource: nptel.iitm.ac.in/IITMADRAS/Mechanical_Measurements, Sub-module 2.13
3. Mention the different types of probes used to measure supersonic flow.
Ans: Please refer web resource: nptel.iitm.ac.in/IITMADRAS/Mechanical_Measurements, Sub-module 2.13
4. Discuss the effect of orientation in using probes for supersonic flow.
Ans: Please refer web resource: nptel.iitm.ac.in/IIT-MADRAS/Mechanical_Measurements,
Sub-module 2.13
5. Discuss time of flight velocimeter in detail
Ans: Please refer web resource: nptel.iitm.ac.in/IITMADRAS/Mechanical_Measurements, Sub-module 2.13 ( figure 126)
Page 13 of 16
6. Explain in detail ultrasonic mean velocity meter
Ans: Please refer web resource: nptel.iitm.ac.in/IITMADRAS/Mechanical_Measurements, Sub-module 2.13 ( figure 128)
Test your skills:
1. Visit a nearby process industry, and identify the various fluid flow and velocity
measuring devices employed in the process
2. Also, learn how they are calibrated and maintained.
3. Design and fabricate a simple flow measuring device (for example an orifice
plate), and learn how to measure flow rate using it.
4. Identify the following:
(a)
Page 14 of 16
(b)
(c)
Page 15 of 16
(d)
(e)
Page 16 of 16