1. S-108.3011 Sensors and Measurement Methods
Flow rate measurement
S Sensors and Measurement Methods

2. Why is flow rate measurement needed?
Provides knowledge required in industry and municipal engineering
Knowing momentary flow rate of gases and liquids
Essential for process control, optimization and security
Knowing the time integral of a flow rate which is the amount passing through
Important to balance calculations in facilities and subprojects
Flow rate measurement

3. Basic concepts of fluid mechanics
Flowing can be divided in several different ways
Frictionless (ideal fluid) and frictioned flow
Laminar and turbulent
Compressible and incompressible
Important properties of the measured medium:
viscosity, temperature, pressure, corrosiveness, solid particles
Flow rate measurement

4. Basic concepts of fluid mechanics
Flow rate 𝑞= 𝑑𝑥 𝑑𝑡
Volume flow rate 𝑞 𝑣 =𝑞∙𝐴= 𝑑𝑉 𝑑𝑡
Mass flow rate 𝑞 𝑚 =𝜌 𝑞 𝑣 = 𝑑𝑚 𝑑𝑡
Conservation of energy applied to fluid mechanics is called Bernoulli’s principle:
𝜌𝑔ℎ+𝑝+ 1 2 𝜌 𝑣 2 =constant
Volume flow rate continuity:
A1v1 = A2v2
Wing of an airplane
Flow rate measurement

5. Basic concepts of fluid mechanics
Viscosity 𝜇 represents the internal friction of the material which is generated by velocity gradients in the observed system
Force maintaining the velocity gradient 𝑓=𝜇𝐴 𝑑𝑣 𝑑𝑥
𝐴 = area of the intersecting layers 𝑑𝑣 𝑑𝑥 = velocity gradient
SI unit of the viscosity Ns/m2 = Pa·s
Small viscosity – well running material
E.g. viscosity of water: 1.0 mPa·s, lubricating oil: 1000–3000 mPa·s
Flow rate measurement

6. Basic concepts of fluid mechanics
Laminar flow
Particles move parallel
Slower movement on the sides
Profile of the flow rate
Turbulent flow
Turbulence in the flowing material
Disturbs several measuring instruments
Flow rate measurement

7. Basic concepts of fluid mechanics
Reynolds number = inertial force of mass / viscous force
Re= 𝜌 𝑣 𝑠 2 𝐿 𝜇 𝑣 𝑠 𝐿 2 = 𝜌 𝑣 𝑠 𝐿 𝜇
𝑣 𝑠 average flow rate
𝐿 specific length of the flow e.g. diameter of a circular tube
𝜇 viscosity of the flow medium (=friction)
𝜌 density of the flow medium
With small Re the flow is laminar
The transition from laminar to turbulent flow is indicated with a critical Re
Recrit depends on the flow configuration. In a tube, with circular cross section, Recrit = 2300
Flow rate measurement

8. Meters for pressure difference
Most common type of flow rate meters
Very suitable for measuring the flow of liquids, gases and steams
Can be divided into two classes:
Meters based on throttling device
Orifice plate
Flow nozzle
Venturi tube
Meters based on stagnation pressure
Pitot tube
Target flow measurement
Flow rate measurement

9. Throttling device Not wanted quantity! Measured
Pr – decrease in total pressure
Not wanted
quantity!
Measured
Flow rate measurement

10. Throttling device
Bernoulli’s principle: 𝑝 𝜌 𝑣 1 2 = 𝑝 𝜌 𝑣 2 2
Continuity of the flow rate: 𝑞 𝑣 = 1 4 𝜋 𝐷 2 𝑣 1 = 1 4 𝜋 𝑑 2 𝑣 2
⇒ 𝑣 1 = 2∆𝑝 𝜌 𝐷 𝑑 4 −1
𝑞 𝑣 = 1 4 𝜋 𝐷 ∆𝑝 𝜌 𝐷 𝑑 4 −1 =𝜋 𝐸𝐷 2 𝛽 2 ∆𝑝 8𝜌 ,
where 𝐸= 1 1− 𝛽 4 is approaching factor, and 𝛽= 𝑑 𝐷
Flow rate measurement

11. Throttling devices Orifice Nozzle The most common throttling device
inexpensive, plenty of experince using it in practice
Can be manufactured from several different materials
Also for corrosive materials
Not suitable for fluids with large impurities
Risk of blocking the flow
Nozzle
Advantages compared to orifice:
Smaller pr
Lower risk of blocking the flow
Flow rate measurement

12. Venturi tube
Smaller decrease in total pressure than in the case of orifices or nozzles
Large size
Entry cone taper 30°, exit cone taper 5°
Often a shortened version is used (”Dall tube”)
expensive
Flow rate measurement

13. V-cone sensor Most recent type, more compact than a venturi tube
Flow rate measurement

14. Stagnation pressure meters
An obstacle, which has one end closed, is placed inside a linepipe
Inside the tube shaped obstacle, there is a flow rate 𝑣 2 =0
Dynamic pressure i.e. stagnation pressure: 𝑝 2 = 𝑝 𝜌 𝑣
Flow rate: 𝑣 1 = 2 𝜌 ∆𝑝
Flow rate measurement

15. Pitot tube Measures both dynamic and static pressure caused by a flow
In industry, it is used to measure pure liquids and gases. It can also be used to measure the air flow rate of airplanes
Flow rate measurement

16. Target flow measurement
A flow applies a force to a target and this force is measured
Force applied to target: 𝐹=𝑝𝐴= 1 2 𝑘𝐴𝜌 𝑣 2
𝑘 is the shape factor of the target, 𝐴 is the area of the target
Flows going either way can be measured
On the other hand, it is sensitive to vibrations and shocks
Most suitable for measuring pure liquids and gases
Inaccuracy about ± 3 %.
Flow rate measurement

17. Magnetic flow rate measurement
An induced voltage 𝐸 is created in a magnetic field due to a conductive liquid moving
If the electrodes, magnetic field and the flow channel are perpendicular:
𝐸=𝑣𝐵𝐷
Voltage is small (mV), protection against interference is important
Due to electrochemical potentials an alternating magnetic field is used
Independent on the density, viscosity, temperature and flow rate profile of the measured liquid
Does not contain moving parts → durable
Does not disturb the flow
Expensive
Suitable only for conductive liquids: conductivity > 5 mS/cm
Electrodes on the walls
Flow rate measurement

18. Ultrasound: transit time measurement
Transit time difference is measured (both forward current and reversed current)
Flow rate: 𝑣= 𝑐 2 ∆𝑡 2𝑙 cos 𝛼
The method is suitable for several kinds of flows (even gases), requiring that the speed of sound in this medium is known
Temperature dependency
Can be built completely outside the channel
Flow rate measurement

19. Transit time measurement
Multiplexer channel measurement allows to measure average flow rate during the whole flow channel
If the diameter of the flow channel is small, it is difficult to get an accurate result → an arrangement is used, where the ultrasound is parallel with the flow
Flow rate measurement

20. Applying Doppler effect
Ultrasound is reflected from bubbles and impurities in the flow
Usually less accurate compared to transit time measurement
Impurities
Flow rate measurement

21. Vortex flowmeter based on vibration
Fixed obstacle causes periodic vortexes
Occurrence frequency of the vortexes is directly proportional to flow rate (Reynolds number)
Frequency is measured with e.g. piezoelectric force sensor or ultrasound
Flow rate measurement

22. Vortex flowmeter
Regular vortexes may form if Reynolds number is 300 –
Frequency: 𝑓= 𝑆𝑣 𝑑 , where 𝑆 = Strouhal number, 𝑑 = width of the obstacle
Reynolds: inertia/friction, Strouhal: frequency/inertia
Accuracy is deteriorated for example by contamination, air bubbles, solid impurity particles and change in viscosity
Air bubbles in liquid deteriorate the signal-to-noise ratio of detecting
Suitable also for measuring low flow rates with inaccuracy even below 1%
Using a narrow obstacle causes a small pressure loss
Flow rate measurement

23. Measuring mass flow rate
Mass flow rate can be measured with a volume flow rate meter:
𝑚=𝑉𝜌
When a constant density is assumed
If the density of the measured medium is not constant or it contains air bubbles, the mass flow rate measured with a volume flow rate meter is not reliable!
Flow rate measurement

24. Coriolis flow meter Directly measures mass flow rate
One or two vibrating tubes at inlet and outlet side. Tubes are U-, S-, or W-shaped
As the flow goes through the vibrating tube, the tube starts to bend and coriolis force changes the direction at the inlet side
Flow rate measurement

25. Coriolis flow meter Bending depends on the mass flow rate
Bending is measured with location sensors
Analysis on frequency, phase difference or the amplitude of the flow tube vibration frequency
Both velocity and density are got independently!
Velocity from the phase difference
Density from the frequency
Vibration properties are temperature dependent
Monitoring temperature during the process
Temperature corrections can easily be made
Flow rate measurement

26. Thermic methods Based on a cooling effect of a flow
A thin heated wire or film loses part of its heat to a flow
Temperature is measured resistively and another sensor measures the temperature of the flow
Low response time and high sensitivity
Suitable for measuring slow flows
Impurities in a flow damage wires
Applied to gas flow measurements
Flow rate measurement

27. Cross correlation flow meter
Based on measuring the transition time of particles flowing in a channel between two sensors
Measuring quantity may be e.g. optical or ultrasound
Does not disturb the flow at all!
Other quantities are possible too
Suitable for measuring solid mediums because there is no need to place additional obstacles to the flowing channel
Flow rate measurement

28. About the accuracy of flow rate measurements
Effect of the installation point
A flow stabilizes after a long and straigth tube
Changes
Density (non-uniform material), velocity distribution
Electric conductivity
Temperature distribution (thermal expansion of the tube)
Flow circumstances (roughness of the surface, critical dimensions of the pressure difference instrument)
Measured material is always different compared to material used in calibration
Pressure variation must be considered in gas measurements
Flow rate measurement

29. Flow rate meters with changing aperture
Revision: aperture size of the throttling device is constant in pressure difference meters; flow rate is determined with the pressure difference between the entry and exit side
In meters with changing aperture, the pressure stays roughly the same. The flow rate determines the aperture size
Flow rate measurement

30. Rotameter Glass or metal
Scale on the wall of a glass tube rotameter, in the case of metal rotatometer scale can be e.g. magnetic
Does not require expensive equipment → inexpensive meter
Suitable for liquids and gases
Also suitable for slow flows
Movement of the float must be attenuated if the flow has much variation
Floating level sensor
Flow rate measurement

31. Rotameter – the shape of the float
The shape of the float strongly affects its propeties:
1. Easy to manufacture → used in small rotameters
2. General float, cone head → very durable
3. For small flows
4. Low sensitivity to viscosity
5. Sensitive to changes in viscosity
→ used as a viscosity sensor when the flow rate is constant
→ scale must be produced to each measured material
Flow rate measurement

32. Volume counters Used in flow rate measurements of liquids
Good accuracy
→ Used to calibrate other flow rate meters
Trivial example: a bucket and a stopwatch
Flow rate measurement

33. Oval wheel flow meter
Oval shaped cogwheels spin due to pressure difference between the entry and the exit side
As the cogwheels spins 180°, a volume V1+V2 of liquid has passed through the meter
On the negative side: sensitive to impurity particles
Error about 0,5 %
Flow rate measurement

34. Mutating disc flow meter
Used as household water flow meters
Pressure difference between the inlet and the exit side forces a circular disc to nutate
A constant volume of liquid passes through the meter during every spin
Flow rate measurement

35. Current meter
A rotor which contains as frictionless as possible bearing. A flow forces the rotor to rotate
The speed of rotation of the rotor is proportional to flow rate
The movement of the current meter is tranferred electrically or mechanically to a counter
Flow rate measurement

36. Turbine meter The most common type of current meters
Specific models for gases and liquids
Error is in the case of liquids about 0,3 %, and gases 1 %
Turbulences may cause an error of several percents
Contamination → suitable only for pure flows
Fast response time → flow rate can change rapidly
Liquid turbine meter (flow straighteners remove turbulences from the flow)
Gas turbine meter
Flow rate measurement

37. Blade wheel counter Commonly used in water measurements
Flow rate is determined from the speed of rotation
Error about 2 %
Flow rate measurement