1. MECH 373 Instrumentation and Measurements
Lecture 22
Systems for Measuring Fluid Rate (Chapter 10)
• Variable-Area Flowmeters

2. Measurement Systems
• In engineering experiments and in process plants, we often need to know the quantity of a fluid flowing through a conduit.

3. Technical Basis on Fluid Systems

4. Technical Basis on Fluid Systems

5. Technical Basis on Fluid Systems

6. Systems for Measuring Fluid Flow Rate
Variable-Area Flowmeters
• A variable-area flowmeter is a meter that measures fluid flow by allowing the cross sectional area of the device to vary in response to the flow, causing some measurable effect that indicates the rate.
• This class of flowmeters consists of devices in which the flow area of the meter varies with flow rate and the value of the flow rate is determined by sensing the position of the component causing the area change.
• The most common of these devices is known as the rotameter.
Rotameter
• The rotameter consists of a weighted object called a float, which is free to move, within a vertical tube. Flow entering from the bottom of the tube passes over the float as shown below:
A variable-area flowmeter is a flowmeter that measures fluid flow by allowing the cross sectional area of the device to vary in response to the flow, causing some measurable effect that indicates the rate.

7. Systems for Measuring Fluid Flow Rate
• The principle of the device is based on the balance between the drag force, the weight and buoyancy forces acting on the float in the moving fluid.
• In operation, the float rises to some position within the tube at which the force balance exists. The height of this position increases with flow velocity and, hence, the flow rate.
• The force balance is:
where FD is the drag force caused by the upward-moving fluid, FB is the buoyant force acting on the fluid, and FW is the weight of the float. The buoyant force is equal to the weight of the displaced fluid:
where, ∀ is the float volume, is the density of the flowing fluid, and g is the acceleration due to gravity.
• The weight is given by:
where, is the density of the float.

8. Systems for Measuring Fluid Flow Rate
• The drag force can be described by the drag coefficient:
where CD is the drag coefficient, Afr is the frontal area of the float (in the direction of the flow), and Vref is a reference fluid velocity. In this case, we use Va, the velocity in the annular area between the float and the tapered tube, as Vref.
• Substituting:
• Solving for Va, we obtain
For gases, , so

9. Systems for Measuring Fluid Flow Rate
• The float can be designed such that CD is approximately independent of the float position.
• Since the volume flow rate is:
• Va is constant, the flow rate is proportional to the annular area, Aa.
• It is possible to design the rotameter so that the annular area is a linear function of the float vertical position y. Hence, a measure of the float vertical position is a linear function of the flow rate.
• Although it is possible to use devices that sense float position, most rotameters are not used for remote sensing of flow but are instead read visually and used to check or adjust the fluid flow rate.
• Rotatmeters have the advantages of being easy to read, having a low pressure drop, and having a scale that is linear with flow.
• Most rotameteres must be mounted with the axis vertical, but there are rotameters that can be installed in any orientation and that use a spring instead of the weight of the float to counter the fluid drag force.

10. Systems for Measuring Fluid Flow Rate
• While it is not common to have a sensor for remote sensing of flow rate, it is common in the process industries to have a sensing switch that will trip an alarm if the flow exceeds some system limit.
• The accuracy of higher-quality rotameters can be better than ±2% of full scale, but many are used to give a general indication of flow and are accurate only to the order of ±10%.
• Rotameters are usually calibrated to produce the best accuracy for a particular application.
• To avoid a new calibration, a rotameter can sometimes be calibrated for one fluid and used to measure the flow of another fluid or the same fluid at another temperature or pressure. A simple method to permit use with another fluid is based on the above equations.

11. MECH 373 Instrumentation and Measurements
Course Review
Youmin Zhang
Phone: x5741, Office Location: EV 4-109
Course Website: Access from your “My Concordia” portal

12. Course Outline 1. Introduction, Chapter 1 [1.1]
• course objective and requirements; why measurement systems,
experimental design
2. General Characteristics of Measurement Systems, Chapter 2 [2.1, 2.2, 2.3]
• components
• instrumentation
• error – systematic & random, accuracy, precision, sensitivity
• calibration, traceability of standards
• dynamic measurement systems – response, damping, etc
3. Measurement Systems with Electrical Signals, Chapter 3 [3.1, 3.2 (3.2.1, 3.2.3, 3.2.4), 3.3]
• sensors, amplification, attenuation, filtering
• measurement instruments
• sensor principles and characteristics
4. Computer-based Data Acquisition Systems, Chapter 4 [4.1, 4.2, 4.3 (4.3.1, 4.3.2, 4.3.4), 4.4]
• system components – principles of A/D & D/A conversion
1. Definition and classification of dynamic systems (chapter 1)
Lumped/distributed, continuous-time/discrete-time, linear/nonlinear systems, quantization and superposition property
2. Translational mechanical systems (chapter 2)
Variables, absolute and relative displacements, spring and damper laws, free-body diagrams, Newton’s Laws, energy and power, series/parallel connections
3. Standard forms for system models (chapter 3)
Input-output and state variable equations, matrix formulation
4. Block diagrams and computer simulation with Matlab/Simulink (chapter 4)
Basics on using Matlab/Simulink for system modeling, simulation and analysis
5. Rotational mechanical systems (chapter 5)
Variables, absolute and relative angular displacements, spring and damper laws, free body diagrams, moment of inertia, Newton-Euler’s Law, lever and gears
6. Electrical systems (chapter 6)
Variables, element laws for resistor, capacitor and inductor, energy and power, open and short circuits, Kirchhoff’s Laws (current and voltage), resistive circuits, series/parallel connections, impedance, operational amplifiers
7. Analysis and solution techniques for linear systems (chapters 7 and 8)
Laplace transform and its properties, transfer function, natural and forced responses of first-order (emphasis on circuits) and second-order (emphasis on translational/ rotational) systems, transient and steady-state responses, frequency response.
8. Developing a linear model (chapter 9)
Linearization of nonlinear models and linear representation of nonlinear components, computer simulation of nonlinear and linearized systems
9. Electromechanical systems (chapter 10)
Resistive coupling and the voltage divider, coupling by a magnetic field: Laplace force and Faraday’s law for induced voltages, devices coupled by magnetic fields: microphone, galvanometer and DC motor
10. Thermal and fluid systems (chapters 11, 12)
Thermal and fluid capacitances, resistances and sources, 1st Law of Thermodynamics, conservation of mass, system dynamic models

13. Course Outline
5. Sampling and Analysis of Time-Varying Signals, Chapter 5 [5.1, 5.2, 5.3]
• characteristics of time-varying signals
• sampling rate considerations
• filtering
6. Statistical Analysis of Experimental Data, Chapter 6 [6.1, 6.2, 6.3 (6.3.2), 6.4 (6.4.1), 6.5, 6.6 (6.6.1, 6.6.2, 6.6.3, 6.6.4)]
• noises
• experimental considerations
7 Experimental Uncertainty Analysis, Chapter 7 [7.1, 7.2, 7.3, 7.4, 7.7]
• propagation of uncertainty
• uncertainty analysis
8. Sensor Systems for Engineering Applications, [8.1.1, 8.2.1, 8.3.1, 8.5.1, 8.5.4, 8.6.1, 9.1.2, 9.2.1, , ]
• measurement of various parameters of interest to engineers, e.g.
displacement, velocity, temperature, pressure, vibration, stress, flow rate
etc.
1. Definition and classification of dynamic systems (chapter 1)
Lumped/distributed, continuous-time/discrete-time, linear/nonlinear systems, quantization and superposition property
2. Translational mechanical systems (chapter 2)
Variables, absolute and relative displacements, spring and damper laws, free-body diagrams, Newton’s Laws, energy and power, series/parallel connections
3. Standard forms for system models (chapter 3)
Input-output and state variable equations, matrix formulation
4. Block diagrams and computer simulation with Matlab/Simulink (chapter 4)
Basics on using Matlab/Simulink for system modeling, simulation and analysis
5. Rotational mechanical systems (chapter 5)
Variables, absolute and relative angular displacements, spring and damper laws, free body diagrams, moment of inertia, Newton-Euler’s Law, lever and gears
6. Electrical systems (chapter 6)
Variables, element laws for resistor, capacitor and inductor, energy and power, open and short circuits, Kirchhoff’s Laws (current and voltage), resistive circuits, series/parallel connections, impedance, operational amplifiers
7. Analysis and solution techniques for linear systems (chapters 7 and 8)
Laplace transform and its properties, transfer function, natural and forced responses of first-order (emphasis on circuits) and second-order (emphasis on translational/ rotational) systems, transient and steady-state responses, frequency response.
8. Developing a linear model (chapter 9)
Linearization of nonlinear models and linear representation of nonlinear components, computer simulation of nonlinear and linearized systems
9. Electromechanical systems (chapter 10)
Resistive coupling and the voltage divider, coupling by a magnetic field: Laplace force and Faraday’s law for induced voltages, devices coupled by magnetic fields: microphone, galvanometer and DC motor
10. Thermal and fluid systems (chapters 11, 12)
Thermal and fluid capacitances, resistances and sources, 1st Law of Thermodynamics, conservation of mass, system dynamic models

14. Course Objective / Requirement
Objective: Introduce the fundamental principles that need to be followed when setting up a measurement experiment. Develop a basic understanding of measurement systems and its role in engineering. Learn how to analyze experimental data.
Requirements:
Quizzes (two): 10%
Midterm: %
Laboratories: %
Final exam: %
Need to pass (50% marks) the Laboratory

15. MECH 373 Instrumentation and Measurement
Lecture 1
(Course Website: Access from your “My Concordia” portal)
Introduction:
Introduction to measurement systems

16. MECH 373 Instrumentation and Measurement
Lecture 2
(Course Website: Access from your “My Concordia” portal)
General Characteristics of Measurement Systems (Chapter 2)
• Dealing with error
– Error reduction techniques
– Standards
– Calibration
Next lecture:
• Dynamic measurements
– Zero order, first order, second order systems
– Time constant, response time, rise time, settling time
– Frequency response
• Experimental design

17. MECH 373 Instrumentation and Measurement
Lecture 3
(Course Website: Access from your “My Concordia” portal)
General Characteristics of Measurement Systems (Chapter 2)
• Dynamic measurements
– Zero order, first order, second order systems
– Time constant, response time, rise time, settling time
– Frequency response
• Experimental design

18. MECH 373 Instrumentation and Measurements
Lecture 4
(Course Website: Access from your “My Concordia” portal)
Measurement Systems with Electrical Signals (Chapter 3)
• Electrical signal measurement systems
• Signal conditioners
Amplification
Attenuation
Filtering

19. MECH 373 Instrumentation and Measurements
Lecture 5
(Course Website: Access from your “My Concordia” portal)
Measurement Systems with Electrical Signals (Chapter 3)
• Electrical signal measurement systems
• Signal conditioners
Amplification
Attenuation
Filtering

20. MECH 373 Instrumentation and Measurements
Lecture 6
(Course Website: Access from your “My Concordia” portal)
Measurement Systems with Electrical Signals (Chapter 3)
• Electrical signal measurement systems
• Signal conditioners
Filtering
Indicating and recording devices

21. MECH 373 Instrumentation and Measurements
Lecture 7
(Course Website: Access from your “My Concordia” portal)
Computerized Data-Acquisition Systems
(Chapter 4)
• Computer systems
• Representing numbers in computer systems

22. MECH 373 Instrumentation and Measurements
Lecture 7
(Course Website: Access from your “My Concordia” portal)
Computerized Data-Acquisition Systems
(Chapter 4)
• Data-acquisition components

23. MECH 373 Instrumentation and Measurements
Lecture 8
(Course Website: Access from your “My Concordia” portal)
Computerized Data-Acquisition Systems
(Chapter 4)
• Data-acquisition components
multiplexers
A/D converters
D/A converters

24. MECH 373 Instrumentation and Measurements
Lecture 9
(Course Website: Access from your “My Concordia” portal)
Discrete Sampling & Analysis of Time-Varying Signals (Chapter 5)
• Sampling-Rate Theorem
Sampling
Nyquist frequency
Aliasing

25. MECH 373 Instrumentation and Measurements
Lecture 10
Discrete Sampling & Analysis of Time-Varying Signals (Chapter 5)
• Sampling-Rate Theorem (review)
• Spectral Analysis of Time-Varying Signal
• Spectral Analysis uisng the Fourier Transform

26. MECH 373 Instrumentation and Measurements
Lecture 11
Discrete Sampling & Analysis of Time-Varying Signals (Chapter 5)
• Sampling-Rate Theorem (review)
• Spectral Analysis of Time-Varying Signal
• Spectral Analysis uisng the Fourier Transform

27. MECH 373 Instrumentation and Measurements
Lecture 12
Statistical Analysis of Experimental Data (Chapter 6)
• Introduction
• General Concepts and Definitions
• Probability

28. MECH 373 Instrumentation and Measurements
Lecture 13
Statistical Analysis of Experimental Data (Chapter 6)
• Introduction
• General Concepts and Definitions
• Probability
• Probability Distribution Function

29. MECH 373 Instrumentation and Measurements
Lecture 14
Statistical Analysis of Experimental Data (Chapter 6)
• Introduction
• General Concepts and Definitions
• Probability
• Probability Distribution Function
• Parameter Estimation

30. MECH 373 Instrumentation and Measurements
Lecture 15
Statistical Analysis of Experimental Data (Chapter 6)
• Introduction
• General Concepts and Definitions
• Probability
• Probability Distribution Function
• Parameter Estimation
• Criterion for Rejecting Questionable Data Points
• Correlation of Experimental Data
• Least-Squares Linear Fit
• Outliers in x-y Data Sets

31. MECH 373 Instrumentation and Measurements
Lecture 16
Experimental Uncertainty Analysis (Chapter 7)
• Introduction
• Types of Errors
• Propagation of Uncertainties

32. MECH 373 Instrumentation and Measurements
Lecture 17
Experimental Uncertainty Analysis (Chapter 7)
• Introduction
• Types of Errors
• Propagation of Uncertainties
• Consideration of Systematic and Random
Components of Uncertainty
• Sources of Elemental Error
• Step-by-Step Procedure for Analysis

33. MECH 373 Instrumentation and Measurements
Lecture 18
Measurement of Solid-Mechanical Quantities (Chapter 8)
• Measuring Strain
• Measuring Displacement
• Measuring Linear Velocity
• Measuring Accepleration and Vibaration
• Measuring Force

34. MECH 373 Instrumentation and Measurements
Lecture 19
Measurement of Solid-Mechanical Quantities (Chapter 8)
• Measuring Strain
• Measuring Displacement
• Measuring Linear Velocity
• Measuring Accepleration and Vibaration
• Measuring Force

35. MECH 373 Instrumentation and Measurements
Lecture 20
Measuring Pressure and Temperature (Chapter 9)
• Measuring Pressure
• Measuring Temperature

36. MECH 373 Instrumentation and Measurements
Lecture 21
Measuring Pressure and Temperature (Chapter 9)
• Measuring Pressure
• Measuring Temperature

37. MECH 373 Instrumentation and Measurements
Lecture 22
Systems for Measuring Fluid Rate (Chapter 10)
• Variable-Area Flowmeters

38. MECH 373 Instrumentation and Measurements
Final Exam:
MECH 373/2 X, 12/5/2007, 14:00-17:00, H407
Office hours before final exam:
29/11/07 (Thursday)  13:00-15:00, EV 4-109
   30/12/07 (Friday) :00-15:00, EV 4-109
   03/12/07 (Monday) 10:00-12:00, 13:00-15:00, EV 4-109
    4/12/07 (Tuesday) :00-16:00, EV 4-109
16:15-17:30, H-620
Further office hours can be scheduled by appointment