# ME303: Thermal-Fluid Systems

Unit 2: Measurement of Flow   In order to assess pumping and piping operations, you must know the mass and volumetric flow rates and velocities in the system, which you can infer from the pressure differences and resulting actions upon various sensors.  Some of these methods may seem as crude as watching a weather vane or the motion of a flag in the wind, but they can be essential for monitoring equipment and process performance.

Unit 2 Time Advisory
This unit should take you 13 hours to complete.

☐    Introductory Reading: 1 hour

☐    Subunit 2.1: 5 hours

☐    Subunit 2.2: 5 hours

☐    Subunit 2.3: 1 hour

☐    End of Unit Self-Assessment: 1 hour

Unit2 Learning Outcomes
Upon successful completion of this unit, the student will be able to:

• Apply and understand Bernoulli’s principle to fluid flow situations.
• Apply pressure measurements and explain how they relate to fluid flow.
• Describe the advantages and disadvantages of several methods for estimating fluid flow and fluid velocity.

• Reading: Omega’s Transactions Vol. 4 “A Flow Measurement Orientation” Link: Omega’s Transactions Vol. 4 “A Flow Measurement Orientation” (HTML)

Instructions: Read the brief section to appreciate the history and progression of flow measurements.  When did Daniel Bernoulli publish his work on hydrodynamics?

• Reading: Scribd.com’s Introduction to Instrumentation, Sensors, and Process Control: “Chapter 9: Fluids” Link: Scribd.com’s Introduction to Instrumentation, Sensors, and Process Control:Chapter 9: Fluids” (PDF)

Also available in:

iBooks

Instructions: Read this chapter (pages 129-148) and use it as an overall reference for this entire unit.

Terms of Use: The article above is released under a Creative Commons Attribution-Non-Commercial License 3.0 (HTML).  It is attributed to Scribd.com and the original version can be found here (PDF).

2.1 Inference by Pressure Measurements   2.1.1 Bernoulli’s Equation   - Reading: eFluids: Bicycle Aerodynamics: “Chapter 6: Bernoulli’s Equation” Link: eFluids: Bicycle Aerodynamics: “Chapter 6: Bernoulli’s Equation” (HTML)

Instructions: Read this short section.  Make sure that you understand the restrictions of Bernoulli’s equation.  Ask yourself when Bernoulli’s equation might be useful.  Why do you think that the concept is important for bicycle aerodynamics?  You may read the short section on Pitot tubes in anticipation of section 2.1.4 of this Unit.

• Reading: Cecil Adams’ The Straight Dope: “How Does a Gas Pump Know to Shut Itself Off?” Link: Cecil Adams’ The Straight Dope: “How Does a Gas Pump Know to Shut Itself Off?” (HTML)

Instructions: Skim the article and draw a sketch to convince yourself of how Bernoulli’s principle explains the behavior of gasoline pumps.

2.1.2 Pressure Measurements   - Reading: eFluids: Bicycle Aerodynamics: “Chapter 4: Pressure” Link: eFluids: Bicycle Aerodynamics: “Chapter 4: Pressure” (HTML)

Instructions: As you read this section about pressure in aerodynamics, ask yourself which features would be different for liquids.

• Reading: Georgia State University’s “Pressure Measurement” Link: Georgia State University’s “Pressure Measurement” (HTML)

Instructions: Read the section and play with the fluid pressure calculator.  This section should be a review for you.  As you read, consider the effect that fluid density has upon the calculations.

• Reading: Wikipedia’s “Pressure Measurement” Link: Wikipedia’s “Pressure Measurement” (PDF)

Instructions: Read the material here for a survey of the area.  Pay particular attention to units of measurement and definitions of terms, i.e. gauge, differential, absolute, static, and dynamic.

Terms of Use: The article above is released under a Creative Commons Attribution-Share-Alike License 3.0 (HTML).  You can find the original Wikipedia version of this article here (HTML).

• Reading: Omega Instruments’ “Process Pressure Measurement” Link: Omega Instruments’ “Process Pressure Measurement” (HTML)

Instructions: Read these pages after you have completed the other readings for this subunit.  This text gives a practical, commercial, and contemporary engineering perspective on the techniques, importance, and utility of pressure measurements.

2.1.3 Orifice Plates, Venturi Meters, Pressure Drops, and Discharge Coefficients   - Reading: The Engineering ToolBox’s “Orifice, Nozzle, and Venturi Flow Rate Meters” Link: The Engineering ToolBox’s “Orifice, Nozzle, and Venturi Flow Rate Meters” (HTML)

Instructions: Read the theory section first and consider the following questions.   What assumptions go into the development of this treatment?  When would an orifice plate or Venturi meter not be amenable to this treatment?  What is the physical meaning of the discharge coefficient?

`````` Perform calculations to determine the difference in the pressure
drop induced by equal mass flow rates of air and water through
different orifice plates and Venturi devices.  Hint: In the
treatment used for the analysis of an orifice plate, what is the
difference between air and water?  You may consider a range of
discharge coefficients.

displayed on the webpage above.
``````
• Reading: The Saylor Foundation’s “Note on Pressure Drop Calculations for Orifice Plates and Venturi Meters” Link: The Saylor Foundation’s “Note on Pressure Drop Calculations for Orifice Plates and Venturi Meters” (PDF)

Instructions: After completing subunits 2.1.3 and 2.1.4, refer to the Saylor Foundations “Note on Pressure Drop Calculations for Orifice Plates and Venturi Meters” to reinforce your knowledge and check your calculations.

2.1.4 Pitot Tubes   - Reading: NASA’s “Pitot Static Tube” Link: NASA’s “Pitot Static Tube”(PDF)

Instructions: Read the webpage, and consider how the theory differs for incompressible and compressible flows.  What sort of spatial resolution for velocity might be obtained with a Pitot tube?  What other difficulties might be encountered with using Pitot tubes?

Terms of Use: This material is in the public domain.

2.2 Velocimetry or Anemometry   - Reading: Wikipedia’s “Velocimetry” and “Anemometer” Links: Wikipedia’s “Velocimetry” (PDF) and “Anemometer” (PDF)

`````` Instructions: With advances in instrumentation, many complex
methods for velocimetry and anemometry have emerged.  The operation
of these methods is very complex, but you should be acquainted with
their existence.  Read these two articles and consider the following
questions.  What is the difference between velocity measurement and
speed measurement?  What is the difference between velocity
measurement and flow rate measurement?  Name a few techniques based
upon laser technology and a technique based upon heat transfer.

Terms of Use: The articles above are released under a [Creative
can find the original Wikipedia versions of these articles
[here](http://en.wikipedia.org/wiki/Velocimetry) (HTML) and
[here](http://en.wikipedia.org/wiki/Anemometer) (HTML).
``````

2.3 Volume or Mass Flow Measurements   2.3.1 Weirs   - Reading: The Civil Engineering Portal’s “Weirs” Link: The Civil Engineering Portal’s “Weirs” (HTML)

Instructions: Read the text to determine which physical variables of weir construction and operation are related to flow over the weir.

2.3.2 Rotameters   - Reading: SensorMag: John E. Scheer’s “The Basics of Rotometers” Link: SensorMag: John E. Scheer’s “The Basics of Rotometers” (HTML)

Instructions: This is very accessible reading on rotometers from a practical perspective.  Please read the text in its entirety.