Measurements in Fluid Mechanics058:180:001 (ME:5180:0001)

Time & Location: 2:30P - 3:20P MWF 218 MLH

Office Hours: 4:00P – 5:00P MWF 223B-5 HL

Instructor: Lichuan Guilichuan-gui@uiowa.edu

http://lcgui.net

2

Lecture 21. Temperature measurement

3

Temperature measurement

Temperature scales- three temperature scales in use today, Fahrenheit (F), Celsius (C) and Kelvin (K)

Fahrenheit temperature scale

- 212 for the boiling point of water

- 32 for the freezing point of water

- interval divided into 180 parts

Celsius, or centigrade, scale

- 100 for the boiling point of water

- 0 for the freezing point of water

- conversion formula: F = 9/5C + 32

Kelvin temperature scale - base unit in International System (SI) of measurement- zero point at absolute zero- difference between the freezing and boiling points of water is 100 degrees

- conversion formula: K = C + 273

4

Temperature measurement

Thermometers

- liquid-in-glass thermometers

Thermal expansion thermometers

- based on the thermoelectric effect

Thermocouples

- based on the relationship between temperature and electric resistance

Resistance thermometers

- include metallic resistance sensors (RTDs), and semiconductor resistance sensors

- bimetallic thermometers

Coil elements

5

Temperature measurement

Liquid-in-glass thermometers

- constriction may be used to measure maximal or minimal temperature

- a bulb, a reservoir in which the working liquid can expand or contract in volume

- a stem, a glass tube containing a tiny capillary connected to the bulb and enlarged at the bottom into a bulb that is partially filled with a working liquid. The tube's bore is extremely small - less than 0.5 mm in diameter

- a temperature scale is fixed or engraved on the stem supporting the capillary tube to indicate the range and the value of the temperature. The liquid-in-glass thermometers is usually calibrated against a standard thermometer and at the melting point of water

- a reference point, a calibration point, the most common being the ice point

- a working liquid, usually mercury or alcohol

- an inert gas is used for mercury intended to high temperature. The thermometer is filled with an inert gas such as argon or nitrogen above the mercury to reduce its volatilization.

6

Temperature measurement

Liquid-in-glass thermometers

- Typical resolution: 0.05-1 K

- Immersion types:partial Immersion (inserted in fluid up to marked line) total immersion (inserted in fluid up to liquid column) complete immersion (entirely immersed in fluid)

- total immersion required to avoid errors due to temperature difference between immersed and non-immersed sections

- stem correction necessary with partial immersion thermometers

- number of degrees (K) of the non-immersed portion

∆ 𝑇=0.00016𝑁 (𝑇 𝑖𝑚𝑚−𝑇 𝑛𝑜𝑛−𝑖𝑚𝑚 ) - temperature of the immersed portion - temperature of the non-immersed portion

𝑻 𝒊𝒎𝒎

𝑻𝒏𝒐𝒏− 𝒊𝒎𝒎

𝑵

e.g. for mercury-in-glass thermometers:

- disadvantage: poor spatial and temporal resolutions

- advantage: excellent laboratory standards for calibration of other instruments

7

Temperature measurement

Bimetallic thermometers

- two thin plates of different materials

- bonded together tightly with one end fixed & another free - vastly different thermal expansion coefficient

- curvature of the assembly changed due to temperature variation

- helically or spiral coiled assembly used to amplify motion resulting from temperature change

Bimetallic thermometer (flat, spiral strip)

- bimetallic assemblies also used in thermostatic controls

- typical resolution about 1% of full scale, and maximal operation temperature around 500C

8

Temperature measurement

Thermocouples

Thermocouple configuration

Seebeck effect- Any electrical conductor will develop a potential difference

(thermoelectric voltage) between two of its points that have a temperature difference.

- two dissimilar metallic wires (e.g. A and B) joined firmly at two junctions- one junction exposed to the temperature of interest (e.g. T1)- the other one (reference junction) kept at known constant temperature (e.g. T2) - reference junction conventionally immersed in an ice bath for reference temperature of 0C - constant reference temperature also provided with an electronically controlled heated block - common types of thermocouples and their properties

- typical resolution in the order of 1C

- highest temperature of 2930C by tungsten-rhenium type

9

Temperature measurement

ThermocouplesSensor & measuring circuit

10

Temperature measurement

Resistance thermometers

Resistance temperature detectors (RTDs)

- pure metal thermometers of platinum (most popular and accurate), nickel, or copper

- typical resolution of 0.1 K, possible high resolution of 0.0001 K

- non-linear response fitted with low-order polynomials e.g. resistance Rpt of platinum RTD in the range 0f 100-700C described by Callendar-Van Dusen equation

Rpt0 – resistance at 0C

Cold-wires- similar construction to HW

Thermistors - semiconductor elements whose resistance is a very strong function of temperature.

- high frequency response in temperature measurement

- extremely high sensitivity to temperature

- non-linear response

11

Discussion on homework assignment

- Questions and Problems: 8 on page 286

12

Homework

- Questions and Problems: 6 on page 305- Read textbook 12.1-12.2 on page 290 - 296

- Due on 10/14