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Module 2: Review of Probes and Transducers
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Critical Damping - Optical Measurement Techniques in Thermal Sciences - Lecture Slides, Slides of Mechanical Engineering
Some concept of Optical Measurement Techniques in Thermal Sciences are Absorption Techniques, Alternative Approaches, Calibration Details, Computerized Tomography, Convolution Backprojection. Main points of this lecture are: Critical Damping, Probes, Transducers, Pitot Tube, Air Flow, Uniform Velocity, Limb Diameter, Critically Damped, Manometer, Possible Uncertainty
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2012/2013
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Module 2: Review of Probes and Transducers
Problems
The Lecture Contains:
Problems
Module 2: Review of Probes and Transducers
Problems
Problems
1. A pitot tube is exposed to air flow which has a uniform velocity of 10 m/s. The probe is connected
to a U-tube manometer with a water column of m total length. The limb diameter is so chosen that the manometer is critically damped. Find the time required to make a measurement on the manometer. Hint : Show that the limb diameter is 0.78 mm. To reach 99% of the steady state reading (or better), show that time should satisfy the inequality
where
Module 2: Review of Probes and Transducers
Problems
4. A thermometer initially at is immersed in a vacuum furnace whose walls are at C.
Formulate the thermometer response as a first order system and determine its time constant. Assume black body radiation. Assume the bead-to-furnace shape factor to be unity. Stefan-Boltzmann constant W/m 2 K 4 ; mass of the sensor g, specific heat and surface area. Hint : Show that the thermocouple bead temperature will increase as per the differential equation
where is the mass of the bead, is its surface area. The solution of the differential equation can be obtained analytically, by linearizing the second term; alternatively, an iterative numerical solution can be obtained, say, by a finite difference scheme.
Module 2: Review of Probes and Transducers
Problems
5. Analyze the frequency response of a thermocouple assuming the bead to be purely spherical.
Assume a spatially distributed system i.e.. Compare the attenuation frequency determined here with the value obtained from lumped parameter analysis.
6. A pitot tube is found to have a time constant of ms in the measurement of differential pressure.
If the fluid velocity varies with time as m/s ( in seconds) determine the velocity function recorded by the pitot tube. If changes as, m/s find the steady state error in the pitot tube measurement of velocity.
7. Develop an experiment to study growth of a turbulent boundary-layer and the wall shear stress for
flow over a rough flat plate. Discuss carefully the characteristics of the roughness elements in terms of their size and distribution. Discuss the choice of the sensors to be used. Comment on the distribution of a given number of points (say, 21) within the boundary-layer.