# hw5 - (d Plot the thermocouple response versus time for...

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ME 365 PROBLEM SET 5 Spring 2012 Please work each problem on a separate sheet. Problem 1: A Pt – Pt/13% Rd (type R) bare-junction thermocouple has an approximately spherical junction with a diameter of 0.3 mm. It is used to measure the temperature of gases in a combustion tunnel. When the flame is ignited, it produces an approximate step increase of the gas temperature of 900 K. The average heat-transfer coefficient on the surface of the thermocouple is 500 W/m 2 -ºC. The gas temperature before ignition is 300 K. Platinum has a density of 21,450 kg/m 3 and a specific heat of 134 J/kg-K. (a) Find the time constant of the thermocouple. (b) After how much time and how many time constants will the measurement error be less than 1% of the final temperature change? (c) If the same thermocouple is used in an aqueous environment in which the heat transfer coefficient is 6000 W/m 2 -ºC what will be the thermocouple time constant?

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Unformatted text preview: (d) Plot the thermocouple response versus time for both cases. (on the same plot) Problem 2: The following data has been collected for a unit step response of a particular system. Time (sec) Y(t) volts 0.0 1.0 0.4 1.66 0.8 2.10 1.2 2.40 1.6 2.60 2.0 2.73 2.4 2.80 2.8 2.88 3.2 2.92 3.6 2.94 4.0 2.96 Using an appropriate plot, determine whether the system is first order and, if so, determine its static sensitivity K and time constant τ . ME 365 PROBLEM SET 5 Spring 2012 Problem 3: (a) The following equation describes the behavior of a second-order system Determine the natural frequency and damping ratio of the system, convert it to standard form (equation 30 page 5-22) and find the steady-state response. (b) A mass-spring-damping system has the following characteristics: m = 20g, b = 5N-s/m, and k = 10 N/cm. Calculate the natural frequency and damping ratio of this system. Is the system overdamped or underdamped?...
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## This note was uploaded on 02/22/2012 for the course ME 365 taught by Professor Merkle during the Spring '07 term at Purdue.

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hw5 - (d Plot the thermocouple response versus time for...

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