jeffoshiro lab 1 assignment

Upload: jeffrey-oshiro

Post on 02-Jun-2018

217 views

Category:

Documents


0 download

TRANSCRIPT

  • 8/10/2019 JeffOshiro Lab 1 Assignment

    1/4

    1

    Jeffrey Oshiro

    ME 402

    Dr. Bingham

    January 24, 2013

    Lab 1: First-Order Time Response of a Thermal System

    Q1: Comparing Model Prediction and Experimental Measurements

    In this procedure the heating and cooling curves for various water temperatures were examined to

    determine a time constant for the first-order system. An example of a first-order time response is

    shown inFigure 1. This model plots the variable (velocity of a falling object) against time. The results of

    the procedure were compared qualitatively to this model. This was to determine if the thermal systems

    behaved like a first-order system. The time constants of the results were also compared to the time

    constant of a predicted model. This was to determine how well the predicted model accurately

    represents the behavior of the actual system. For this procedure, the results for Run1 of the timeresponse for Hot Water to Room Temperate Water inFigure 2 will serve as the predicted model.

    The heating and cooling curves for the time response of Hot Water to Room Temperature Water is

    shown inFigure 2. The results for Warm Water to Room Temperature Water is shown inFigure 3. The

    results for Hot Water to Air is shown inFigure 4.

    Figure 1: Example of a first-order system

  • 8/10/2019 JeffOshiro Lab 1 Assignment

    2/4

    2

    The results of the all the procedures look consistent with the example (Figure 1)of how a first-order

    system behaves. They all display that characteristic exponential change from the initial state before

    reaching the steady-state. However, there are some inconsistencies in several trial runs. In Run1 in

    Figure 2 there is a bump in the curve before the 10 s mark. This could be due to shifting the probe in the

    hot water during data recording. Run3 ofFigure 2 also has a bump at around . This might be due

    to shifting the probe.

    ForFigure 2 andFigure 3,the steady-state of the heating curves gets progressively smaller with each

    run. This is due to the hot or warm water cooling over time and with each transfer of heat from the

    water to the probe. It is also observed that the heating curves forFigure 2 andFigure 3 also become

    progressively steeper as it reaches the steady-state and flatten out quicker after reaching the steady-

    state. The flattening could be due to the hot or warm water cooling.

    The results of the heating curve data of all the procedures are summarized inTable 1. The results of the

    cooling curve data are summarized inTable 2. InTable 1 andTable 2,and represents the initial

    temperature and steady-state temperature of the respective curves. The time constantwas

    determined by calculating 63.2% of the absolute difference betweenand (the amplitude of the

    step-unit) and graphically finding the time when that value occurs in the curve. The percent error wascalculated as the absolute difference between the time constant of a particular curve and the time

    constant of the corresponding heating or cooling curve of the predicted model (Run1 ofFigure 2)

    divided by the time constant of the predicted model.

    Figure 2: A plot of the heating and cooling curves for hot water to room temperature water.

    In the absence of a predicted model, the curve "Run 1" will serve as the prediction.

  • 8/10/2019 JeffOshiro Lab 1 Assignment

    3/4

    3

    Figure 4: The heating and cooling curve for the time response from hot water to air.

    Figure 3: The heating and cooling curves for the time response from warm water to room

    temperature water.

  • 8/10/2019 JeffOshiro Lab 1 Assignment

    4/4

    4

    Q2: Defending a Hypothesis with Evidence

    The time-constant of the step response of a first-order system is independent of the amplitude of the

    step unit. If the time-constant depended on the amplitude of the step inputTable 1 andTable 2 would

    show a correlation between the percent error and the amplitudes. However, there doesnt seem to be

    any consistency with the percent errors and the amplitudes.

    Table 2: Cooling Curve Data Summary

    Cooling

    Ti(C) Tf(C) Amplitude % Error

    Hot to Room

    81.25 22.102 0.8787 59.148 N/A

    75.6774 20.9288 1.1297 54.7486 28.56493

    72.1578 20.9288 1.318 51.229 49.99431

    Warm to

    Room

    53.5196 20.2793 1.0042 33.2403 14.28246

    51.3408 20.7263 0.8787 30.6145 4.04E-13

    46.8715 22.1788 1.2552 24.6927 42.84739

    Hot to Air 86.9204 29.5321 38.5983 57.3883 4292.66

    Table 1: Heating Curve Data Summary

    Heating

    Run Ti(C) Tf(C) Amplitude % Error

    Hot to Room

    1 26.0126 84.8054 0.6904 58.7928 N/A

    2 23.2751 76.6302 1.0042 53.3551 45.45191

    3 22.3953 73.3942 0.8159 50.9989 18.17787

    Warm to

    Room

    1 22.1788 53.6313 0.8786 31.4525 27.25956

    2 20.6145 51.642 0.6904 31.0275 0

    3 19.7765 46.7598 0.6904 26.9833 1.61E-14

    Hot to Air 1 21.2221 87.1159 0.5648 65.8938 18.19235