A Thermal fluids lab report
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Section number and heading, with analysis (95 points)
Use the headings and numbers below, with each item requested clearly identified in your write-up. If there is an instruction to create a plot or table, that item is expected to be included in your report. The caveat to that last note is in cases where it is stated to not include a table or a plot.
4.1 Raw Data
The items noted in Tables 1-3 constitute your raw data (Table 1 is repeated for upscale and downscale readings). Creating tables in Excel with that information will likely make your life easier as you will be able to use copy-paste functions to do all the calculations and make the plots. Otherwise, the analysis will get tedious.
Create your own format for presenting that information and show your tables. Insert a column to the right of the column that contains the standard pressure difference reading. In that column include a calculation that converts the standard pressure difference values (either inches of water from the inclined manometer or mbar from the deadweight tester) into units of Pascals.
Make sure your tables are neat and have appropriate titles. Include a sentence that describes what data each table includes. Also, make sure you comment on the number of significant figures included (resolution), especially for the manometers that are based on an eye reading.
4.2 Evaluate Hysteresis of Calibration Equations for Inclined Manometer Standard
Recall that the calibration for pressure sensors will have the pressure difference on the y-axis and the measurement reading on the x-axis. All pressure differences are to be in Pascals for these plots (and all subsequent analysis).
For each U-tube manometer, create 1 plot for the upscale readings and 1 plot for the downscale readings (2 plots for each sensor, each with multiple trials plotted as their own series identified in the plot legend). Add in a best-fit line (linear should work fine) for each trial.
Assuming you ran 3 trials, your plots will each have 3 lines. Obtain the equation for each trial best fit line. This will be your calibration equation, and useful for future labs when you might use these pressure sensors. Create a table that shows the slope for each trial within the upscale and downscale conditions (total of 6 slopes for each sensor).
The slope function in Excel can make doing this for all cases go quickly. For the PX26, calculate the average and the 95% confidence interval for the slope of calibration curves based on the three trials (ignore bias here).
Create a table that shows the average slope and the 95% confidence interval for the upscale and downscale conditions for each sensor (4 total sensors with upscale and downscale for each implies 8 different average values).
Discuss the difference in the average slope between the upscale and downscale cases for each sensor noting that if the confidence interval values overlap, one would say that the slopes are the same from a statistics point of view.
4.3 Provide a Calibration Equation for Each Sensor
From your analysis in 4.2, determine if separate equations for upscale and downscale conditions are needed. If not, then average the upscale and downscale slopes for a given sensor, and re-calculate the 95% confidence interval.
Provide a calibration equation for each sensor, including the PX26 calibrated against the inclined manometer and the deadweight tester. Make sure you identify the expected units for each of the terms in order to use your calibration equation (for example, the units for the PX26 would likely be DCV).
4.4 Calculate the Sensitivity for Each Sensor
Using your calibration equations from 4.3, calculate the sensitivity for each sensor. Be sure to identify the input and the output parameters for each sensor. And be sure to include units!
4.5 Estimate the Fluid Density for the Water and Mercury Manometers
Using the manometer theory described in this manual and your results based on experiment from section
4.4, estimate the density of water and mercury.
Look up density values for water and mercury from a reference. Create a table that shows your estimate of the density based on experimental data and the value you found from the reference (make sure you provide cite the reference using proper citation format). Discuss how close the values are and possible explanations for any differences