## Determining the Internal Pressure of a Soda Can

Purpose

During this experiment the internal pressure of a soda can is determined. A strain gage is bonded to the outside surface of the can while sealed and under pressure from the manufacturer. Once opened, the strain gage reads a compressive strain that can be used to estimate the internal gage pressure of the can.

Equipment list

• Soda Can (room temperature)

• Strain gage rosette, NI strain gage conditioner

• Soldering supplies: iron, solder, isopropyl alcohol, cyanoacrylate glue, polyurethane sealer

• Caliper, multimeter

Procedure

1. Measure all dimensions you will need for the analysis. 2. Measure the outside diameter of the can first, then start the wiring of the quarter bridge completion blocks (small blue rectangular blocks with wiring embossed on the side, must say 120 ohms on the bottom).

3. Use the sandpaper to lightly sand the can near the center so that the strain gage will adhere better. Immediately after sanding, neutralize the surface using the isopropyl alcohol.

4. Ensure that the surface is completely dry. Place a drop of cyanoacrylate glue on the cleaned surface and drop the strain gage rosette on top, aligning the 0 ◦ and 90◦ gages with the circumferential and longitudinal axes.

Ensure that the gage is firmly seated. The glue should dry to a tack in 2 minutes and be ready for the next step in 5-10 minutes. There is a right side up for the gage. Strain gage rosettes can deal with misalignments (that’s why there’s a third gage in the middle), so your placement doesn’t have to be perfect. One method of affixing the rosette to the glue is to use a piece of scotch tape to transfer the rosette. Another method is to (carefully) use a pair of tweezers. Be sure to clean the tweezers if you do that!

5. Use a thin layer of polyurethane to cover the gage and exposed metal near the solder tabs. This will help prevent a short-circuit.

6. Carefully solder the strain gage wires to each tab. You will wire all three gages individually (total of 9 wires). Don’t forget to tin the wires first. Tape the free wires to another location on the can provide strain relief so you don’t rip the gage off if the wire is tugged. Use a multimeter to check that each gage works as expected.

7. Wire up each individual gage as a quarter bridge, for a total of three channels in the NI 9237. 8. Write LabVIEW code to collect data from all three strain gages. For this experiment you get one shot to collect the data, so no need to use the normal double-while-loop construct. Instead, just set the number of samples and sampling rate to collect 5-10 seconds of continuous data and write it directly to a file. Setup the strain gage channels using the DAQ Assistant. Adjust the sampling rate to no lower than 5k samples/second. Calibrate each strain gage (remember we are not using a shunt calibrator).

Your calibration values should be very close to 0% error. If they are not, or if you receive an out-of-range error, input values are incorrect or something is wired incorrectly. If calibration appears to be successful but you still get a high error rate, reset the offset voltage to 0 and recalibrate.

Make sure your code works before continuing the experiment! That’s a lot of work to redo if something goes wrong…

Last updated: September 14, 2015, EAD 1 PRESSURE VESSEL MECH 3315 Mechanics Lab 9. Run the code then quickly open the can, trying to avoid applying pressure to the can with your hands. 10. After testing, pour out the soda and cut open the can measure the thickness. 11. Return the experiment to its initial state and put away all equipment used.

Theory and analysis Consider a cylindrical pressure vessel with radius r and wall thickness t subjected to an internal pressure p. In defining a coordinate system it’s natural to take advantage of the axial symmetry, aligning one coordinate along the axial direction and the other coordinate circumferentially.

The principal stresses are then the longitudinal stress σz and circumferential stress σθ. For a thin-walled pressure vessel, where the tangential stress can be assumed constant throughout the thickness (as a rule of thumb, when the radius is larger than ten times the wall thickness), the stresses can be written as σz = pr 2t σθ = pr t .

Note that the circumferential stress is twice the longitudinal stress – this is why a hotdog normally splits lengthwise when it’s overcooked! If we want to convert stresses to strains, we need to use the biaxial equations, which relate the stresses and strains through Young’s modulus E and the Poisson ratio ν, z = 1 E (σz − νσθ) θ = 1 E (σθ − νσz).

Read the accompanying references on strain gage rosettes to determine how to determine the principal strains (here, longitudinal and circumferential) from the three strain gages.

Report requirements Please see the handout on laboratory technical papers for a general discussion. All values should be reported with combined (bias + precision) uncertainty. Particular results for this lab must include:

• Plot: strain from each gage as a function of time

• Determine the pressure based on measured strain values. Compare to known values for the internal pressure of a soda can (and provide references to these values).

• Complete propagation of uncertainty – how critical are measurements of the diameter and thickness in the overall pressure uncertainty?

• Discussion: how would a misalignment of the gage effect the calculation of internal pressure?

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