TAM 335 Lab 1: Elementary Lab Procedures

TAM 335 Lab 1 Partial Report

This report includes:

1. An overview of the experiment setup
2. Measurement procedures to determine the relationship between:
3. Pressure change measurements using a differential manometer or two Bourdon pressure gauges
4. Pressure change measurements and volumetric flow rate
5. Experimental results for both relationships
6. Analysis of measurement precision using weight-time data.

Images in the title block and introduction are from the internet and labeled free to share and use. Images in the Supplies section and formulas used in the calculations below are both provided by the TAM 335 Elementary Lab Procedures Lab Manual. The graphs are plotted from data in the provided Excel spreadsheet data table with built-in formulas.

(Quantity) Component

(2) Bourdon pressure gauge

(1) Mercury-filled differential manometer

(1) Balance beam scale

(1) 50 lb beam scale weight markers*

(1) Water tank with drain (drain should be able to be opened and closed)**

(1) Stopwatch***

Also needed if the apparatus needs to be set up:

Water supply

Pipes compatible with water supply, Bourdon gauges, and manometer

Cross pipe fittings compatible with water supply pipes, pressure gauge, manometer pipes

Discharge valve compatible with water supply pipe

*Add a weight marker if adjusting the balance beam cursor is insufficient to make the balance beam rest on the scale's bottom stopper. The experiment requires another weight marker to be placed to overbalance the scale during the trials. Try to maintain a consistent weight marker combination across all trials.

**The water tank should be mounted to the scale so that water weight can be measured.

***If possible, have multiple people operate stopwatches during the experiment to reduce timing error and fluctuations. The measured times should be averaged.

The experiment involves taking batches of measurements at five distinct flow rates settings. While collecting data for each setting, do not change the discharge valve flow rate between measurements; this helps ensure consistency for each measurement at that setting.

The change between settings should be large enough to produce a visible pressure readout change on the Bourdon gauges. For convenience, the first flow rate setting should be the maximum flow rate; the following flow rate settings should be less than the prior.

If the tank threatens to overflow, drain the tank and use a lower flow rate setting or change the weight markers.

Once the desired flow rate setting is selected, read the pressure on the Bourdon gauge indicated by the sharp end of the pointer. Read the height of the mercury on each vertical section (heights above zero marker are positive, while those below the zero marker are negative).

Trial Procedure

1. Ensure the tank drain is open. Adjust the discharge valve so water flows steadily.
2. Adjust the balance beam scale cursor until the balance beam rests on the bottom stop. Keep this setting for the rest of this trial. Reset the stopwatch(es).
3. Adjust the cursor so the balance beam hits the bottom stopper.
4. Close the drain. As soon as the balance beam rises past the balance mark, start the stopwatch(es) and add a sufficiently heavy weight marker to the scale balance pan so the beam hits the bottom stopper again. Record the chosen weight.
5. When the balance beam rises past the balance marker for the second time, stop the stopwatch. Record the time interval, or the average time interval measurement for multiple stopwatches.
6. Repeat steps 1 to 5 four times for each flow rate setting.

Expected Results

1. Plotting Bourdon gauge pressure vs. manometer pressure should show a linear relationship.
2. Plotting Bourdon gauge and manometer pressure change vs. volumetric flow rates should produce a relationship where the pressure change is proportional to the square of the volumetric flow rate.

This is a plot of the pressure differences (pA - pB) determined by Bourdon gauge measurements vs. differential manometer measurements. The dashed grey reference line is the line of unity (a line with slope of 1, or y = x).

Both methods seem reliable, although the predicted relationship near zero diverge significantly.

Because error is very low for both methods, there is no clear winner for reliability. However, as both pressure difference and volumetric flow rate approach zero, the Bourdon gauge measurements more closely approach (0, 0).

The Bourdon gauges are fastened to the main water pipe, while the manometer is connected by pipe from the main water pipe. While both methods are connected at the same points, the instruments themselves are located at different heights than the connection locations, which would produce different pressure readouts. Moreover, while both readouts were very constant when the system stabilized, the Bourdon gauge readouts early in the trial seemed more affected by pipe vibrations. Finally, if lower volumetric flow rate trials were conducted, there may be more agreeance between the two measurement method trends.

In this section, weight-time data will be used to evaluate the precision of the measurements. For steady flow of fluid into the container (i.e. pipe discharges weight W of water in a time interval ∆t), Mass flow rate, M [kg/s], is defined as:

M = W / (g*∆t)

Then the volumetric flow rate, Q [ft^3 /s], can be found:

Q = M / ρ = W / (ρ*g*∆t) = W / (γ*∆t)

W [lb = lbf], weight of fluid in the tank (equal to weight of added weight marker)

g [ft/s^2], gravitational acceleration constant

∆t [s], time interval length to balance the weight marker

ρ [lbm/ft^3], mass density of fluid

γ [lbf/ft^3], specific weight of fluid (γ = ρ*g)

Using our chosen weight marker and the specific weight given in the lab manual:

W = 50 lbf

γw= 62.4 lb/ft^3 (w = liquid water)

Qs, the flow rate using the shortest time interval (reading No. 1) can be found:

∆t1 = 22.35 s

Qs = W / (γw * ∆t1) = 0.035851546 ft^3 /s

Ql, the flow rate using the longest time interval (reading No. 4) can be found:

∆t4 = 46.9475s

Ql = W / (γw * ∆t4) = 0.017067619 ft^3 /s

Then the precision, e, can be estimated by dividing the maximum volumetric flow rate difference by the average value of the highest and lowest volumetric flow rate:

e = (Qs - Ql) / ((Qs + Ql)/2) = 0.71 (2 significant figures)

Then the precision/spread of volumetric flow rates across the trials is about 71%. If this precision calculation were referring to error, this would be very high and likely not accepted in professional settings. However, because the discharge valve was adjusted between settings, this result could be expected given that the pressure differences and visual inspection of the flow rate during the experiment were significantly different.