Ce 321 Introduction to Fluid Mechanics 2004

CE 321 INTRODUCTION TO FLUID MECHANICS 200SPRINGFALLSPRING 200964

LABORATORY 12: FLOW RATE MEASUREMENT

OBJECTIVESS

:TtTo measure flow rates,

Tto assess the uncertainty of the measured

flow rates, and
Tto to determine how to make accurate flow rate measurements.

EQUIPMENT:

HhHydraulic bench, wrist watch, and stopwatch.

APPROACH

: In this lab you will learn to “measure” flow and assess the uncertainty

of the measured values. We have intentionally selected a method that produces

significant uncertainty at times. Once you understand the sources of this

uncertauncertaiinty, you can refine the measurement procedure to obtain accurate flow

rate measurements in later labs.

PROCEDURE:

A. FAMILIARIZE YOURSELF WITH THE EQUIPMENT.

1. Open the dump valve and .s Switch on the power. Open the flow control valve

about ½ turn. (Whenever the power is on, the valve should be open so that

some water flows through the system. Otherwise, the pump will overheat.)

2. Adjust the valve so that maximum flow occurs. O (open valve slowly to

prevent water from shooting around the lab).
3. Trace out the path of water starting at the sump tank.

4. Before making any measurements, fill the measuring tank to the top

several times to remove air trapped in the site gage tube that can cause

measurement errors.Mand make sure that the dump valve seals when it is

closed. This should be done at the beginning of each lab period in which

you measure flow. Before filling the measuring tank, ensure that the sump

contains adequate water, so that the pump does not run dry.

5. Close the dump valve and watch the water level in the site gage rise as

water accumulates in the measuring tank. Open the dump valve once the

water level in upper site gage reaches 5 liters. Drain the tank completely

and fill it to 5 liters several more times whilesimply observing the system’s

behavior.

6. Now repeat the drain-and-fill operation and try measuringmeasure the time

required to accumulate 5 liters of water.;Sstart timing when the bottom of

the meniscus1 1in the site gage reaches the 0 liter mark, and stop when it

reaches the 5-liter mark. Do not bother recording this first set ofese data, as it is simply a trial. Now you are ready to begin collecting data.

1Meniscus1 -the U-shaped upper surface of the water in the site gage. Start timing when the bottom of the meniscus is aligned with the zero mark.

B. COLLECT FLOW-RATE DATA.

1. Open the flow control valve completely, and do not change its position

during the experiment.

2. With the water level well below the 0 level on the upper scaleof the site

gage, measure the time required for the water level to increase from 0 to 1

on the upper scale. You cannot obtain accurate measurements under

these circumstances. That is intentional. Try to obtain measurements that

are as accurate as possible within the limits imposed by the equipment

and procedure.

3. Repeat this measurement 10 times. Record the measured times in

column 2 of Table 1.

4. Without adjusting the flow valve, repeat the procedure of steps 2-3, using

an interval on the site gage from 0 to 5 liters. Record these data in column

4 of Table 1.

C. ESTIMATE THE LEAST COUNT.

1. The smallest change in volume that you can reliably identify using the site

gage is its least count (). Estimate the value of for the measurement

conditions you encountered. Remember that you had to decide when the

water level was exactly zero as the water level was rising. The moving

water level makes it more difficult to identify small changes in volume, so it

should increase your estimate of the least count.

D. TURN OFF THE MOTOR AND OPEN THE DUMP VALVE.

E. COLLECT UNCERTAINTY DATA.

1. Use a quartz wristwatch to define a 5-minute time interval.

2. Measure the length of this interval using one of the lab stopwatches.

3. If the two watches show less than 1% difference, keep the stopwatch.

Otherwise, get a different one and try again.

4. Use the stopwatch to time a 15-second interval on the lab clock. Make

sure you time the lab clock. Be sure to stand so that you minimize

parallax while watching the sweep second hand on the lab clock. WAnd

watch the clock, not the stopwatch. Make 10 measurements and record

them in Table 2. Don’t throw out any of them out!

ANALYSIS

A. CALCULATE AND PLOT THE FLOW RATES.

Put the calculated values in Table 1. Plot the flow rates as a function of the

measurement volume as shown in the attached example.

Assuming steady flow, describe any uncertainty that your flow measurements

suggest. Describe how the measurement volume and time appear to

influence uncertainty.

B. ESTIMATE THE UNCERTAINTIES IN YOUR BASIC MEASUREMENTS.

Assume the uncertainty (V)V in each measured volume is 2(twice the least

count). Estimate the uncertainty t to be twice the standard deviation

observed in the values of t. That is t = 2SD t. Determine the standard

deviation (SDSDt) of the 10 measurements of t using the STDEV function in

EXCEL.

C. ESTIMATE THE UNCERTAINTY IN Q DUE TO UNCERTAINTIES IN V AND T.

Use the propagation of uncertainty equation derived in Lab and your values of

V and t to calculate dQ/Q.

Describe what these calculations show.: Do they suggest that all of the

uncertainty you observed in Q comes from your uncertainty in V and t? Do

they suggest that uncertainty in Q varies as you change the size of the

measurement volume and/or the measuring time? If V and t are the only

sources of error in the experiment, does this equation suggest that you could

obtain measurements that have only 1% uncertainty at this flow rate? (This

final question is for discussion, but not necessary for the lab report.)

D. EXPLORE THE UNCERTAINTY IN Q THAT IS POSSIBLE FOR DIFFERENT MEASUREMENT

SITUATIONS.

Use the propagation of uncertainty equation derived in Lab to develop a table

that shows how dQ/Q varies as a function of Q and V. In this equation, the

filling time (t) is equal to the volume (V) divided by the flow (Q). Use values

of 0.1 l/s Q 0.7 l/s and 2 l/s V 10 l/s.

Later during thisin the semester you will run experiments where the flow is set

using the valve and determine the flow rate by measuring volume and time where the flow is set using the valve..

In order to assess the uncertainty in calculated values you will need to obtain

values of Q that have less uncertainty than a specified amount. Use the

approach suggested by your lab instructor and your data to develop a method

for making precise measurements of Q. Remember that you will not know the

value of Q before you measure V and t.

E. DETERMINE A METHOD FOR MEASURING FLOW ACCURATELY IN FUTURE

EXPERIMENTS.

Use the information developed in part D and assume that it will be sufficient to

obtain values of Q that have an uncertainty less than 5%. Remember, you will

not know the flow rate until after you have measured it., and y Your method must

take this into account. Describe your method and provide an example of how

you will use it to measure an unknown flow accurately.

CHECK LIST FOR THE FLOW MEASUREMENT LAB

DATA APPEAR TO BE REASONABLY ACCURATE

Your calculated values of Q should show a trend similar to what can be observed

in Sample Fig. 1.

Check the values of your uncertainty estimates. Are they reasonable given the

measurement device and the circumstances?

RESULTS SECTION

 Your facts are correct, clearly stated, and supported by the data you present.

Did you describe any uncertainty that your flow measurements suggest? Did you

describe how the measurement volume and time appear to influence uncertainty

in flow?

Did you state the amount of uncertainty that you estimated your measured values

are subject to? Did you describe the method of estimating you used to make the

estimates?

Did you describe what your uncertainty calculations show about the values of Q

that you measured? Do they suggest that all of the uncertainty you observed in

Q came from your uncertainty in V and t? Do they suggest that uncertainty in Q

varies as you change the size of the measurement volume and/or the measuring

time? If V and t are the only sources of uncertainty in the experiment, does this

equation suggest that you could obtain measurements that have only 1%

uncertainty at this flow rate? (This last question is for discussion and is not

necessary for the lab report.)

DISCUSSION

The logical arguments are correct and clearly stated.

Did you describe the method you have developed for accurately measuring flow

in future experiments? Will your method meet the accuracy criteria?

Did you present a logical argument that justifies the method? Did you describe

how you would account for the fact that you will not know the flow rate until after

you have measured it?

Did you provide an example that shows how you can use your method to

measure an unknown flow accurately?

Make sure the important results and conclusions are restated in the Conclusions

Section and summarized in the Abstract