CE 321 INTRODUCTION TO FLUID MECHANICS Fall 2009 LABORATORY 1: FLOW RATE MEASUREMENT

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1 CE 321 INTRODUCTION TO FLUID MECHANICS Fall 2009 LABORATORY 1: FLOW RATE MEASUREMENT OBJECTIVESS To measure flow rates To assess the uncertainty of the measured flow rates To determine how to make accurate flow rate measurements EQUIPMENT Hydraulic 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 uncertainty, 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 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. 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. 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 1

2 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 while observing the system s behavior. 6. Now repeat the drain-and-fill operation and measure the time required to accumulate 5 liters of water. Start timing when the bottom of the meniscus 1 in the site gage reaches the 0 liter mark, and stop when it reaches the 5-liter mark. Do not bother recording this first set of data, as it is simply a trial. Meniscus 1 -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 scale of 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 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 2

3 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. Watch the clock, not the stopwatch. Make 10 measurements and record them in Table 2. Don t throw 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 (δ V)in each measured volume is 2 (twice the least 3

4 count). Estimate δ t to be twice the standard deviation observed in the values of t. That is δ t = 2SD t. Determine the standard deviation (SD 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 δv and δ 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 in the semester you will 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. 4

5 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 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 5

6 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. 6

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