Crew Parker Lab 1 Report

MAE 107 Lab Report 1 Fall 2020 Crew Parker ID: 14186406 Instructor: Dr. Y. Wang TA: Cody Lab 1 Report Summary To perform this lab, a water pump was utilized with a water tank and manometer to output a consistent mass flow rate of water out of a tube. Two different graduated cylinders, one of 1000mL volume and another of 100mL volume, are used to measure how much water had flowed from the tube. Four different combinations of graduated cylinder and mass flow rate are measured in the same way. With a slower water flow rate and the 1000mL cylinder, the cylinder is held under the stream of water until it reaches a predetermined volume. This volume is set to 500mL to speed up the lab, but any volume is acceptable if time is being measured, as mass flow rate will be consistent independent of the final volume. One group member fills the cylinder to 500mL, while simultaneously holding a timer and timing when they begin and end filling the cylinder. Another group member records the final volume and time of the trial. The volume is calculated to the nearest 5mL by placing the cylinder on a flat surface and observing the meniscus. This process is repeated 5 times for each member of the group, to attain better accuracy of results. This sequence is then repeated with all group members for three more combinations: 100mL cylinder with low flow rate, 1000mL cylinder with high flow rate, and 100mL cylinder with high flow rate. The results included very few outliers and matched our calculations very closely ( see Sample Calculations ) . The average mass flow rates for the the three cylinders were 33.05 mL/s for the low flow rate/large cylinder, 32.50 mL/s for the low flow rate/small cylinder, and 55.29 mL/s for the high flow rate/large cylinder. Crew Parker 1

MAE 107 Lab Report 1 Fall 2020 Questions Q1.) In the sample of experimental data, please estimate the precisions and range of each equipment. a. The large graduated cylinder has a precision of 0.1mL and a range of 0 - 1000mL. The small graduated cylinder has a precision of 0.01mL and a range of 0 - 50mL. The stopwatch has a precision of 0.001 sec and a range of 0.00 - 359999.99 sec. Q6.) Plot the Rayleigh distributions for three means 1 m/s, 5 m/s, 10 m/s, respectively, using Matlab or other programming languages, and attach the codes. a. See Graphs. Q8.) What are the two categories of experimental errors? Please give examples using a ruler and stopwatch. a. The two categories of experimental error are bias and uncertainty. Bias is essentially where equipment or methods cause data to be skewed in a certain way. Uncertainty has to do with the random variance associated with precision of data measurement. Bias with a ruler may be the user observing the ruler from the wrong angle and skewing the data a certain direction. Uncertainty with a stopwatch may occur if the number of digits the watch can measure causes rounding to occur. Q11.) In a thermocouple, voltage (e) is measured to be 1 V. K= 300 o C/V. δe=0.001 V, then δT=? a. See Sample Calculations. Q12.) In Example 2, redo the calculation by using V=0.0955 liter and t = 1.08 sec. a. See Sample Calculations. Q13.) In Example 3, add the extra data (3.1, 3.4, 3.2, 3.3) and redo the calculations. a. See Sample Calculations. Q2.) Plot the frequency distributions of Q. Comment on the distributions: are there any outliers? Please get rid of the outliers. Why are the distributions different? a. See Graphs. b. The distributions did not change very much when the outliers were removed. They essentially just become more similar to the expected probability distribution curve with no outliers included. Q3.) Evaluate Equation 6 using the average values of t and V (without outliers) to determine the predicted root-mean-square error δQ. a. See Sample Calculations. Q4.) Compare the root-mean-square error δQ with the square root of the correct unbiased sample variance, i.e. standard deviation S Q , and comment. a. The root-mean-square error of the low flow rate/large cylinder is 0.29 mL/s, the low flow rate/small cylinder is 4.68 mL/s, and the high flow rate/large cylinder is 0.58 mL/s. b. The Standard deviation of the low flow rate/large cylinder is 0.75 mL/s, the low flow rate/small cylinder is 4.03 mL/s, and the high flow rate/large cylinder is 1.89 mL/s. Crew Parker 2

MAE 107 Lab Report 1 Fall 2020 Lab Data: Crew Parker 4

MAE 107 Lab Report 1 Fall 2020 Graphs Q6.) MATLAB Rayleigh Distributions Crew Parker 5

MAE 107 Lab Report 1 Fall 2020 Sample Calculations Q11.) δT= K(δe) = (300 [ o C/V])(0.001 [V]) = 0.3 o C Q12.) = = 0.01638 1 1.08 2 (0. 0005) 2 + 0.0955 2 1.08 4 (0. 2) 2 Q = 0.088 40 ± 0.0164 l/sec Q13.) 3.25 𝑥 = 3.0+3.1+3.2+3.3+3.4+3.5 6 = Crew Parker 7

MAE 107 Lab Report 1 Fall 2020 = 0.0292 σ 𝑥 2 = 1 6 𝑖=1 6 ∑ (3. 0 − 3. 25) 2 s x 2 = 0.035 = 1 6−1 𝑖=1 6 ∑ (3. 0 − 3. 25) 2 Q3.) δV = 5 mL, δt = 0.005 sec a. Low Flow Rate, Large Cylinder V avg = 691.64 mL and t avg = 20.86 sec δQ = = 0.29 mL/sec 1 20.86 2 5 2 + 691.64 2 20.86 4 0. 005 2 b. Low Flow Rate, Small Cylinder V avg = 34.26 mL and t avg = 1.07 sec δQ = = 4.68 mL/sec 1 1.07 2 5 2 + 34.26 2 1.07 4 0. 005 2 c. High Flow Rate, Large Cylinder V avg = 537.17 mL and t avg = 9.72 sec δQ = = 0.58 mL/sec 1 9.72 2 5 2 + 537.17 2 9.72 4 0. 005 2 Crew Parker 8