HW #1 - 3

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computational methods - linear regression   do not use spreadsheet program to find answer.

A flow meter sensor is connected to the microcontroller card to convert the signal and display it as a volume flow rate (L/min.) on the data show screen. Standard volume (graduated cylinder) with stopwatch were employed to calibrate the assemble system, and the calibration results were tabulated as following: Measuri L/min. 51 52 54.5 57 68 ng value Real L/min. 53 55 57 64 71 76 77 0 73 74 80 value Determine: 1- Absolute relative error (ARE). 2- Mean value, deviation (error) value and standard deviation (σ). 3- Draw the calibration curve.

Lab 2-Measurement Asynch - Tagged.pdf Page 4 of 7 ? Part I: Taking Measurements & Estimating Uncertainties for a single measurement www.stefanelli.eng.br The mass of the object is_ 0 i Parts on a tripie peam palance 0 0 10 20 30 1 100 2 3 40 200 4 +/- 50 60 70 5 300 7 400 80 Qv Search 8 90 9 500 100 9 10 g www.stefanelli.eng.br

5.35 Subsonic aircraft use a pitot tube (impact pressure tube) and a static pressure port to determine aircraft airspeed by U = 2Ap Pair 2PH₂8H = where H = Aр/Pнg is Pair the differential pressure expressed in either inches Hg or mm Hg. The value of H can be measured to within 1% (95%) uncertainty. For a measured H of 20 mm Hg, estimate the airspeed and the uncertainty in airspeed at sea level due to H. Use International Standard Atmosphere (ISA) conditions of 15°C and 101,320 Pa abs. For the densities, use PH₂(kg/m³) = 13595-2.57(°C) ±0.1 and treat dry air as an ideal gas so that pair (kg/m³) 3.4837 x 10³p(Pa abs)/T(K) ± 0.001. Neglect the uncertainties in the two densities in the analysis. =

56.0 mL of two different liquids are poured through a funnel with a narrow exit tube, and the time for all of the liquid to flow through is recorded. Here are some results: time to flow through funnel trial Liquid X Liquid Y 1.60 s 3.62 s 1.52 s 3.44 s 1.44 s 3.56 s Note: the two liquids have the same density. Which statement below is true about these liquids based only on the data in the table? O The intermolecular forces in liquid X are stronger than those in liquid Y. The boiling point of liquid X is higher than the boiling point of liquid Y. The viscosity of liquid X is greater than the viscosity of liquid Y. The surface tension of liquid X is greater than the surface tension of liquid Y. The viscosity of liquid X is less than the viscosity of liquid Y. 3.

QUESTION 3 Solve the following differential equation in Matlab using ode45.m. Use time interval of 0.1 second. (Don't use options in ode45 to change teh tolerance.) df (t) +ƒ (t) ×sin(t) =0 dt f(0)=0.8. What is f(t=3.7)? 0.120 0.126 0.491 0.847 0.635 ○ 0.695 QUESTION 4

1| 2 | 3 | 4| 5 | 6 7 8 9 10 Measurement Flow Rate (liters/hr)| 1066 1022 | 1143 995 1004| 927 | 1024 | 945 979 | 1059 1. The table above contains 10 measurements taken of the volume flow rate through a pump running at a fixed operating conditions. Find the following statistical quantitie for this data set: a. The average flow rate: Vave liters/hr. b. The median flow rate: Vmedian liters/hr. c. The sample standard deviation: 0, liters/hr.

Cardiologists use the short-range scaling exponent α1, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article “Applying Fractal Analysis to Short Sets of Heart Rate Variability Data” compared values of α1 computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y) could be predicted the short-term one (x). Following are the data (obtained by digitizing a graph).  Short Long 0.54 0.55 1.02 0.79 1.4 0.81 0.88 0.9 1.68 1.05 1.16 1.05 0.82 1.05 0.93 1.07 1.26 1.1 1.18 1.19 0.81 1.19 0.81 1.2 1.28 1.23 1.18 1.23 0.71 1.24   Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text.     Compute the least-squares line for predicting the long-term measurement from the short-term measurement.…

T'sec In helical spring experiment a student plotted the graph of T2 versus the oscillating mass (M), and Used the slope to find the spring :constant, the value of k is 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 O. O a. 13.3 N/m O b. 6.8N/m O c. 5 N/m O d. 3.3 N/m O e. 24 N/m 5 10 15 20 25 30 35 40 45 50 55 60 65 M (9) 70 75 80

find initial velocity using following equation:

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The "spring-like effect" in a golf club could be determined by measuring the coeffi cient of restitution (the ratio of the outbound velocity to the inbound velocity of a golf ball fired at the clubhead). Twelve randomly selected drivers produced by two clubmakers are tested and the coefficient of restitution measured. The data follow: Club 1: 0.8406, 0.8104, 0.8234, 0.8198, 0.8235, 0.8562, 0.8123, 0.7976, 0.8184, 0.8265, 0.7773, 0.7871 Club 2: 0.8305, 0.7905, 0.8352, 0.8380, 0.8145, 0.8465, 0.8244, 0.8014, 0.8309, 0.8405, 0.8256, 0.8476 Test the hypothesis that both brands of ball have equal mean overall distance. Use a = 0.05 and assume equal variances. Answer the following questions regarding the t-test. 1. How many degrees-of-freedom are there in this problem (needed for finding the critical t- values). 2. What is the absolute values of the critical t-value for this problem? We are using a two- tailed t-test with a significance level of 5%. (use four significant figures) 3. What is…