Exam 1 solution ME 340.pdf - Exam 1 ME 340 1 An engineer...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Exam 1 ME 340 1. An engineer needs to measure velocity using a pitot tube with a pressure transducer, and has been asked about the accuracy ofthe resulting measurements. The method is quite inexpensive, but the engineer’s boss is worried about the uncertainty in the result. The boss thinks that a much more expensive measurement is needed. The expensive measurement system has a 2% uncertainty (95% confidence) in velocity at the level of the measurement. The more expensive method does not depend on the air density, p. The engineer prepares an uncertainty analysis of the pitot tube based on the data below. The question is: Should the engineer use the pitot tube or the more expensive technique? Pitot + transducer characteristics: Full scale: 1” H20 Sensitivity error: 1% full scale Linearity error: 1% of reading Transducer resolution: 0.005” H20 50 data points were taken. Average Pressure: 0.5” H20, Standard Deviation of Readings: 0.01” H20 ECAp ,0 pressure measurement. The constant C' Is a conversion factor which converts the velocity into m/s for the set-up being used. Data Reduction Equation: U = —where p is the density of the air being measured and Ap' Is the )9 (a) What is the 95% confidence level uncertainty for (units of in H20): - u u " ‘ a. SenSItIVIty I to ] HID b. Linearity i,WS“" Q“ 743.. afimfifl c. Transducer resolution I." '959..__$h._ = teams” I” “ma '2. $6 (b) What is the uncertainty in the measured pressure (not the average pressure)? 1 ‘2. '2 “)z‘ :2 i/ Col) +(fms)r~(:em3 90“; fié (c) What is the 95% statistical confidence interval of the average pressure? )2: -/V-/=~ ’7"? w 263': I Mr ,0 ; ~56 (d) Find the uncertainty in the measured velocity (not average velocity) caused by the measurement of pres-sure 2‘(assume C and p are both 1 for this part): 3 =1 L AF . 2;?— M) (air): 2AF ’2' ‘ / /O :- 0: 2: AF 1/ 4- '/ g (‘ ii: ’° 92 = E ; —'- = i Mu: , /..- at 5:115“ “P x? 4-5 “““““ cNWWETaT‘? H ' "" at": ,01/5’ “r a"? ' i/(e) What is the 95% statistical confidence interval for the average velocity based on the average Pressure? F: .j. (7 P I: K 0028? U. 4' U3: \fzf. 522w) .: l3. 002%“? — I: Jififlfifll' F 2 cl‘iiitZ ,9? ?Z 4, EL 4 AQO‘ZZJ/ " v/ (1‘) What other information or data would you like to know before answering the boss’ Question? E3: INN. Host a finellf'H/xc—n (A . thy. flxfia'fifiufi 5% a'l‘flm 00) Can exFTsc::eiafii=Hm' 2. An engineer was attempting to fit some calibration data to a curve fit. She knew the data was non-linear, but was not sure of the exact formulation. She attempted to fit a cubic polynomial to the data using a technique taught in her statistics class. The attempted curve fit output and the plot of the output is given. Equation fit: 31 = a0 + aix + a2(x — 232 + as (x — if SUMMARY OUTPUT Regression Statistics Multiple R 0982414819 R Square 0965138878 Adjusted R Squal 0947708316 Standard Error 7585038057 Observations 10 AN OVA df 55 M5 F Signmicance F Regression 3 9556859961 3185619987 5537049924 9.14569E-05 Residual [3] 3451968139 5753280232 Total 9 9902056775 Coe icr‘en ts Standard Error P- value _ __ Lower 95% Upper 95% 7 Intercept —8. 922093089 1040399029 0857564535 0424057893 3437974022 1653555405 x- 1111859579 2166790833 513136553 0002154128 5816649623 16. 42054196 (x-xmeanii‘z (x-xmean)"3 0. 914754467 —0.041571478 0330096411 2.771173619 0032372223 0136478069 -0.305334511 0770426684 0107037646 1.722471288 41375621283 0292273327 96 Identify the coefficients for ea . h term, an, al, a2, a3 < 9(— Which coefficients are significantly different than zero? (support the answer) owns nets-15m :4th tin-cm 76.261— L fine—g “PW-£723 9472 a» M" m J arr/— > 67625—2; a, I all STBDt‘gmfl'lfi/at 74‘5’ 96 What is the 95% confidence interval on each coefficients? € "MWIWW How many degrees of freedom went into the estimate ofthe error? G (52.9. 4.9:: V6.) ‘96 What i'sth995%confidence intervalon the fit? 5+4 8%“: 3' 5-85- 3 S35 g X _ fig": 2.252- %e i "tum L : raa :t 2267-7585" WT .r—M/fi éjai’ 643 Is the fit acceptable? If not, what should the engineer do next (don’t ask for more data)? m 3mg M 2:3 74W 4! Scientists studying the population of foxes and mice in a remote Indiana county took data on the mice and fox populations monthly over a period of 20 years. A student processed the data using an FFT and presented them with results below. (-98% U909?- SPeCi‘WM 3 l/ a. What is the lowest and highest frequency present in the FT (not including the DC component)? C 59“- Wxis-L— N’ZoMZ-IZVD spew—a wheat/Wt ”were. 40 I 5%: /Mo'rt" lead-gust} geygré/aa mfg-7R .20 96 b. What was the average fox population over the 20 year period? M 40 :76“ O ,25' L0 7C 96 c. What is the primary PERIOD of the cycle in the fox population? 4amz-“L” I '25—” 96 d. What is the secondary PERIOD of the cycle in the fox population? liar-Lin 3 r / e. Describe how you would use this data to determine the variance in the fox population over the 20 year period. TuKe C: A fired +£UL Hm, Comte: 5K The figure below is the step response of a measurement system. 99- a. Describe the most likely system order (Zero, First or Second Order System} S-eCoflC‘ 0‘? fl 3(- b. What is the ringing frequency ofthe measurement system? ’ 49d =J.__. .2: "25.92 Ha #213 ”A 2 avid-s: «£313 96- c. lfi;=0.3, what isthe naturalfrequency ofthe system? (422‘ 1 CO"? 11/??? of‘ '6‘: gag-1:9 4;): gawk/E a)”: 5‘59,QQ raid- d. Write the transfer function of the system \ 3.2“? . a W“‘“‘” 6(3):“ [3.67-3u0“ 52+ -ooHS'” 5 4‘13” e. Sketch the frequency response of the system (approximately). / f. For the measurements needed, the response of the system is acceptable if the measured value is within 25% of the actual values. What is the bandwidth of the system FOR TH ESE MEASURMENTS? State the bandwidth in terms of frequencies. fire“ Q‘éwe—aia a: van": a5" rs mam-49a %&M¢3fb~_ a» as: a ‘75; a, o 44*er as 5-5 / g. The engineer has a requirement to measure frequencies up to 100 hz,-can this measurement system be used (using the criteria from part f)? Why or why not? ,- r- user-fl N - / diam «rifle-f Wm a: f 713%” ‘70 fife- ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern