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**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- ...

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