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Instrumentation, Measurements, and Statistics

by: Chester Goldner III

Instrumentation, Measurements, and Statistics M E 345

Marketplace > Pennsylvania State University > Mechanical Engineering > M E 345 > Instrumentation Measurements and Statistics
Chester Goldner III
Penn State
GPA 3.79

John Cimbala

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John Cimbala
Class Notes
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This 0 page Class Notes was uploaded by Chester Goldner III on Sunday November 1, 2015. The Class Notes belongs to M E 345 at Pennsylvania State University taught by John Cimbala in Fall. Since its upload, it has received 17 views. For similar materials see /class/233070/m-e-345-pennsylvania-state-university in Mechanical Engineering at Pennsylvania State University.

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Date Created: 11/01/15
M E 345 Fall 2009 Professor John M Cimbala Today we will Do another example problem dimensional analysis Review the pdf module Errors and Calibration Do some example problems errors and calibration Review the pdf module Basic Statistics Do some example problems basic statistics Example Dimensional analysis pipe ow Given Consider fully developed laminar ow through a V D gt 11 very long round tube Volume ow rate V is a function of the tube s inner diameter D uid viscosity u and axial pressure gradient dPdx Pressure gradient dPdx To do If D is doubled holding u and dPdx fixed by what factor does V change Solution Use dimensional analysis to generate a nondimensional functional relationship v a Us A W lil lil Step2 kgES iLS t ltn 39 m Ml 6 J Pu 33 mm mm quotMLquot quot quot 39 q 3zx Step 3 Step 4 Pu 3 vm u l 39 l d 5 I WAX Step5 K b trig W39s V43 M or 2653 o C hf v M M 1 MM 3 M m 1 o gm bu t o 44 u 39 quotl Step 6 V AN I b I Answer If D is doubled holding u and dPdx fixed V goes up by a factor of 1 or Example Errors and calibration Given The actual true voltage is 46020 V 26 voltage readings are taken and the average voltage reading is 46015 V To do a Calculate the systematic bias error and the mean bias error for this set of measurements b Calculate the random precision error of a reading that is 46010 V Solution 8 UM Avquot 4A A lieu quotHug 1 t 0000 V 39 0 0 a Q f WW VAN g 391 annoy b a L MAW w 46019 1 on Example Errors and calibration Given The actual true temperature is 22100 C Six thermometer readings are taken 2215 2222 2209 2221 2218 and 2224 C To do Calculate the mean systematic error and mean bias error for this set of data and calculate the accuracy error inaccuracy and the precision error for each measurement T C Inaccuracy T Tm 0C Precision error Ti 0C 22157 11x 21100 1 on TLJE 39LZ81 new 1 o03 2222 on am 2209 E m 430 oo9 2221 em 003 2218 008 m 2224 I o m o06 Solution MM my 11I a 3921 33 r u 39 5 m N l39Nt V c uJ fvl W MGEJW quotquot cm H id 39I7f MSE V 0 in yaw 0 39 51 Am See also Excel spreadsheet on the website for this same problem Example Basic statistics Given Ten houses are sold in the State College area during a particular time period The selling prices are listed in increasing order rounded to the nearest 500 dollars 1 h l J lh fu h d Sunfwdc JV 1quot INC 51m 4v VF 39nu L 2 3 4 5 6 7 8 9 A O To do Calculate the mean mode and median and discuss Solution M 1 5 Hoo A 3 quot Unk n n NW Mun i Mi ox an Amw quotm C A Amid L ujc pm My L ov f 4 m If Imllv u in Metal man u LtHu39 Example Basic statistics Given The true exact temperature of a hot water tank is 8968 C Ten temperature readings are taken with a digital thermometer The sample mean is 8937 891 894 892 896 893 894 mm ms m w M W 895 6 LA 0 L 897 F5 7 894 891 To do Calculate the following giVing your answers to the appropriate number of significant digits a The systematic error of the instrument based on these readings b The sample median S c The sample mode a w mr Solution L m na L0 Ma 5


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