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# 143 Class Note for M E 345 with Professor Cimbala at PSU

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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 25 views.

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Date Created: 02/06/15
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 gt u 39 very long round tube Volume ow rate V is a function of the D I 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 AP A Step1 V FM 5 J A 1quot 4 L3 Q quotquot Step2 l M M lttl loci 6W V quot393 m u N Pu 33 M4 mm quotHoquot quot quot q 3zx Step4 m 3 We Wu M b m WAx Step5 K b Mkk xy Step 3 1 A m a M c tm 39l V43 M 3th l 51 1 Mo 1 M5quot 3 mo quoter a L o 3 M 49 u t o 2 A u q ow 3 Av4 1U 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 1 M81 1 Qlr W l w VA quotM o 39 um wow b L 39 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 2215 11x 21100 1 on TLJE 39LZ81 new 1 o03 2222 on am 2209 3303 oo 409 2221 em 003 2218 008 m 2224 I o m o06 Solution MM my 11I a 3921 33 l u g u 5 m N l39Nt Vlc uJ fvlwzo0z MGE Jaww om 2 Mt Wbu MSE 0K 89 v 4 th M 15 4quot J s and 71 cw 3 JMU MW 00812 39 a m yaw w 4quot 39 3 1 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 242000 l 2 253000 h s J u fu h d 3 264000 San5M 3 4 267500 5 269000 6 278000 7 mumquot 39quot L mquot L 7 286500 8 299000 9 327000 10 748000 To do Calculate the mean n10d and median and discuss Solution M 1 5 Hoo A 3 quot Unk n n NW new i Mi ox an Amw quotm C A Amid L ujc pm My 1 ov f ti n Aft Inullu 30 Jul moh l mu u Lea 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 WRK PM Mr N wR NAN 895 an L6 897 h FM 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 c The sample mode a 531 war 1 0 3 C Ln mtm 2931 c Lax Nah K391 39c Solution

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