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# Instrumentation, Measurements, and Statistics M E 345

Penn State

GPA 3.79

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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 13 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

ME345 Fall 2009 Professor John M Cimbala Today we will Do some more example problems significant digits Review the pdf module Dimensional Analysis Do some example problems dimensional analysis Example Signi cant digits Gas mileage calculations a Given You travel 2100 miles in your new car and use 700 gallons of gas To do Calculate your gas mileage in units of miles per gallon Give your answer to the appropriate number of significant digits Solution M PJ quot 300 my 10s L9H r b Given You estimate that your car gets 28 miles per gallon Gas costs 2899 per gallon To do How much does it cost to travel 455 miles Give your answer to the appropriate number of signi cant digits Cm Wry ltusa 341 909 Solution 1 X H7JOX7 Y Aw M7 or M 0 Given You fill up your tank drive 3165 miles and pay 4489 to fill up your tank again Gas costs 2799 per gallon To do Calculate your gas mileage in units of miles per gallon Give your answer to the appropriate number of significant digits Solution e 31 m39 2133 39V Paquot l A 973quot quot 1 9 AVku r UH M Example Signi cant digits Given Three quantities are measured a 755 b 6044 and c 10451 To do a Calculate a b giving your answer to the appropriate precision and number of significant digits Solution b Given the same three quantities a 755 b 6044 and c 10451 Calculate a b 0 giving your answer to the appropriate precision and number of signi cant digits Solution OK My on 4 Jun 40101 Example Primary dimensions shear stress force per unit length and power a Given In uid mechanics shear stress 239 is expressed in units of Nm2 To do Express the primary dimensions of r ie write an expression for T Solution F mLv N quot quot b Given Ray is conducting an experiment in which quantity a has dimensions of force per unit length A quot To do Express the primary dimensions of a ie write an expression for a Solution 2 F m J1 M a3 v z 39T 2 1 L t y 5c c Given Power W has the dimensions of energy per unit time To do Write the dimensions of power in terms of primary dimensions Solution Em 7 R u quot Vl wc PW Hat 339 FxL MLL V LI Niquot T Kk k U Example Dimensional analysis shaft power Given The output power W of a spinning shaft is a function of torque T and angular velocity 0 To do Express the relationship between W T and a in dimensionless form Solution Step1 E 399 quot EINgt 2 whyMl X7 Step3 Yy 03 LI wt JUL M39L t Lin39o 3 3390 J NV 9 313A 1 0 kiwiquot 3 7quot Step 4 ewlt MW l w f wk T OJ 0 A a K w T w mww39w Waist Kquotamp mquot H o l 0 390 m 2 m M 3 m q 52 quot La A L1 Lu Lu H 1 a 0 0 7 IL 0 Z i k 1 k 5c k w a Sm 2 T 4 mow Cons fM Y

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