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

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Date Created: 02/06/15

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 PM quot 300 m 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 M931 quot19 is I Q 972qJ nf A 3 IAN l3 l3 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 1 4 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 1 6 H 4 o Solution 1 1 0H 1ch 0 Given the same three quan 39ties a 755 b 6044 and c 10451 Calculate the average of a b and c to the ap ropriate precision and number of significant digits Solution 10391 L 8515 3 39 vanWA 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 Nmz To do Express the primary dimensions of r ie write an expression for T Solution WHYth iis we 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 391 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 L 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 W To do Express the relationship between W T and a in dimensionless form T Solution 0 Step1 W Z 399 quot E Step 2 3 k m i wag2 Step3 y 23 LI Wt J quotI 3 k 3 331LL7U NV 9 313A 1 0 kiwiquot 3 7quot Step 4 ewlt MW l w f wk T 1 OJ 0 A a K w T w mww39w 1 a l ins EV S iii 0 a M39 m t m M 3 m q 52 quot La 7 L1 L 1quot H 1 a d I 7 I 0 1 0 3c 5 Jc r 439 quot S QEKC 4 MUM Covuhn t a k l

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