Hw10soln

Hw10soln - ME 375 Homework 10 Solution Problem 1 a Derive...

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Unformatted text preview: ME 375 Homework 10 : Solution April 28, 2009 Problem 1 a) Derive the dfferential equation that relates y to P: From the FBD we can derive the following equation Solution: Figure 1: FBD M ¨ y + B ˙ y = ( P- P r ) A- mg b) Write an expression for the fluid flow rate Q in terms of y and/or its derivatives. Solution: Q = A ˙ y 1 Problem 2 a) Find R f , I, C: Solution: R f = 128 μL πd 4 = (128)(1 . 03)(10- 2 )(50) π (0 . 02) 4 = 1 . 311(10 8 ) Unit for R f : [ Nsec m 5 ] I = ρL A = (8 . 91)(50) . 02 2 4 π = 1 . 42(10 6 ) Unit for I: [ kg m 4 ] C = A ρg = . 25 2 4 π (8 . 91)(9 . 81) = 5 . 6(10- 4 ) Unit for C: [ m 5 N ] b) Derive the system transfer function when P r is the input and the reservoir pressure P 3 r is the output. Solution: Figure 2: Electrical Equivalent Scheme P 3 r P s = 1 IC f s 2 + R f C f s + 1 2 c) Find ω n and ζ IC f s 2 + R f C f s + 1 = s 2 ω 2 n + 2 ζ ω n s + 1 ω n = 1 IC f = 0 . 035 rad/sec ζ = R f C f ω n 2 = 1303 Since ζ >> 1, we need to determine the 2 first-order poles.1, we need to determine the 2 first-order poles....
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This note was uploaded on 08/28/2010 for the course ME 375 taught by Professor Meckle during the Spring '10 term at Purdue.

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Hw10soln - ME 375 Homework 10 Solution Problem 1 a Derive...

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