Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
5th Edition
ISBN: 9780321816252
Author: C. Henry Edwards, David E. Penney, David Calvis
Publisher: PEARSON
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Chapter 5.4, Problem 27P
(a)
Program Plan Intro
Program Description: Purpose of the problem is to obtain the natural frequencies of oscillation for the given system.
(b)
Program Plan Intro
Program Description: Purpose of the problem is to obtain the critical speed for wavelength of
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The circular rod shown is made of the steel alloy AISI 4140 OQT 900. It has a diameter of
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1. the equivalent spring constant K,
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SITUATION 1 (Fluid Flow in a Closed Conduit)
Consider a fluid, with density (p) of 998.21 kg/m³ and dynamic viscosity (u) of 1.002 x 103 N-s/m², flowing in a 2000-meter long, 50-mm diameter
smooth round pipe with velocity of 2.5 m/s. The energy loss on the pipe flow (he) due to friction between the pipe and the fluid is determined using
Darcy-Weisbach equation, given as
h₁ = f (²) (1/1)
where f is the friction factor, L is the length of the pipe, D is the diameter of the pipe, V is the velocity of the flow, and g is the gravitational
acceleration. The friction factor may be determined using an empirical equation developed by Nikuradse for flow in smooth pipes, given as
1
=0.869 In (Re√7)-0.8
where Re is the Reynolds number of the flow, determined as
VDp
R₂ =
μl
The friction factor equation given is only valid for flows with Reynolds number higher than 4000 (turbulent flow).
Guide Questions:
Determine the Reynolds number of the flow. Is the Nikuradse equation for friction factor…
Determine the transfer function, of the rotational mechanical system shown in
T(s)
Figure Q2. The variables 6,(t) and 02(t) refer to angular displacement of motion,
while T(t) is a torque applied to the system. Given the value of spring, damping
coefficient and inertia as;
J: 5 kg-m?
Di: 5 N-m-s/rad
J2: 10 kg-m?
K : 6 N-m/rad
K2 : 5 N-m/rad
D::4 N-m-s/rad
D3:2 N-m-s/rad
T(t)
e,(1)
D2
K2
0000
D1
D3
Figure Q2
Chapter 5 Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
Ch. 5.1 - Let A=[2347] and B=[3451]. Find (a) 2A+3B; (b)...Ch. 5.1 - Prob. 2PCh. 5.1 - Find AB and BA given A=[203415] and B=[137032].Ch. 5.1 - Prob. 4PCh. 5.1 - Prob. 5PCh. 5.1 - Prob. 6PCh. 5.1 - Prob. 7PCh. 5.1 - Prob. 8PCh. 5.1 - Prob. 9PCh. 5.1 - Prob. 10P
Ch. 5.1 - Prob. 11PCh. 5.1 - Prob. 12PCh. 5.1 - Prob. 13PCh. 5.1 - Prob. 14PCh. 5.1 - Prob. 15PCh. 5.1 - Prob. 16PCh. 5.1 - Prob. 17PCh. 5.1 - Prob. 18PCh. 5.1 - Prob. 19PCh. 5.1 - Prob. 20PCh. 5.1 - Prob. 21PCh. 5.1 - Prob. 22PCh. 5.1 - Prob. 23PCh. 5.1 - Prob. 24PCh. 5.1 - Prob. 25PCh. 5.1 - Prob. 26PCh. 5.1 - Prob. 27PCh. 5.1 - Prob. 28PCh. 5.1 - Prob. 29PCh. 5.1 - Prob. 30PCh. 5.1 - Prob. 31PCh. 5.1 - Prob. 32PCh. 5.1 - Prob. 33PCh. 5.1 - Prob. 34PCh. 5.1 - Prob. 35PCh. 5.1 - Prob. 36PCh. 5.1 - Prob. 37PCh. 5.1 - Prob. 38PCh. 5.1 - Prob. 39PCh. 5.1 - Prob. 40PCh. 5.1 - Prob. 41PCh. 5.1 - Prob. 42PCh. 5.1 - Prob. 43PCh. 5.1 - Prob. 44PCh. 5.1 - Prob. 45PCh. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 5PCh. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.2 - Prob. 9PCh. 5.2 - Prob. 10PCh. 5.2 - Prob. 11PCh. 5.2 - Prob. 12PCh. 5.2 - Prob. 13PCh. 5.2 - Prob. 14PCh. 5.2 - Prob. 15PCh. 5.2 - Prob. 16PCh. 5.2 - Prob. 17PCh. 5.2 - Prob. 18PCh. 5.2 - Prob. 19PCh. 5.2 - Prob. 20PCh. 5.2 - Prob. 21PCh. 5.2 - Prob. 22PCh. 5.2 - Prob. 23PCh. 5.2 - Prob. 24PCh. 5.2 - Prob. 25PCh. 5.2 - Prob. 26PCh. 5.2 - Prob. 27PCh. 5.2 - Prob. 28PCh. 5.2 - Prob. 29PCh. 5.2 - Prob. 30PCh. 5.2 - Prob. 31PCh. 5.2 - Prob. 32PCh. 5.2 - Prob. 33PCh. 5.2 - Prob. 34PCh. 5.2 - Prob. 35PCh. 5.2 - Prob. 36PCh. 5.2 - Prob. 37PCh. 5.2 - Prob. 38PCh. 5.2 - Prob. 39PCh. 5.2 - Prob. 40PCh. 5.2 - Prob. 41PCh. 5.2 - Prob. 42PCh. 5.2 - Prob. 43PCh. 5.2 - Prob. 44PCh. 5.2 - Prob. 45PCh. 5.2 - Prob. 46PCh. 5.2 - Prob. 47PCh. 5.2 - Prob. 48PCh. 5.2 - Prob. 49PCh. 5.2 - Prob. 50PCh. 5.3 - Prob. 1PCh. 5.3 - Prob. 2PCh. 5.3 - Prob. 3PCh. 5.3 - Prob. 4PCh. 5.3 - Prob. 5PCh. 5.3 - Prob. 6PCh. 5.3 - Prob. 7PCh. 5.3 - Prob. 8PCh. 5.3 - Prob. 9PCh. 5.3 - Prob. 10PCh. 5.3 - Prob. 11PCh. 5.3 - Prob. 12PCh. 5.3 - Prob. 13PCh. 5.3 - Prob. 14PCh. 5.3 - Prob. 15PCh. 5.3 - Prob. 16PCh. 5.3 - Prob. 17PCh. 5.3 - Prob. 18PCh. 5.3 - Prob. 19PCh. 5.3 - Prob. 20PCh. 5.3 - Prob. 21PCh. 5.3 - Prob. 22PCh. 5.3 - Prob. 23PCh. 5.3 - Prob. 24PCh. 5.3 - Prob. 25PCh. 5.3 - Prob. 26PCh. 5.3 - Prob. 27PCh. 5.3 - Prob. 28PCh. 5.3 - Prob. 29PCh. 5.3 - Prob. 30PCh. 5.3 - Prob. 31PCh. 5.3 - Prob. 32PCh. 5.3 - Prob. 33PCh. 5.3 - Verify Eq. (53) by substituting the expressions...Ch. 5.3 - Prob. 35PCh. 5.3 - Prob. 36PCh. 5.3 - Prob. 37PCh. 5.3 - Prob. 38PCh. 5.3 - Prob. 39PCh. 5.3 - Prob. 40PCh. 5.4 - Prob. 1PCh. 5.4 - Prob. 2PCh. 5.4 - Prob. 3PCh. 5.4 - Prob. 4PCh. 5.4 - Prob. 5PCh. 5.4 - Prob. 6PCh. 5.4 - Prob. 7PCh. 5.4 - Prob. 8PCh. 5.4 - Prob. 9PCh. 5.4 - Prob. 10PCh. 5.4 - Prob. 11PCh. 5.4 - Prob. 12PCh. 5.4 - Prob. 13PCh. 5.4 - Prob. 14PCh. 5.4 - Prob. 15PCh. 5.4 - Prob. 16PCh. 5.4 - Prob. 17PCh. 5.4 - Prob. 18PCh. 5.4 - Prob. 19PCh. 5.4 - Prob. 20PCh. 5.4 - Prob. 21PCh. 5.4 - Prob. 22PCh. 5.4 - Prob. 23PCh. 5.4 - Prob. 24PCh. 5.4 - Prob. 25PCh. 5.4 - Prob. 26PCh. 5.4 - Prob. 27PCh. 5.4 - Prob. 28PCh. 5.4 - Prob. 29PCh. 5.5 - Prob. 1PCh. 5.5 - Prob. 2PCh. 5.5 - Prob. 3PCh. 5.5 - Prob. 4PCh. 5.5 - Prob. 5PCh. 5.5 - Prob. 6PCh. 5.5 - Prob. 7PCh. 5.5 - Prob. 8PCh. 5.5 - Prob. 9PCh. 5.5 - Prob. 10PCh. 5.5 - Prob. 11PCh. 5.5 - Prob. 12PCh. 5.5 - Prob. 13PCh. 5.5 - Prob. 14PCh. 5.5 - Prob. 15PCh. 5.5 - Prob. 16PCh. 5.5 - Prob. 17PCh. 5.5 - Prob. 18PCh. 5.5 - Prob. 19PCh. 5.5 - Prob. 20PCh. 5.5 - Prob. 21PCh. 5.5 - Prob. 22PCh. 5.5 - Prob. 23PCh. 5.5 - Prob. 24PCh. 5.5 - Prob. 25PCh. 5.5 - Prob. 26PCh. 5.5 - Prob. 27PCh. 5.5 - Prob. 28PCh. 5.5 - Prob. 29PCh. 5.5 - Prob. 30PCh. 5.5 - Prob. 31PCh. 5.5 - Prob. 32PCh. 5.5 - Prob. 33PCh. 5.5 - Prob. 34PCh. 5.5 - Prob. 35PCh. 5.5 - Prob. 36PCh. 5.6 - Prob. 1PCh. 5.6 - Prob. 2PCh. 5.6 - Prob. 3PCh. 5.6 - Prob. 4PCh. 5.6 - Prob. 5PCh. 5.6 - Prob. 6PCh. 5.6 - Prob. 7PCh. 5.6 - Prob. 8PCh. 5.6 - Prob. 9PCh. 5.6 - Prob. 10PCh. 5.6 - Prob. 11PCh. 5.6 - Prob. 12PCh. 5.6 - Prob. 13PCh. 5.6 - Prob. 14PCh. 5.6 - Prob. 15PCh. 5.6 - Prob. 16PCh. 5.6 - Prob. 17PCh. 5.6 - Prob. 18PCh. 5.6 - Prob. 19PCh. 5.6 - Prob. 20PCh. 5.6 - Prob. 21PCh. 5.6 - Prob. 22PCh. 5.6 - Prob. 23PCh. 5.6 - Prob. 24PCh. 5.6 - Prob. 25PCh. 5.6 - Prob. 26PCh. 5.6 - Prob. 27PCh. 5.6 - Prob. 28PCh. 5.6 - Prob. 29PCh. 5.6 - Prob. 30PCh. 5.6 - Prob. 31PCh. 5.6 - Prob. 32PCh. 5.6 - Prob. 33PCh. 5.6 - Prob. 34PCh. 5.6 - Prob. 35PCh. 5.6 - Prob. 36PCh. 5.6 - Prob. 37PCh. 5.6 - Prob. 38PCh. 5.6 - Prob. 39PCh. 5.6 - Prob. 40PCh. 5.7 - Prob. 1PCh. 5.7 - Prob. 2PCh. 5.7 - Prob. 3PCh. 5.7 - Prob. 4PCh. 5.7 - Prob. 5PCh. 5.7 - Prob. 6PCh. 5.7 - Prob. 7PCh. 5.7 - Prob. 8PCh. 5.7 - Prob. 9PCh. 5.7 - Prob. 10PCh. 5.7 - Prob. 11PCh. 5.7 - Prob. 12PCh. 5.7 - Prob. 13PCh. 5.7 - Prob. 14PCh. 5.7 - Prob. 15PCh. 5.7 - Prob. 16PCh. 5.7 - Prob. 17PCh. 5.7 - Prob. 18PCh. 5.7 - Prob. 19PCh. 5.7 - Prob. 20PCh. 5.7 - Prob. 21PCh. 5.7 - Prob. 22PCh. 5.7 - Prob. 23PCh. 5.7 - Prob. 24PCh. 5.7 - Prob. 25PCh. 5.7 - Prob. 26PCh. 5.7 - Prob. 27PCh. 5.7 - Prob. 28PCh. 5.7 - Prob. 29PCh. 5.7 - Prob. 30PCh. 5.7 - Prob. 31PCh. 5.7 - Prob. 32PCh. 5.7 - Prob. 33PCh. 5.7 - Prob. 34P
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