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Fundamentals of Engineering Thermodynamics
8th Edition
ISBN: 9781118412930
Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey
Publisher: WILEY
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Question
Chapter 5.11, Problem 64P
To determine
Whether the power input of
The coefficient of performance of air conditioner.
Expert Solution & Answer
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Spur gears
Note : Exam is open notes &tables / Answer all questions.
Q.1. The press shown for Figure.1 has a rated load
of 22 kN. The twin screws have double start Acme
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Coefficients of friction are 0.05 for the threads and
0.08 for the collar bearings. Collar diameters are 90
mm. The gears have an efficiency of 95 percent and a
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(a) When the motor is turned on, how fast will the
press head move? (Vm= , Vser. =
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(5M)
(b) What should be the horsepower rating of the
motor? (TR=, Tc= Pser. =
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Bronze
bushings
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watt, Pm= watt, Pm= h.p.) (20M)
2['s
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Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.
Chapter 5 Solutions
Fundamentals of Engineering Thermodynamics
Ch. 5.11 - Prob. 1ECh. 5.11 - 2. Are health risks associated with consuming...Ch. 5.11 - Prob. 3ECh. 5.11 - Prob. 4ECh. 5.11 - Prob. 5ECh. 5.11 - 6. Does the second law impose performance limits...Ch. 5.11 - Prob. 7ECh. 5.11 - 8. What is delaying the appearance in new car...Ch. 5.11 - Prob. 9ECh. 5.11 - 10. How significant is the roughness at a pipe’s...
Ch. 5.11 - Prob. 11ECh. 5.11 - 12. What factors influence the actual coefficient...Ch. 5.11 - Prob. 13ECh. 5.11 - 14. How does the thermal glider (Sec. 5.4) sustain...Ch. 5.11 - 1. A reversible heat pump cycle operates between...Ch. 5.11 - Prob. 2CUCh. 5.11 - 3. Referring to the list of Sec. 5.3.1,...Ch. 5.11 - 4. Uses of the second law of thermodynamics...Ch. 5.11 - Prob. 5CUCh. 5.11 - Prob. 6CUCh. 5.11 - Prob. 7CUCh. 5.11 - Prob. 8CUCh. 5.11 - Prob. 9CUCh. 5.11 - Prob. 10CUCh. 5.11 - Prob. 11CUCh. 5.11 - Prob. 12CUCh. 5.11 - Prob. 13CUCh. 5.11 - Prob. 14CUCh. 5.11 - Prob. 15CUCh. 5.11 - Prob. 16CUCh. 5.11 - Prob. 17CUCh. 5.11 - 18. Referring to Fig. 5.15, if the boiler and...Ch. 5.11 - Prob. 19CUCh. 5.11 - Prob. 20CUCh. 5.11 - Prob. 21CUCh. 5.11 - 22. A cell phone initially has a fully charged...Ch. 5.11 - Prob. 23CUCh. 5.11 - Prob. 24CUCh. 5.11 - Prob. 25CUCh. 5.11 - Prob. 26CUCh. 5.11 - Prob. 27CUCh. 5.11 - 28. As shown in Fig. P5.28C, energy transfer...Ch. 5.11 - 29. As shown in Fig. P5.29C, a rigid, insulated...Ch. 5.11 - 30. As shown in Fig. P5.30C, when the steam in the...Ch. 5.11 - Prob. 31CUCh. 5.11 - Prob. 32CUCh. 5.11 - Prob. 33CUCh. 5.11 - Prob. 34CUCh. 5.11 - Prob. 35CUCh. 5.11 - Prob. 36CUCh. 5.11 - Prob. 37CUCh. 5.11 - Prob. 38CUCh. 5.11 - Prob. 39CUCh. 5.11 - Prob. 40CUCh. 5.11 - Prob. 41CUCh. 5.11 - Prob. 42CUCh. 5.11 - 43. The maximum coefficient of performance of any...Ch. 5.11 - Prob. 44CUCh. 5.11 - Prob. 45CUCh. 5.11 - Prob. 46CUCh. 5.11 - 47. When an isolated system undergoes a process,...Ch. 5.11 - Prob. 48CUCh. 5.11 - Prob. 49CUCh. 5.11 - Prob. 50CUCh. 5.11 - 5.1 Complete the demonstration of the equivalence...Ch. 5.11 - 5.2 Shown in Fig. P5.2 is a proposed system that...Ch. 5.11 - 5.3 Classify the following processes of a closed...Ch. 5.11 - Prob. 4PCh. 5.11 - Prob. 5PCh. 5.11 - Prob. 6PCh. 5.11 - 5.7 Provide the details left to the reader in the...Ch. 5.11 - 5.8 Using the Kelvin–Planck statement of the...Ch. 5.11 - Prob. 9PCh. 5.11 - Prob. 10PCh. 5.11 - Prob. 11PCh. 5.11 - Prob. 12PCh. 5.11 - Prob. 13PCh. 5.11 - Prob. 14PCh. 5.11 - 5.15 To increase the thermal efficiency of a...Ch. 5.11 - Prob. 16PCh. 5.11 - Prob. 17PCh. 5.11 - Prob. 18PCh. 5.11 - 5.19 A power cycle operating at steady state...Ch. 5.11 - 5.20 As shown in Fig. P5.20, a reversible power...Ch. 5.11 - Prob. 21PCh. 5.11 - Prob. 22PCh. 5.11 - Prob. 23PCh. 5.11 - Prob. 24PCh. 5.11 - Prob. 25PCh. 5.11 - Prob. 26PCh. 5.11 - Prob. 27PCh. 5.11 - Prob. 28PCh. 5.11 - Prob. 29PCh. 5.11 - Prob. 30PCh. 5.11 - Prob. 31PCh. 5.11 - Prob. 32PCh. 5.11 - Prob. 33PCh. 5.11 - 5.34 A power cycle operates between hot and cold...Ch. 5.11 - Prob. 35PCh. 5.11 - 5.36 An inventor claims to have developed a power...Ch. 5.11 - Prob. 37PCh. 5.11 - Prob. 38PCh. 5.11 - 5.39 As shown in Fig. P5.39, a system undergoing a...Ch. 5.11 - Prob. 40PCh. 5.11 - Prob. 41PCh. 5.11 - Prob. 42PCh. 5.11 - Prob. 43PCh. 5.11 - 5.44 A reversible refrigeration cycle operates...Ch. 5.11 - Prob. 45PCh. 5.11 - 5.46 A heating system must maintain the interior...Ch. 5.11 - Prob. 47PCh. 5.11 - 5.48 The thermal efficiency of a reversible power...Ch. 5.11 - 5.49 Shown in Fig. P5.49 is a system consisting of...Ch. 5.11 - 5.50 An inventor has developed a refrigerator...Ch. 5.11 - 5.51 An inventor claims to have developed a food...Ch. 5.11 - 5.52 An inventor claims to have developed a...Ch. 5.11 - 5.53 An inventor claims to have devised a...Ch. 5.11 - 5.54 Data are provided for two reversible...Ch. 5.11 - 5.55 By removing energy by heat transfer from its...Ch. 5.11 - 5.56 At steady state, a refrigeration cycle...Ch. 5.11 - Prob. 57PCh. 5.11 - 5.58 At steady state, a refrigeration cycle...Ch. 5.11 - Prob. 59PCh. 5.11 - Prob. 60PCh. 5.11 - Prob. 61PCh. 5.11 - Prob. 62PCh. 5.11 - Prob. 63PCh. 5.11 - 5.64 As shown in Fig P5.64, an air conditioner...Ch. 5.11 - Prob. 65PCh. 5.11 - Prob. 66PCh. 5.11 - 5.68 The refrigerator shown in Fig. P5.68 operates...Ch. 5.11 - Prob. 69PCh. 5.11 - 5.70 By supplying energy at an average rate of...Ch. 5.11 - 5.71 A heat pump with a coefficient of performance...Ch. 5.11 - 5.72 As shown in Fig. P5.72, a heat pump provides...Ch. 5.11 - 5.73 As shown in Fig. P 5.73, a heat pump receives...Ch. 5.11 - Prob. 74PCh. 5.11 - Prob. 75PCh. 5.11 - Prob. 76PCh. 5.11 - Prob. 77PCh. 5.11 - Prob. 78PCh. 5.11 - Prob. 79PCh. 5.11 - Prob. 80PCh. 5.11 - 5.81 A quantity of water within a piston–cylinder...Ch. 5.11 - Prob. 82PCh. 5.11 - 5.83 Two kilograms of air within a piston–cylinder...Ch. 5.11 - Prob. 84PCh. 5.11 - Prob. 85PCh. 5.11 - Prob. 86PCh. 5.11 - Prob. 87PCh. 5.11 - Prob. 88PCh. 5.11 - Prob. 89PCh. 5.11 - 5.90 Figure P5.90 gives the schematic of a vapor...Ch. 5.11 - Prob. 91PCh. 5.11 - Prob. 92PCh. 5.11 - 5.93 As shown in Fig. P5.93, a system executes a...Ch. 5.11 - Prob. 94P
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- Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
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