Refrigeration and Air Conditioning Technology (MindTap Course List)
8th Edition
ISBN: 9781305578296
Author: John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Publisher: Cengage Learning
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Chapter 26, Problem 14RQ
Explain how the oil separator, oil reservoir, pressure differential valve, and oil-level regulators work together tomaintain the correct oil level in parallel compressors.
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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.
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.
Problem 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).
Chapter 26 Solutions
Refrigeration and Air Conditioning Technology (MindTap Course List)
Ch. 26 - The two broad categories of display cases are...Ch. 26 - How are conditions maintained in open display...Ch. 26 - What are mullion heaters?Ch. 26 - The three temperature ranges for refrigeration...Ch. 26 - The two methods for rejecting heat from...Ch. 26 - When the compressors are located in the equipment...Ch. 26 - When one large compressor is used, what desirable...Ch. 26 - Define a parallel compressor system and list five...Ch. 26 - Three disadvantages of parallel compressor systems...Ch. 26 - What is the difference between an even and an...
Ch. 26 - Exactly matching the refrigeration load with the...Ch. 26 - What is the function of the pressure transducer in...Ch. 26 - What is the function of the microprocessor-based...Ch. 26 - Explain how the oil separator, oil reservoir,...Ch. 26 - Large or small compressors on parallel compressor...Ch. 26 - A(n)_______varies the frequency of an...Ch. 26 - Prob. 17RQCh. 26 - Prob. 18RQCh. 26 - Three advantages of unitary, stand-alone...Ch. 26 - How is defrost accomplished when the equipment...Ch. 26 - True or False: The two types of defrosts used with...Ch. 26 - What special precautions should be taken with...Ch. 26 - Prob. 23RQCh. 26 - What special valve is used in a refrigerated air...Ch. 26 - Briefly explain what is meant by a surge-type...Ch. 26 - Briefly explain what is meant by a subcritical...Ch. 26 - Briefly explain what is meant by a transcritical...Ch. 26 - Prob. 28RQCh. 26 - Prob. 29RQCh. 26 - Prob. 30RQCh. 26 - Prob. 31RQCh. 26 - Prob. 32RQCh. 26 - Prob. 33RQ
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- Problem 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_forwardI 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_forward
- B1 Please help on the attached question.arrow_forwardQu 4 A cylindrical metal specimen 15.0 mm in diameter and 150 mm long is to be subjected to a tensile stress of 50 MPa; at this stress level, the resulting deformation will be totally elastic. If the elongation must be less than 0.072 mm, which of the metals in Table 1 are suitable candidates? If, in addition, the maximum permissible diameter decrease is 2.3 × 10-3 mm when the tensile stress of 50 MPa is applied, which of the metals that satisfy the criterion in part (a) are suitable candidates? see on the tables given part a and b i need to show all work problems formula step by step please make sure is correctly material sciencearrow_forwardZ4 please help on the attached question.arrow_forward
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