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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 4.12, Problem 11CU
To determine
The device that creates the restriction in a line to decrease the pressure of a gas or liquid.
Expert Solution & Answer
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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 4 Solutions
Fundamentals of Engineering Thermodynamics
Ch. 4.12 - Prob. 1ECh. 4.12 - 2. When a drip coffeemaker on-off switch is turned...Ch. 4.12 - Prob. 3ECh. 4.12 - Prob. 4ECh. 4.12 - Prob. 5ECh. 4.12 - Prob. 6ECh. 4.12 - Prob. 7ECh. 4.12 - Prob. 8ECh. 4.12 - Prob. 9ECh. 4.12 - 10. How does the operator of a pumper-tanker fire...
Ch. 4.12 - Prob. 11ECh. 4.12 - Prob. 12ECh. 4.12 - 13. If the expansion valve of a refrigerator...Ch. 4.12 - Prob. 14ECh. 4.12 - Prob. 15ECh. 4.12 - Prob. 1CUCh. 4.12 - 6. Liquid flows at steady state at a rate of 2...Ch. 4.12 - 7. A flow idealized as a throttling process...Ch. 4.12 - 8. __________ is the work associated with the...Ch. 4.12 - 9. Steady flow devices that result in a drop in...Ch. 4.12 - 10. Steam enters a horizontal pipe operating at...Ch. 4.12 - Prob. 11CUCh. 4.12 - Prob. 12CUCh. 4.12 - Prob. 13CUCh. 4.12 - 14. _______ means all properties are unchanging in...Ch. 4.12 - Prob. 15CUCh. 4.12 - Prob. 16CUCh. 4.12 - 17. ________ operation involves state changes with...Ch. 4.12 - Prob. 18CUCh. 4.12 - 19. A horizontal air diffuser operates with inlet...Ch. 4.12 - 20. Mass flow rate for a flow modeled as...Ch. 4.12 - Prob. 21CUCh. 4.12 - Prob. 22CUCh. 4.12 - Prob. 23CUCh. 4.12 - 24. The mechanisms of energy transfer for a...Ch. 4.12 - 25. For one-dimensional flow, mass flow rate is...Ch. 4.12 - 26. At steady state, conservation of mass asserts...Ch. 4.12 - Prob. 27CUCh. 4.12 - Prob. 28CUCh. 4.12 - Prob. 29CUCh. 4.12 - Prob. 30CUCh. 4.12 - Prob. 31CUCh. 4.12 - Prob. 32CUCh. 4.12 - 33. A significant increase in pressure can be...Ch. 4.12 - Prob. 34CUCh. 4.12 - Prob. 35CUCh. 4.12 - Prob. 36CUCh. 4.12 - 37. Factors that may allow one to model a control...Ch. 4.12 - Prob. 38CUCh. 4.12 - Prob. 39CUCh. 4.12 - Prob. 40CUCh. 4.12 - Prob. 41CUCh. 4.12 - Prob. 42CUCh. 4.12 - Prob. 43CUCh. 4.12 - 44. The human body is an example of an integrated...Ch. 4.12 - Prob. 45CUCh. 4.12 - Prob. 46CUCh. 4.12 - 47. The thermodynamic performance of a device such...Ch. 4.12 - 48. For every control volume at steady state, the...Ch. 4.12 - Prob. 49CUCh. 4.12 - Prob. 50CUCh. 4.12 - Prob. 51CUCh. 4.12 - 52. At steady state, identical electric fans...Ch. 4.12 - Prob. 1PCh. 4.12 - Prob. 2PCh. 4.12 - 4.3 Steam enters a 1.6-cm-diameter pipe at 80 bar...Ch. 4.12 - Prob. 4PCh. 4.12 - Prob. 5PCh. 4.12 - Prob. 6PCh. 4.12 - 4.7 Figure P4.7 provides data for water entering...Ch. 4.12 - Prob. 8PCh. 4.12 - Prob. 9PCh. 4.12 - 4.10 Data are provided for the crude oil storage...Ch. 4.12 - 4.11 An 8-ft3 tank contains air at an initial...Ch. 4.12 - Prob. 12PCh. 4.12 - Prob. 13PCh. 4.12 - Prob. 14PCh. 4.12 - 4.15 Liquid water flows isothermally at 20°C...Ch. 4.12 - Prob. 16PCh. 4.12 - Prob. 17PCh. 4.12 - Prob. 18PCh. 4.12 - 4.19 As shown in Fig. P4.19, steam at 80 bar,...Ch. 4.12 - Prob. 20PCh. 4.12 - Prob. 21PCh. 4.12 - Prob. 22PCh. 4.12 - Prob. 23PCh. 4.12 - 4.24 Refrigerant 134a enters a horizontal pipe...Ch. 4.12 - 4.25 As shown in Fig. P4.25, air enters a pipe at...Ch. 4.12 - 4.26 Air enters a horizontal, constant-diameter...Ch. 4.12 - 4.27 Air at 600 kPa, 330 K enters a...Ch. 4.12 - 4.28 At steady state, air at 200 kPa, 325 K, and...Ch. 4.12 - 4.29 Refrigerant 134a flows at steady state...Ch. 4.12 - 4.30 As shown in Fig. P4.30, electronic components...Ch. 4.12 - 4.31 Steam enters a nozzle operating at steady...Ch. 4.12 - 4.32 Refrigerant 134a enters a well-insulated...Ch. 4.12 - 4.33 Air enters a nozzle operating at steady state...Ch. 4.12 - Prob. 34PCh. 4.12 - Prob. 35PCh. 4.12 - 4.36 Nitrogen, modeled as an ideal gas, flows at a...Ch. 4.12 - Prob. 37PCh. 4.12 - Prob. 38PCh. 4.12 - Prob. 39PCh. 4.12 - 4.40 Oxygen gas enters a well-insulated diffuser...Ch. 4.12 - Prob. 41PCh. 4.12 - 4.42 Steam enters a well-insulated turbine...Ch. 4.12 - Prob. 43PCh. 4.12 - 4.44 Air expands through a turbine operating at...Ch. 4.12 - Prob. 45PCh. 4.12 - 4.46 A well-insulated turbine operating at steady...Ch. 4.12 - Prob. 47PCh. 4.12 - Prob. 48PCh. 4.12 - Prob. 49PCh. 4.12 - Prob. 50PCh. 4.12 - Prob. 51PCh. 4.12 - Prob. 52PCh. 4.12 - Prob. 53PCh. 4.12 - 4.54 Nitrogen is compressed in an axial-flow...Ch. 4.12 - Prob. 55PCh. 4.12 - Prob. 56PCh. 4.12 - Prob. 57PCh. 4.12 - Prob. 58PCh. 4.12 - Prob. 59PCh. 4.12 - 4.60 Refrigerant 134a enters an insulated...Ch. 4.12 - Prob. 61PCh. 4.12 - Prob. 62PCh. 4.12 - 4.63 Air enters a compressor operating at steady...Ch. 4.12 - 4.64 Air enters a compressor operating at steady...Ch. 4.12 - Prob. 65PCh. 4.12 - Prob. 66PCh. 4.12 - Prob. 67PCh. 4.12 - 4.68 As shown in Fig. P4.68, a power washer used...Ch. 4.12 - Prob. 69PCh. 4.12 - Prob. 70PCh. 4.12 - Prob. 71PCh. 4.12 - 4.72 Oil enters a counterflow heat exchanger at...Ch. 4.12 - Prob. 73PCh. 4.12 - Prob. 74PCh. 4.12 - Prob. 75PCh. 4.12 - Prob. 76PCh. 4.12 - Prob. 77PCh. 4.12 - Prob. 78PCh. 4.12 - Prob. 79PCh. 4.12 - Prob. 80PCh. 4.12 - Prob. 83PCh. 4.12 - Prob. 84PCh. 4.12 - Prob. 85PCh. 4.12 - Prob. 86PCh. 4.12 - Prob. 87PCh. 4.12 - Prob. 88PCh. 4.12 - Prob. 89PCh. 4.12 - Prob. 90PCh. 4.12 - Prob. 91PCh. 4.12 - Prob. 92PCh. 4.12 - Prob. 93PCh. 4.12 - Prob. 94PCh. 4.12 - Prob. 95PCh. 4.12 - Prob. 96PCh. 4.12 - 4.97 As shown in Fig. P4.97, Refrigerant 22 enters...Ch. 4.12 - Prob. 98PCh. 4.12 - Prob. 99PCh. 4.12 - Prob. 100PCh. 4.12 - Prob. 101PCh. 4.12 - 4.102 Steady-state operating data for a simple...Ch. 4.12 - Prob. 103PCh. 4.12 - Prob. 104PCh. 4.12 - Prob. 105PCh. 4.12 - Prob. 106PCh. 4.12 - Prob. 107PCh. 4.12 - Prob. 108PCh. 4.12 - Prob. 109PCh. 4.12 - Prob. 110PCh. 4.12 - Prob. 111PCh. 4.12 - Prob. 112PCh. 4.12 - 4.113 An insulated, rigid tank whose volume is 10...Ch. 4.12 - Prob. 114PCh. 4.12 - Prob. 115PCh. 4.12 - Prob. 116PCh. 4.12 - Prob. 117PCh. 4.12 - Prob. 119PCh. 4.12 - Prob. 122PCh. 4.12 - Prob. 127PCh. 4.12 - Prob. 128PCh. 4.12 - 4.130 The procedure to inflate a hot-air balloon...
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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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