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Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 14.12, Problem 2KCP
To determine
The difference between positive ion cores and valance electrons.
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The feed flow rate to an adiabatic continuous stirred tank reactor (CSTR) in which an exothermicreaction is occurring is increased from 1000 to 1400. kg/h, causing the outlet temperature to change as shown:a) Briefly explain on a physical basis why the temperature in this system oscillates after a step increasein the inlet flow rate. Be clear, complete, and concise. c) You know that this oscillating response cannot be that of two first order processes with real timeconstant acting in series. Assuming the reaction is first order and the CSTR operates with constant holdup,derive the block diagram with all transfer functions indicating how the temperature would respond to the feedflow rate step change (W’(s) as input and T’(s) as output). An intermediate variable in this block diagram willbe the concentration of A in the reactor, represented by CA’(s). d) A correct result for part c) will include a feedback loop in the block diagram, indicating the responsein T to a change in w is not…
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
threads, a diameter of 50 mm, and a pitch of 6 mm.
Coefficients of friction are 0.05 for the threads and
0.08 for the collar bearings. Collar diameters are 90
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speed ratio of 60:1. A slip clutch, on the motor shaft,
prevents overloading. The full-load motor speed is
1720 rev/min.
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press head move? (Vm= , Vser. =
)
(5M)
(b) What should be the horsepower rating of the
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Bearings
watt, Pm= watt, Pm= h.p.) (20M)
2['s
Fig.1
Worm
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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.
Chapter 14 Solutions
Foundations of Materials Science and Engineering
Ch. 14.12 - Describe the classic model for electrical...Ch. 14.12 - Prob. 2KCPCh. 14.12 - Prob. 3KCPCh. 14.12 - Prob. 4KCPCh. 14.12 - Prob. 5KCPCh. 14.12 - Define the following quantities pertaining to the...Ch. 14.12 - Prob. 7KCPCh. 14.12 - What structural defects contribute to the residual...Ch. 14.12 - Prob. 9KCPCh. 14.12 - Prob. 10KCP
Ch. 14.12 - Prob. 11KCPCh. 14.12 - Prob. 12KCPCh. 14.12 - Prob. 13KCPCh. 14.12 - Prob. 14KCPCh. 14.12 - Prob. 15KCPCh. 14.12 - Prob. 16KCPCh. 14.12 - Prob. 17KCPCh. 14.12 - Prob. 18KCPCh. 14.12 - Prob. 19KCPCh. 14.12 - Prob. 20KCPCh. 14.12 - Prob. 21KCPCh. 14.12 - Prob. 22KCPCh. 14.12 - Prob. 23KCPCh. 14.12 - Prob. 24KCPCh. 14.12 - Prob. 25KCPCh. 14.12 - Prob. 26KCPCh. 14.12 - Prob. 27KCPCh. 14.12 - Describe the movement of the majority and minority...Ch. 14.12 - Prob. 29KCPCh. 14.12 - Prob. 30KCPCh. 14.12 - What is a zener diode? How does this device...Ch. 14.12 - Prob. 32KCPCh. 14.12 - Prob. 33KCPCh. 14.12 - Prob. 34KCPCh. 14.12 - Prob. 35KCPCh. 14.12 - Describe how the planar bipolar transistor can...Ch. 14.12 - Prob. 37KCPCh. 14.12 - Prob. 38KCPCh. 14.12 - Prob. 39KCPCh. 14.12 - Prob. 40KCPCh. 14.12 - Prob. 41KCPCh. 14.12 - Prob. 42KCPCh. 14.12 - Prob. 43KCPCh. 14.12 - Prob. 44KCPCh. 14.12 - Prob. 45KCPCh. 14.12 - Prob. 46KCPCh. 14.12 - Prob. 47KCPCh. 14.12 - Prob. 48KCPCh. 14.12 - Prob. 49KCPCh. 14.12 - Prob. 50KCPCh. 14.12 - Prob. 51KCPCh. 14.12 - Prob. 52KCPCh. 14.12 - Prob. 53KCPCh. 14.12 - What are ferroelectric domains? How can they be...Ch. 14.12 - Prob. 55KCPCh. 14.12 - Prob. 56KCPCh. 14.12 - What are the PZT piezoelectric materials? In what...Ch. 14.12 - Prob. 58AAPCh. 14.12 - Prob. 59AAPCh. 14.12 - Prob. 60AAPCh. 14.12 - Prob. 61AAPCh. 14.12 - Prob. 62AAPCh. 14.12 - Prob. 63AAPCh. 14.12 - Prob. 64AAPCh. 14.12 - Prob. 65AAPCh. 14.12 - Prob. 66AAPCh. 14.12 - Prob. 67AAPCh. 14.12 - Prob. 68AAPCh. 14.12 - Prob. 69AAPCh. 14.12 - Prob. 70AAPCh. 14.12 - Phosphorus is added to make an n-type silicon...Ch. 14.12 - Prob. 72AAPCh. 14.12 - A silicon wafer is doped with 2.50 1016 boron...Ch. 14.12 - A silicon wafer is doped with 2.50 1015...Ch. 14.12 - Prob. 75AAPCh. 14.12 - Prob. 76AAPCh. 14.12 - Prob. 77AAPCh. 14.12 - What fabrication techniques are used to encourage...Ch. 14.12 - Prob. 79AAPCh. 14.12 - Prob. 80AAPCh. 14.12 - Calculate the intrinsic electrical conductivity of...Ch. 14.12 - Prob. 82AAPCh. 14.12 - Prob. 83AAPCh. 14.12 - Prob. 85AAPCh. 14.12 - Prob. 86AAPCh. 14.12 - Prob. 87AAPCh. 14.12 - Prob. 88AAPCh. 14.12 - Prob. 89AAPCh. 14.12 - Prob. 90AAPCh. 14.12 - Prob. 91AAPCh. 14.12 - Prob. 92SEPCh. 14.12 - Prob. 93SEPCh. 14.12 - Design a p-type semiconductor based on Si that...Ch. 14.12 - Prob. 95SEPCh. 14.12 - Prob. 96SEPCh. 14.12 - Prob. 97SEPCh. 14.12 - Prob. 98SEPCh. 14.12 - Prob. 99SEPCh. 14.12 - Prob. 100SEP
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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.arrow_forwardProblem 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_forward
- 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
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