EBK FLUID MECHANICS: FUNDAMENTALS AND A
4th Edition
ISBN: 8220103676205
Author: CENGEL
Publisher: YUZU
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 12, Problem 141P
To determine
One dimensional compressible flow functions and present results by duplicating
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
An aluminum rod of length L
=
1m has mass density p = 2700 kg and
Young's modulus E = 70 GPa. The rod is fixed at both ends. The exact
natural eigenfrequencies of the rod are wexact
E
=
√
ρ
for n=1,2,3,. . . .
1. What is the minimum number of linear elements necessary to
determine the fundamental frequency w₁ of the system? Discretize
the rod in that many elements of equal length, assemble the global
system of equations KU = w² MU, and find the fundamental
frequency w₁. Compute the relative error e₁ = (w1 - wexact) /w exact
Sketch the fundamental mode of vibration.
2. Use COMSOL to solve the same problem. Show the steps necessary
to find the fundamental frequency and mode of the rod. What is the
relative error using linear elements and a normal mesh?
A ball with a mass of 5.0 kg is hanging from a string and is initially at rest.
A bullet with a mass of 10.0 g and a velocity of 200.0 m/s is fired at the ball.
The bullet embeds itself inside the ball.
How high (h) do the ball and the bullet rise?
Gravitational acceleration: g=9.81g = 9.81g=9.81 m/s².
Don't use chatgpt.
Need handwritten solution.
Mechanical engineering
Chapter 12 Solutions
EBK FLUID MECHANICS: FUNDAMENTALS AND A
Ch. 12 - What is dynamic temperature?Ch. 12 - Calculate the stagnation temperature and pressure...Ch. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8EPCh. 12 - Prob. 9PCh. 12 - Products of combustion enter a gas turbine with a...Ch. 12 - Is it possible to accelerate a gas to a supersonic...Ch. 12 - Prob. 72EPCh. 12 - Prob. 73P
Ch. 12 - Prob. 74PCh. 12 - Prob. 75PCh. 12 - For an ideal gas flowing through a normal shock,...Ch. 12 - Prob. 77CPCh. 12 - On a T-s diagram of Raleigh flow, what do the...Ch. 12 - What is the effect of heat gain and heat toss on...Ch. 12 - Prob. 80CPCh. 12 - Prob. 81CPCh. 12 - Prob. 82CPCh. 12 - Argon gas enters a constant cross-sectional area...Ch. 12 - Prob. 84EPCh. 12 - Prob. 85PCh. 12 - Prob. 86PCh. 12 - Prob. 87EPCh. 12 - Prob. 88PCh. 12 - Prob. 89PCh. 12 - Prob. 90PCh. 12 - Prob. 91PCh. 12 - Prob. 93CPCh. 12 - Prob. 94CPCh. 12 - Prob. 95CPCh. 12 - Prob. 96CPCh. 12 - Prob. 97CPCh. 12 - Prob. 98CPCh. 12 - Prob. 99CPCh. 12 - Prob. 100CPCh. 12 - Prob. 101PCh. 12 - Air enters a 5-cm-diameter, 4-m-long adiabatic...Ch. 12 - Helium gas with k=1.667 enters a 6-in-diameter...Ch. 12 - Air enters a 12-cm-diameter adiabatic duct at...Ch. 12 - Prob. 105PCh. 12 - Air flows through a 6-in-diameter, 50-ft-long...Ch. 12 - Air in a room at T0=300k and P0=100kPa is drawn...Ch. 12 - Prob. 110PCh. 12 - Prob. 112PCh. 12 - Prob. 113PCh. 12 - Prob. 114PCh. 12 - Prob. 115PCh. 12 - Prob. 116EPCh. 12 - A subsonic airplane is flying at a 5000-m altitude...Ch. 12 - Prob. 118PCh. 12 - Prob. 119PCh. 12 - Prob. 120PCh. 12 - Prob. 121PCh. 12 - Prob. 122PCh. 12 - Prob. 123PCh. 12 - An aircraft flies with a Mach number Ma1=0.9 at an...Ch. 12 - Prob. 125PCh. 12 - Helium expands in a nozzle from 220 psia, 740 R,...Ch. 12 - Prob. 127PCh. 12 - Prob. 128PCh. 12 - Prob. 129PCh. 12 - Prob. 130PCh. 12 - Prob. 131PCh. 12 - Prob. 132PCh. 12 - Prob. 133PCh. 12 - Prob. 134PCh. 12 - Prob. 135PCh. 12 - Prob. 136PCh. 12 - Prob. 137PCh. 12 - Prob. 138PCh. 12 - Air is cooled as it flows through a 30-cm-diameter...Ch. 12 - Prob. 140PCh. 12 - Prob. 141PCh. 12 - Prob. 142PCh. 12 - Prob. 145PCh. 12 - Prob. 148PCh. 12 - Prob. 149PCh. 12 - Prob. 150PCh. 12 - Prob. 151PCh. 12 - Prob. 153PCh. 12 - Prob. 154PCh. 12 - Prob. 155PCh. 12 - Prob. 156PCh. 12 - Prob. 157PCh. 12 - Prob. 158PCh. 12 - Prob. 159PCh. 12 - Prob. 160PCh. 12 - Prob. 161PCh. 12 - Prob. 162PCh. 12 - Assuming you have a thermometer and a device to...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Mechanical engineering question.arrow_forwardA shaft is loaded in bending and torsion such that Ma = 70 N·m, T₁ = 45 N · m, M = 55 N. m, and T = 35 N m. For the shaft, S₁ = 700 MPa and S = 560 MPa, and a fully corrected endurance limit of S₂ = 210 MPa is assumed. Let K = 2.2 and K = 1.8. With a Se design factor of 2.0 determine the minimum acceptable diameter of the shaft using the a) DE- Goodman b) DE-Morrow c) DE-Gerber d) DE-SWTarrow_forwardThe 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…arrow_forward
- 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 mm. The gears have an efficiency of 95 percent and a speed ratio of 60:1. A slip clutch, on the motor shaft, prevents overloading. The full-load motor speed is 1720 rev/min. (a) When the motor is turned on, how fast will the press head move? (Vm= , Vser. = ) (5M) (b) What should be the horsepower rating of the motor? (TR=, Tc= Pser. = " Bronze bushings Foot Motor Bearings watt, Pm= watt, Pm= h.p.) (20M) 2['s Fig.1 Worm Collar bearingarrow_forwardProblem 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.arrow_forwardAn 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_forward
- 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
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License