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### hw_07

Course: ME 521, Fall 2007
School: Penn State
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Word Count: 385

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In Due: class, Friday October 26, 2007 Name ME 521 Fall Semester, 2007 Homework Set # 7 Professor J. M. Cimbala For instructor or TA use only: Problem Score Points 1 15 2 15 3 20 4 50 Total: 100 1. 2. 3. 4. (15 pts) Text problem 3.7. Do two parts, i.e. split the stream function into an inner and outer part, and match the two at r = R. For consistency, assume = 0 at the origin. (a) Calculate for r R. (b)...

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Penn State - ME - 521
Due: In class, Friday November 30, 2007NameME 521 Fall Semester, 2007Homework Set # 10Professor J. M. CimbalaFor instructor or TA use only: Problem Score Points 1 15 2 30 3 25 4 30 Total: 1001.2.3.(15 pts) Text problem 6.3. The reason
Penn State - ME - 521
Due: In class, Friday September 14, 2007NameME 521 Fall Semester, 2007Homework Set # 2Professor J. M. CimbalaFor instructor or TA use only: Problem Score Points 1 30 2 15 3 15 4 15 5 15 6 10 Total: 1001.2.3.(30 pts) Mathematical manip
Penn State - ME - 521
t (min) 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240c data (mg/m3) 220 173 109 94 60 41 39 20 18 10 9 6 4 3 3 2 1
Cornell - MATH - 1920
Formula PageWednesday, January 26, 2005 2:46 AMA B = |A|*|B| cos () cos () = cos (-) sin () = - sin (-) Law of Cosines: |A| + |B| - 2|A|*|B| cos = |(B - A)|CIRCLE centered at 3, -5 with a radius of 7. (x - 3) + (y + 5) = 49Plane in space: Ve
Penn State - ME - 521
Vorticity Production at a Wall How Does Vorticity get Produced?Author: John M. Cimbala, Penn State University Latest revision: 11 October 2007Note: Consider steady, incompressible, Newtonian flow in which gravity is neglected and the wall is stat
Penn State - ME - 521
Sample simultaneous equation solver using Excel: J. M. Cimbala, August 2001 Here is how I set this up to solve three equations simultaneously: Tools-Add-Ins-Solver Add-in-OK Set up cells B27 through D27 with initial guesses (I used 1.0 for each varia
Penn State - ME - 521
Homework Set 3, Problem 5, Fall 2006 J. M. Cimbalatime 8:00 8:05 8:10 8:15 8:20 8:25 8:30 8:35 8:40 8:45 8:50 8:55 9:00 9:05 9:10 9:15 9:20 9:25 9:30 9:35 9:40 9:45 9:50 9:55 10:00 10:05 10:10 10:15 10:20 10:25 10:30 10:35 10:40 10:45 10:50 10:55 1
Penn State - ME - 521
M E 521: Foundations of Fluid Mechanics I, Fall Semester 2007Latest update: 29 August 2007Lectures: Text: Prerequisite: Web Pages:Instructor: TA/Grader:Mon., Wed., Fri.: 1:25-2:15 p.m., Room 220 Hammond [Note the time and room change.] Fluid M
Penn State - ME - 521
Particle number distribution for Homework 10, Problem 5, ME 405, Fall 2006 J. M. CimbalaGiven: j = class (bin number) 1 2 3 4 5 6 7 8 9 10 11 12 13 D p ,min,j (lower limit) 0.4 0.8 1.2 2 3 4 5 6 8 10 12 15 20 D p ,max,j n j = count (upper per class
Cornell - MATH - 1920
14.7 - Stokes TheoremMonday, May 02, 2005 2:12 PM
Penn State - ME - 521
Control Volume Example: Flat Plate Boundary LayerAuthor: John M. Cimbala, Penn State University Latest revision: 20 September 2007Given:Consider flow over a two-dimensional flat plate. The freestream flow upstream of the plate is steady, uniform
Cornell - MATH - 1920
14.3. Path Independence, Potential fcns. and Conservative FieldsTuesday, April 12, 2005 12:07 PM
Penn State - ME - 521
Example of how to solve simultaneous equations using Excel J. M. Cimbala, August 2005 Consider the following set of 3 simultaneous equations for 3 unknowns, a, b, and c: 3a + b - 2c = 4 4a - 3b + 2c = 0 2a - 4c = 5 Although it is not necessary, it is
Penn State - ME - 521
Due: In class, Friday September 28, 2007NameME 521 Fall Semester, 2007Homework Set # 4Professor J. M. CimbalaFor instructor or TA use only: Problem Score Points 1 15 2 10 3 10 4 15 5 10 6 40 Total: 1001. 2.3. 4.5.(15 pts) Text problem
Cornell - MATH - 1920
Wednesday, April 06, 2005 5:19 PM
Penn State - ME - 521
ME 405 Class Handout - Particle Size Statistics for Grouped Data, J. M. Cimbala, Latest revision: November 2006(Based on data from William C. Hinds, Aerosol Technology, Wiley, New York, 1982.) Note: All sizes are diameters in micrometers (or microns
Penn State - ME - 521
Leibniz Theorem and the Reynolds Transport Theorem for Control VolumesAuthor: John M. Cimbala, Penn State University Latest revision: 20 September 20071-D Leibniz TheoremThe one-dimensional form of the Leibniz theorem allows us to differentiate a
Penn State - ME - 521
Various Forms of the Bernoulli EquationAuthor: John M. Cimbala, Penn State University Latest revision: 25 September 2007Note: The fluid is assumed to be Newtonian, and gravity is assumed to act in the negative z direction [positive z is &quot;up&quot;]. All
Cornell - MATH - 1920
13.6 Triple Integrals in Cylindrical and Spherical CoordinatesWednesday, April 06, 2005 5:19 PM
Penn State - ME - 521
Due: In class, Friday November 9, 2007NameME 521 Fall Semester, 2007Homework Set # 9Professor J. M. CimbalaFor instructor or TA use only: Problem Score Points 1 15 2 15 3 20 4 20 5 15 6 15 Total: 1001. 2.(15 pts) Text problem 3.8. Note: D
Cornell - MATH - 1920
14.2. Vector Fields, Work, Circulation and FlowThursday, May 12, 2005 1:40 PM
Penn State - ME - 521
Due: In class, Friday October 5, 2007NameME 521 Fall Semester, 2007Homework Set # 5Professor J. M. CimbalaFor instructor or TA use only: Problem Score Points 1 15 2 15 3 50 4 20 Total: 1001.2.(15 pts) Text problem 3.1. For consistency,
Cornell - MATH - 1920
14.1 - Line IntegralsFriday, April 08, 2005 1:57 AM
Penn State - ME - 521
Eigenvalues, Eigenvectors, and Tensor InvariantsAuthor: John M. Cimbala, Penn State University Latest revision: 20 September 2007Let unprimed coordinates x1, x2, and x3 denote the original axes. Let primed coordinates x1, x2, and x3 denote the rot
Cornell - MATH - 1920
13.3 - Double Integrals in Polar FormWednesday, April 06, 2005 5:51 PM
Penn State - ME - 521
Due: In class, Friday September 7, 2007NameME 521 Fall Semester, 2007Homework Set # 1Professor J. M. CimbalaFor instructor or TA use only: Problem Score Points 1 10 2 20 3 10 4 10 5 10 6 10 7 20 8 10 Total: 1001.2.3.4.5. 6. 7.(10
Cornell - MATH - 1920
13.2. Areas, Moments and Centers of MassWednesday, April 06, 2005 5:51 PM
Penn State - ME - 521
Two-D stagnation point similarity solution using the Runge-Kutta methodJ. M. Cimbala Set the origin to 1 instead of zero (for vectors and arrays): ORIGIN := 1Note also that the number of displayed digits is adjusted by Format-Number, change Displa
Cornell - MATH - 1920
13.1. Double IntegralsWednesday, April 06, 2005 5:52 PM
Penn State - ME - 521
Axes Transformation Rules and Tensor Notation Rules for Cartesian TensorsAuthor: John M. Cimbala, Penn State University Latest revision: 20 September 2007Axes Transformation RulesLet unprimed coordinates x1, x2, and x3 denote the original axes. L
Penn State - ME - 521
Due: In class, Friday December 7, 2007NameME 521 Fall Semester, 2007Homework Set # 11Professor J. M. CimbalaFor instructor or TA use only: Problem Score Points 1 10 2 15 3 10 4 30 5 35 Total: 1001.(10 pts) Consider creeping flow (Stokes f
Penn State - ME - 521
Blasius flat plate boundary layer similarity solution by the Runge-Kutta methodJ. M. Cimbala The equation to solve is f' + cff' = 0, where prime denotes d/d. Here, let c = 1/2. c := 0.5 ORIGIN := 1We will define a vector Y which contains three unk
Cornell - MATH - 1920
12: Practice ExercisesSunday, May 08, 2005 9:23 PM
Penn State - ME - 521
The Heat Flux-Vorticity AnalogyAuthor: John M. Cimbala, Penn State University Latest revision: 10 October 2007Note: For simplicity, consider two-dimensional incompressible, Newtonian flow in the x-y plane.1. Heat Fluxy Consider a wall that is
Penn State - ME - 521
Motion of Fluid ParticlesAuthor: John M. Cimbala, Penn State University Latest revision: 20 September 2007A fluid particle can undergo four different types of motion, which we express as rates: rate of translation, rate of dilatation, rate of shea
Cornell - MATH - 1920
14.4 -Green's Theorem in the planeSunday, April 17, 2005 8:39 PM
Cornell - MATH - 1920
14.5. Surface IntegralsSunday, April 24, 2005 6:37 PM
Penn State - ME - 521
Due: In class, Friday September 21, 2007NameME 521 Fall Semester, 2007Homework Set # 3Professor J. M. CimbalaFor instructor or TA use only: Problem Score Points 1 10 2 20 3 15 4 10 5 45 Total: 1001.2.3.4.(10 pts) Text problem 2.2. N
Cornell - MATH - 1920
7.11.13.
Penn State - ME - 521
Elementary Planar Irrotational Flows in Complex VariablesAuthor: John M. Cimbala, Penn State University Latest revision: 17 October 2007Note: Consider steady, incompressible, irrotational, Newtonian fluid flow in which gravity is neglected. The fl
Penn State - ME - 521
Simple Runge-Kutta solution of an ODE J. M. Cimbala, September 2001 The equation to be solved is dy/dt = B - Ay, where in general A and B can be functions of time. The data are plotted on a separate sheet called &quot;plot of y vs t&quot;. tstart = deltat = y(
Cornell - MATH - 1920
14.6 - Parameterized SurfacesMonday, April 25, 2005 1:49 AM
Cornell - MATH - 1920
12.9 - Lagrange MultipliersSaturday, April 09, 2005 8:23 PM
Penn State - ME - 521
ME 405 Fall 2006Professor John M. Cimbala Lecture 2911/13/2006Today, we will: Complete the hood/exhaust fan example problem from last time Go over Exam 2 Discuss Computational Fluid Dynamics in Chapter 10Results of Exam 2: Mean: 72.7 Lo
Penn State - ME - 521
Example Problem 5.4 - Smokers in a conference room J. M. Cimbala1000Constants: Q= V= S per cigarrette = c (0) = ca = Time increment for plot: t = 1 min3 6.3 m /min 3 33.3 m 1100 g/min/cigarrette 3 20 g/m 3 20 g/m900800700 c ( g/m3)600 500
Cornell - MATH - 1920
12.8 - Extreme Values and Saddle PointsSaturday, April 09, 2005 8:25 PM
Penn State - ME - 521
ME 405 Fall 2006Professor John M. Cimbala Lecture 3812/06/2006Today, we will: Discuss equations of particle motion in Section 8.4 Demonstrate some particle trajectory calculations using Mathcad Discuss terminal settling velocity in Sectio
Cornell - MATH - 1920
12.7- Directional Derivatives, Gradient vectors and Tangent PlanesFriday, February 25, 2005 10:48 PM
Penn State - ME - 521
EES windows for the EES file Sample_simple_set_of_simultaneous_equations.EES J. M. Cimbala, August 2005
Penn State - ME - 521
Grade efficiency of the cleaner is given: Additional columns for calculation of mass fraction and grade efficiency analysis:Mass distribution at the outlet of the air cleaner: g (D p ,j )out / (M j /m t )out = m j ,out / D(D p ,j ) m j ,out = (mas
Penn State - ME - 521
Section 3.5 Thermal Comfort and Heat StressTable 3.6 Metabolic rate as a function of physical activity for a 70 kg adult man (abstracted from ASHRAE, 1997). activity sleeping seated, quiet standing, relaxed walking about the office seated, heavy lim
Cornell - MATH - 1920
Wednesday, February 16, 2005 7:14 PM
Penn State - ME - 521
Equations for the Conservation of EnergyAuthor: John M. Cimbala, Penn State University Latest revision: 25 September 2007Mechanical Energy EquationNon-conservative form: D 1 ( 2 ui ui ) = ui gi + ui xij Dt jConservative form: where1 2 (
Cornell - MATH - 1920
Wednesday, February 16, 2005 7:14 PM
Penn State - ME - 521
Due: In class, Friday October 12, 2007NameME 521 Fall Semester, 2007Homework Set # 6Professor J. M. CimbalaFor instructor or TA use only: Problem Score Points 1 15 2 15 3 15 4 25 5 30 Total: 1001.2.(15 pts) Text problem 3.2. Do two part
Penn State - ME - 521
Nearly Incompressible Laminar Flow Equations and Solution TechniqueAuthor: John M. Cimbala, Penn State University Latest revision: 31 October 2007Assumptions and Approximations The fluid is Newtonian with constant properties (, , k, , , CP). Th
Cornell - MATH - 1920
11.3. Arc length and Unit tangent vectorTuesday, February 22, 2005 6:07 PM
Cornell - MATH - 1920
10.3 Dot Product:Friday, January 28, 2005 12:37 AMFriday, January 28, 2005 12:37 AM10.5 Lines and PlanesFriday, January 28, 2005 12:37 AM
Penn State - ME - 521
Example How to determine if there is a violation of the exposure limits or standards. Note: Here we use ACGIH TLV standards, which are not enforceable. However, the same kind of analysis can be performed with OSHA PEL values, which are enforceable.
Penn State - ME - 521
Example How to determine if there is a violation of the exposure limits or standards. Note: Here we use ACGIH TLV standards, which are not enforceable. However, the same kind of analysis can be performed with OSHA PEL values, which are enforceable.
Cornell - MATH - 1920
10.2- Vectors in spaceFriday, January 28, 2005 12:37 AM