This website uses cookies to ensure you have the best experience.

Homework 1 Solutions Essay

919 words - 4 pages

CHE 331
Fall 2013

OSU Chemical, Biological and Environmental Engineering
Homework #1 Solutions

Page 1

Solutions for CHE 331 Homework #1:
Problem 1:
a) Develop a mathematical model to predict the concentration of salt (C1) leaving the first tank
as a function of time. Calculate the time for C1 to reach 0.01% of the initial value (0.0001Co).
To simplify the problem, we will make the following assumptions:

Constant volume of liquid in the tank (V) and volumetric flow of water (Fo).
The tank is well-mixed (i.e. C1 is uniform, throughout the tank).
m
The salt dissolves instantly at time t = 0 (i.e. Co = o ).
V

A molar balance (input – output = accumulation) on ...view middle of the document...

V

(7)

Calculation of the time to reach C1 = 0.01% of C0 is straightforward from Equation 7:

t 0.01% = −

⎛V ⎞
V ⎛ C1 ⎞
V
ln⎜ ⎟ = − ln(0.0001) = 9.21⎜ ⎟[time]
F0 ⎝ Co ⎠
F0
⎝ F0 ⎠

(8)

b) Develop a mathematical model to predict C2, the concentration of salt in the second tank.
SKETCH a plot that will show C1 and C2 as a function of time.
Consider a mass balance on the salt in the second tank. The feed stream (C1) contains
salt, so we cannot simply discard the input term in this case. Since the liquid volume in
the tanks is not changing, the output and input streams must again have equal flow rates
(Fo).

FoC1Δt − FoC2 Δt = VC2 t+Δt − VC2 t

⎡ moles ⎤

(9)

As with part a), we divide by Δt and take the limit as Δt→0 to get:

FoC1( t ) − FoC2 ( t ) = V

dC2
dt

, where C1 (t) = Coe

⎡ moles ⎤
⎢ time ⎥

⎛F t⎞
−⎜ o ⎟
⎝ V ⎠

(10)

Notice that C1 will be changing over time, so we cannot simply separate variables and
integrate directly. Instead, we rearrange the differential equation and substitute the
equation form of C1(t).

FoC1( t ) − FoC2 ( t ) dC2
=
V
dt

(11)

CHE 331
Fall 2013

OSU Chemical, Biological and Environmental Engineering
Homework #1 Solutions

Fo (Coe

⎛F t⎞
−⎜ o ⎟
⎝ V ⎠

− C2 (t))

dC2
dt

(12)

dC2 FoC2 (t)
+
dt
V

(13)

V
FoCoe
V

⎛F t⎞
−⎜ o ⎟
⎝ V ⎠

=

Page 3

=

Fo
. Thus, an
V
integrating factor, ξ(t), can be introduced to solve the problem. See the class handout
about integrating factors or a calculus textbook for details:
Equation 15 is of the form Q( t ) = y′ + P( t )y , in which

ξ(t) = e

...

Other Papers Like Homework 1 Solutions

Moffett the Great Divide Essay

1111 words - 5 pages individually and no group work is allowed! I will post the solutions on Saturday for you to prepare the weekly quizzes. Late submission will be unacceptable. Homework will be graded mainly based on your efforts, so timely submission is very important. Students are also encouraged to go over the self-assessment quizzes provided by the publisher: http://wps.aw.com/aw_moffett_fundmult_3/83/21263/5443332.cw/index.html. Class Participation

It 460 Project 2 Essay

952 words - 4 pages finish with me? 2. Currently what are if any the problems associated with staff training? 3. From a HR standpoint, how do you see this benefiting staff training? 1. Business Solutions Group: Lynn Chou (Manager) Stephanie Greene (Business Analysts) Meg Harris (Corporate Trainers) Questions: 1. How can this be designed to be used in your department? 2. Does the department have any specific IT needs? Reference: Catapult

It500 Unit 2 Assignment 1

1789 words - 8 pages Unit 2: Assignment 1: Global Challenges Associated with E-Commerce December 18, 2012 IT500-01N: Critical Concepts and Competencies for the IT Professional Instructor: Dr. Sheila Fournier-Bonilla Kaplan University Unit 2: Assignment 1: Global Challenges Associated with E-Commerce E-Commerce has changed the ways that companies do business, they are no longer confined to certain areas, regions, or even countries. "E-Commerce and m

Patagonia

568 words - 3 pages Homework Chapter 2 1. The elements of the classical management approaches evident at Zara International are as follows: Scientific Management Approach: Inditex select, train and support workers. Zara International hired more than 200 professionals to help them with the up to date fashions. Administrative Principles Approach: Zara International uses management functions such as planning, organizing, leading and controlling. Inditex

Implementing A Program For Single & Working Parents

1254 words - 6 pages single parent or both parents working households, suffered due to parent’s inability to participate in class activities and being unaware of their child’s progress in class. Having a program where parents can follow their child’s progress and address questions regarding their child’s success in the classroom will ensure that both parents and teachers are both pursuing the same goal. Parental involvement has to be defined before solutions to this

College Composition

2273 words - 10 pages Parental Involvement in Secondary Schools: Problems, Solutions, and Effects. Educational Psychology Interactive. Molland, J. (2007). Straight Talk about Schools Today. Free Spirit. Vandergrift, J., & Greene, A. (1992, September). Rethinking Parent Involvement. Educational Leadership, 50(1), 57-59. Wherry, J. (1992, April). Getting Parents Involved. Education Digest, 57(8), 49-50.

Decision Making Process

1497 words - 6 pages structure and entail risk, uncertainty, and conflict” (Bateman, Snell (2011). These factors cause managers not to take action or ignore problems that are occurring. Managers can create efficient solutions for problems by following the decision making process. “The model decision making process has six stages that the decision should follow, which include (1) identify and diagnose the problem, (2) generate alternate solutions (3) evaluate alternatives

Legal 500

1714 words - 7 pages Corporate Governance and Ethical Responsibility Research Paper Essie Sullivan Dr. Cantrell Legal 500 Law, Ethics & Corporate Governance February 11, 2013 1. Determine at least three (3) different internal and external stakeholders that Dr. DoRight might have to deal with on a daily basis at the hospital. Hospital facilities are definitely significant in the well-being of patients and expertise of its medical staff personnel

Ups And Downs

5723 words - 23 pages both sides nCk's divided by (k + 1)'s integrating both sides but don't forget '+ c' HOMEWORK EXERCISES1 Expand both sides of the identity (1 + x)n(1 + x) = (1 + x)n+1 and compare coefficients to prove Pascal's triangle result n+1Ck = nCk-1 + nCk.2 (2010 HSC, Question 7(b)(iii), 2 marks)Expand (1 + x)n and differentiate both sides to prove that.Example 7 (2006 HSC, Question 2(b), 2 marks)(i) By applying the binomial theorem to (1 + x)n and

1024 words - 5 pages filled with 18 year olds who do not need as much help with certain things that I do. I have found myself having to get over my discomfort if I want to succeed. I am taking 4 classes and so I have 4 days a week to get used to it. This person had 1 class, 1 time per week, so by the time he would get back to his class he would be right back at the beginning again. I asked him how he managed to pass this class if he never understood the homework

Healthcare: the Undocumented Can Change the Cost

907 words - 4 pages . The best I ever did in math was geometry in Mr. Jackson’s 9th grade class. My worst experiences, so far, has been in any type of algebra. I had algebra 1 in 8th grade with Mrs. Foster (Sweetwater) and algebra 2 with Mrs. Handlon last year. I am surprised I even passed the classes with B’s. There are so many variables and solutions in algebra equations. The graphs are beyond complicated to understand and the only way to ever finish a test on time

Related Essays

Undemanding Services Essay

794 words - 4 pages Calculus 2 (BT) Homework Assignment #1 Spring 2015 Deadline: 8:00 AM on Thursday, March 26, 2015 Remarks: -Students hand in the solutions to the ﬁrst 25 problems listed below: 20 problems of Chapter 1 and problems 1-5 of Chapter 2. -Students should show the solutions in A4 paper size. The solutions must be in the order as listed. Chapter 1: (20 problems) Section 9.1: 45. Section 9.2: 18, 27, 33, 53, 55. Section 9.3: 4, 5, 39, 42

Bhafdsdfghgfd Essay

2792 words - 12 pages about late submissions, and also disallow submissions after a certain period of time. Use Case Name | Upload Solution Of Homework Submission | Brief Description | In this case the student can upload homework submission in his/her account. | Actor | Student. | Precondition | Logged in the system.Logged in his/her account using username and password. | Basic flow | 1. Check user information. 2. Choose SHS link. 3. Choose Attachment

Private Tutions Essay

948 words - 4 pages outside school, tuition is a necessary evil. Some students treat their tutors as a walking dictionary, expecting them to furnish answers to the homework given by school without thinking through the solutions by themselves over time. This can make them mentally lazy. Conclusion First , need for private tutions comes when ->teachers do not play their part well ,when they teach a particular subject in class room ->and when student doesn't

Sent Essay

324 words - 2 pages Session 1 Homework Solutions 1.1              Capital: What are the two basic sources of funds for all businesses?   Solution:   The two basic sources of funds for all businesses are debt and equity.   1.2              Management role: What is working capital management?   Solution:   It is the management of current assets, such as inventory, and current liabilities, such as money owed to suppliers. 1.8