All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.
Solution for Introduction to Environment Engineering and Science 3rd edition ...shayangreen
Complete Solution for Introduction to Environment Engineering and Science 3rd edition by Gilbert M. Masters
IMPORTANT NOTE:IF YOU WANT TO USE THIS SOLUTION YOU MUST DOWNLOAD THE SECOND EDITION AS WELL.
SOLUTION TO SECOND EDITION IS IN MY PROFILE TOO.
HERE IS THE LINK:
http://www.slideshare.net/shayangreen/solution-for-introduction-to-environment-engineering-and-science-2nd-edition-by-gilbert-m-masters
All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.
Solution for Introduction to Environment Engineering and Science 3rd edition ...shayangreen
Complete Solution for Introduction to Environment Engineering and Science 3rd edition by Gilbert M. Masters
IMPORTANT NOTE:IF YOU WANT TO USE THIS SOLUTION YOU MUST DOWNLOAD THE SECOND EDITION AS WELL.
SOLUTION TO SECOND EDITION IS IN MY PROFILE TOO.
HERE IS THE LINK:
http://www.slideshare.net/shayangreen/solution-for-introduction-to-environment-engineering-and-science-2nd-edition-by-gilbert-m-masters
Solution manual for water resources engineering 3rd edition - david a. chinSalehkhanovic
Solution Manual for Water-Resources Engineering - 3rd Edition
Author(s) : David A. Chin
This solution manual include all problems (Chapters 1 to 17) of textbook. in second section of solution manual, Problems answered using mathcad software .
Solution manual for water resources engineering 3rd edition - david a. chinSalehkhanovic
Solution Manual for Water-Resources Engineering - 3rd Edition
Author(s) : David A. Chin
This solution manual include all problems (Chapters 1 to 17) of textbook. in second section of solution manual, Problems answered using mathcad software .
Anomalous Diffusion Through Homopolar Membrane: One-Dimensional Model by Guilherme Garcia Gimenez and Adélcio C Oliveira* in Evolutions in Mechanical Engineering
390 Guided Projects
Guided Project 31: Cooling coffee
Topics and skills: Derivatives, exponential functions
Imagine pouring a cup of hot coffee and letting it cool at room temperature. How does the temperature of the
coffee decrease in time? How long must you wait until the coffee is cool enough to drink? When should you
add an ounce of cold milk to the coffee to accelerate the cooling as much as possible?
A fairly accurate model to describe the temperature changes in a conducting object is Newton’s Law of
Cooling. Suppose that at time t ≥ 0 an object has a temperature of T(t). The Law of Cooling says that the rate at
which the temperature of the object increases or decreases is given by
( ( ) ) , (1)
dT
k T t A
dt
= − −
where A is the ambient (surrounding) temperature and k > 0 is a constant called the conductivity (which is a
property of the cooling object). Newton’s Law of Cooling assumes that the cooling body has a uniform
temperature throughout its interior. This is not strictly accurate, as a cooling body loses heat through its surface.
1. Explain in words what equation (1) means. Specifically, in terms of T and A, when is 0
dT
dt
> and when is
0
dT
dt
< ? For the case of hot coffee cooling to room temperature, which case do you expect to see?
2. Verify by substitution that the solution to equation (1) subject to the initial condition T(0) = T0 is
0( ) ( ) . (2)
ktT t A T A e−= + −
3. Before graphing the temperature function, use equation (2) to evaluate T(0) and limt→∞ T(t). Are these the
values you expect?
4. Consider the case of a cup of hot coffee cooling with an ambient room temperature of A = 60◦ F and the
initial temperature of the coffee is T0 = 200
◦ F. Use a graphing utility to plot the temperature function for
k = 0.3, 0.2, 0.1, and 0.05. Comment on how the curves change with k. Do larger values of k produce faster
or slower rates of temperature change?
5. For the values of A and T0 in Step 4, estimate the value of k that describes the case in which the coffee
cools to 100 degrees in 10 minutes.
Here is an interesting question. Suppose you want to cool your hot coffee to 100◦ F as quickly as possible.
Suppose also that you have one ounce of cold milk with a temperature of 40◦ F that you can add to the
cooling coffee at any time. When should you add the milk to cool the coffee to 100◦ F as quickly as
possible?
6. We need to make an assumption about the effect of cold milk on the temperature of the coffee. A
reasonable assumption is that when milk is added to coffee, the temperature of the coffee immediately
decreases to the average of the coffee temperature and the milk temperature, where the average is weighted
by the volumes. So if we add 1 ounce of milk with temperature Tm to 8 ounces of coffee with temperature
T, the temperature of the mixture will be
1 8 8
. (3)
1 8 9
m m
new
T T T T
T
⋅ .
390 Guided Projects
Guided Project 31: Cooling coffee
Topics and skills: Derivatives, exponential functions
Imagine pouring a cup of hot coffee and letting it cool at room temperature. How does the temperature of the
coffee decrease in time? How long must you wait until the coffee is cool enough to drink? When should you
add an ounce of cold milk to the coffee to accelerate the cooling as much as possible?
A fairly accurate model to describe the temperature changes in a conducting object is Newton’s Law of
Cooling. Suppose that at time t ≥ 0 an object has a temperature of T(t). The Law of Cooling says that the rate at
which the temperature of the object increases or decreases is given by
( ( ) ) , (1)
dT
k T t A
dt
= − −
where A is the ambient (surrounding) temperature and k > 0 is a constant called the conductivity (which is a
property of the cooling object). Newton’s Law of Cooling assumes that the cooling body has a uniform
temperature throughout its interior. This is not strictly accurate, as a cooling body loses heat through its surface.
1. Explain in words what equation (1) means. Specifically, in terms of T and A, when is 0
dT
dt
> and when is
0
dT
dt
< ? For the case of hot coffee cooling to room temperature, which case do you expect to see?
2. Verify by substitution that the solution to equation (1) subject to the initial condition T(0) = T0 is
0( ) ( ) . (2)
ktT t A T A e−= + −
3. Before graphing the temperature function, use equation (2) to evaluate T(0) and limt→∞ T(t). Are these the
values you expect?
4. Consider the case of a cup of hot coffee cooling with an ambient room temperature of A = 60◦ F and the
initial temperature of the coffee is T0 = 200
◦ F. Use a graphing utility to plot the temperature function for
k = 0.3, 0.2, 0.1, and 0.05. Comment on how the curves change with k. Do larger values of k produce faster
or slower rates of temperature change?
5. For the values of A and T0 in Step 4, estimate the value of k that describes the case in which the coffee
cools to 100 degrees in 10 minutes.
Here is an interesting question. Suppose you want to cool your hot coffee to 100◦ F as quickly as possible.
Suppose also that you have one ounce of cold milk with a temperature of 40◦ F that you can add to the
cooling coffee at any time. When should you add the milk to cool the coffee to 100◦ F as quickly as
possible?
6. We need to make an assumption about the effect of cold milk on the temperature of the coffee. A
reasonable assumption is that when milk is added to coffee, the temperature of the coffee immediately
decreases to the average of the coffee temperature and the milk temperature, where the average is weighted
by the volumes. So if we add 1 ounce of milk with temperature Tm to 8 ounces of coffee with temperature
T, the temperature of the mixture will be
1 8 8
. (3)
1 8 9
m m
new
T T T T
T
⋅ .
The Engineer of Industrial Universtiy of Santander, Elkin Santafe, give us a little summary about direct methods for the solution of systems of equations
1. MATHEMATICAL MODELING AND ENGINEERING PROBLEM SOLVING<br />Figure depicts the various ways in which an average man gains and loses water in one day. One liter in ingested as food, and the body metabolically produces 0.3L. In breathing air, the exchange is 0.05L while inhaling, and 0.4L while exhaling over a one-day period. The body will also lose 0.2, 1.4, 0.2, and 0.35L through sweat, urine, feces, and through the skin, respectively. In order to maintain steady-state condition, how much water must be drunk per day?<br />FecesAirUrineSkinSweat<br />Food<br />Drink<br />Metabolism<br />For free-falling parachutist with linear drag, assume a first jumper is 70kg and has a drag coefficient of 12kg/s. If a second jumper has a drag coefficient of 15kg/s and a mass of 75kg, how long will it take him to reach the same velocity the first jumper reached in 10s?<br />The amount of a uniformly distributed radioactive contaminant contained in a closed reactor is measured by its concentration c (Becquerel/liter of Bq/L). The contaminant decreases at a decay rate proportional to its concentration-that is <br />Decay rate = -kc<br />where k is a constant with units of day-1. Therefore, a mass balance for the reactor can be written as<br />dcdt = -kc<br />change in mass= decreaseby decay<br />Use Euler’s method to solve this equation from t=0 to 1d with k=0.2d-1. Employ a step size of Δt=0.1. The concentration at t=0 is 10Bq/L.<br />Plot the solution on a semilog graph (i.e., ln c versus t) and determine the slope. Interpret your results.<br />Newton’s law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature), <br />dTdt= -k(T-Ta) <br />Where T= the temperature of the body (°C), t= time (min), k= the proportionality constant (per minute), and Ta= the ambient temperature (°C). Suppose that a cup of coffee originally has a temperature of 68°C. Use Euler’s method to compute the temperature from t = 0 to 10 min using a step size of 1min if Ta=21°C and k=0.017/min.<br />Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area<br />dVdt = -kA<br />Where the volume (mm3), t = time (h), k= the evaporation rate (mm/hr), and A= surface area (mm2). Use Euler’s method to compute the volume of the droplet from t = 0 to 10min using step size of 0.25min. Assume that k = 0.1mm/min and that the droplet initially has a radius of 3mm. Assess the validity of your results by determining the radius of your final computed volume and verifying that is consistent with the evaporation rate.<br />A storage tank contains a liquid at depth y where y=0 when the tank is half full. Liquid is withdrawn at a constant flow rate Q to meet demands. The contents are resupplied at a sinusoidal rate 3Qsin2(t).<br />d(Ay)dx=3Qsin3t- Q<br />change involume=inflow- (outflow)<br />Or, since the surface area A is constant<br />dydx=3QAQsin2t- QA<br />Use Euler’s method to solve for the depth y from t = 0 to 10d with a step size of 0.5d. The parameter values are A = 1200 m2 and Q = 500 m3/d. Assume that the initial condition is y = 0.<br />Approximations and Round-off errors<br />Convert the following base-2 numbers to base-10: (a) 101101, (b) 101.101, and (c) 0.01101.<br />Evaluate e-5 using two approaches<br />e-x=1-x+x22-x33!+…<br />and<br />e-x=1e-x=11+x+x22-x33!+…<br />And compare with the true value of 6.737947x10-3. Use 20 terms to evaluate each and compute true and approximate relative errors as terms are added.<br />(a) Evaluate the polynomial<br />Y=x3-7x2+8x-0.35<br />At x=1.37. Use 3-digit arithmetic with chopping. Evaluate the percent relative error.<br />(b) Repeat (a) but express y as<br />y=((x-7)x +8)x - 0.35<br />Evaluate the error and compare with part (a)<br />Determine the number of terms necessary to approximate cos x to 8 significant figures using the Maclaurin series approximation<br />cosx=1-x22+x44!-x66!+x88!-…<br />Calculate the approximation using a value of x = 0.3π. Write a program to determine your result.<br />How can the machine epsilon be employed to formulate a stopping criterion εs for your programs? Provide an example.<br />The infinite series<br />fn=i=1n1/i4<br />Converge on a value of f(n) = π4/90 as n approaches infinity. Write a program in single precision to calculate f(n) for n= 10 000 by computing the sum from i=1 to 10 000. Then repeat the calculation but in reverse order-that is, from i = 10 000 to 1 using increments of -1. In each case, compute the true percent relative error. Explain the results.<br />Truncation Errors and the Taylor Series<br />Use zero- trhough third-order Taylor series expansions to predict f(3) for<br />f(x) = 25x3 – x2 + 7x – 88<br />using a base point at x = 1. Compute the true percent relative error εT for each approximation. Discuss the meaning of the results.<br />Use forward and backward difference approximations of O(h2) to estimate the first derivate of the function examined in before exercise. Perform the evaluation at x=2 using steps sizes of h=0.25 and 0.125. Compare your estimates with the true of the second derivative. <br />Evaluate and interpret the condition numbers for<br />F(x) = |x-1|+1 for x = 1.00001<br />F(x) = e-x for x = 10<br />F(x) = x2+1-xfor x = 200<br />F(x) = e-x-1/x for x = 0.001<br />A missile leaves the ground with an initial velocity Vo forming an angle Φo with the vertical as shown in figure. The maximum desired altitude is αR where R is the radius of the earth. The laws of mechanics can be used to show that<br />sinΦo=1+α1-α1+α vevo2<br />Where ve = the escape velocity of the missile. It is desired to fire the missile and reach the design maximum altitude within an accuracy of +/- 2%. Determine the range of values for Φo if ve/vo = 2 and α=0.25<br />Φo<br />vo<br />R <br />Consider the function f(x) =x3–2x+4 on the interval [-2,2] with h=0.25. Use the forward, backward, and centered finite difference approximations for the first and second derivates so as to graphically illustrate which approximations along with the theoretical, and do the same for the second derivative as well.<br />