MrsDrPoe: Conservation of Momentum, Part II

It's that time again folks! For this Thesis Tuesday, we will continue our discussion on the conservation of momentum equation by looking at a brief example.

Consider water flowing through a 20 deg bend shown below at a rate of 0.025 m3/s. The flow is frictionless, gravitational effects are negligible, and the pressure at section 1 is 150 kPa and section 2 is 74.5 kPa. Determine the x and y components of force required to hold the bend in place.


Alright...let's organize the problem from the given information in the statement, the original figure (not shown), and a fluid property table:

Given: theta = 20 deg, Q1 = 0.025 m3/s, P1 = 150 kPa, P2 = 74.5 kPa, rho = 999 kg/m3, D1 = 0.1 m, D2 = 0.05 m
Find: Fx, Fy
Assume: steady, laminar, incompressible, uniform flow, frictionless, neglect gravity

Now onto the solution (employing the process we outlined last week):

Step 1: We must first choose a CV, keeping in mind the criteria for the "best" CV. In the figure above, the CV we will use is represented by the dashed line- note that it is perpendicular to flow into and out of the bend and that it cuts through the bend support.

Step 2: Next, we must apply the continuity equation:

d/dt(int(rho)dV) + int(rho*(V.n))dA = 0

For steady (d/dt(...) = 0), incompressible (rho = constant), uniform (V = constant) flow with 2 in/out surfaces:

rho*int(V1.n1)dA1 + rho*int(V2.n2)dA2 = rho*|V2|*A2 - rho*|V1|*A1 = 0

Since we know the volumetric flowrate (Q1) and bend diameter at 1, we can find the velocity at 1:

|V1|= Q1/(0.25*pi*D1*D1)

Similarly, since we know the diameters at 1 and 2, we can determine the areas:

A1 = 0.25*pi*D1*D1 (etc.)

Thus, we can solve for the velocity at surface 2:

|V2|= |V1|*D1*D1/(D2*D2) = 12.732 m/s

Step 3: Then we look at the external forces acting on the bend. In this case, we have two pressure forces and the support force of the bend (which we would not "see" if our CV did not intersect the support apparatus):

Fp1 = (p1*A1 0 0)
Fp2 = (Fp2x Fp2y 0) = (-p2*cos(theta)*A2 p2*sin(theta)*A2 0)
Fs = (Fsx Fsy Fsz)

Step 4: Next, we must look at the left side of the linear momentum equation for steady, uniform, incompressible flow with 2 surfaces:

d/dt(int(rho*V)dV + int(rho*V*(V.n))dA

rho*int(V1*(V1.n1))dA1 + rho*int(V2*(V2.n2))dA2

-rho*int(V1*|V1|)dA1 + rho*int(V2*|V2|)dA2

-rho*V1*|V1|*A1 + rho*V2*|V2|*A2

Step 5: Finally, we combine the right and left sides of the momentum equation, splitting it into scalar components (remember: this equation is a vector equation!), and solve for the unknown support forces:

Vector Eqn:

-rho*V1*|V1|*A1 + rho*V2*|V2|*A2 = Fs + Fp1 + Fp2

X-Momentum:

-rho*|V1|*|V1|*A1 + rho*|V2|*|V2|*cos(theta)*A2 = Fsx + rho*A1 -p2*cos(theta)*A2

Fsx = -821.322 N

Y-Momentum:

-rho*|V2|*|V2|*sin(theta)*A2 = Fsy + p2*sin(theta)*A2

Fsy = -158.79 N

Z-Momentum:

0 = Fsz

While it may seem a bit complicated at first, I can assure you that the more problems you work with this outlined process, the easier it becomes. Please be sure to comment with any questions you may have, and stay tuned for more momentum madness next week!

MrsDrPoe: Prospective Deals, 8/9

Good afternoon and happy Money Monday to all! There are a few good deals this week that I thought I'd share with you, but I haven't gone myself yet, so I don't have any pictures.


CVS
$1 ECB back WYB 2 bottles of Herbal Essences or Aussie shampoo or conditioner at $2.48/bottle [$1/1 RP 8/07, FREE bottle (Facebook offer, expired)]

Wags
$8 back in RR WYB $20 in Dr. Scholl's products (coupons here, there, and everywhere)
$1 back in RR WYB 1 bottle Herbal Essences or Aussie shampoo or conditioner at $3.00 [$1/1 RP 8/07, FREE bottle (Facebook offer, expired)]

Kroger
Mangoes - $1 (It's the perfect time to try these)
Sweet corn ears - $0.33 (And for a fantastic side dish, these)
Red seedless grapes - $1.68/lb
Tyson boneless, skinless breasts - $1.79/lb


Be sure to check here for all the deals and coupon matchups this week, and happy saving!

MrsDrPoe: The Land of the Samurai

Happy Foto Friday to all! Today I'd like to share with you some pictures from my recent trip to Japan for the first ASME-JSME-KSME Joint Fluids Engineering Conference. After 15+ hours of flight time (from ATL to SFO to TYO) we arrived at the Tokyo-Narita airport at 4:40 pm local time, but the conference was in Hamamatsu, which meant we had 2.5+ hours of train rides before we reached our final destination. The trains themselves were pretty cool:


As were the views from them (rice patties and Tokyo):


Hamamatsu Station was almost adjacent to our hotel, which was fantastic because by the time we got there, it was 9:30 pm local time, and we were exhausted. After checking into my room at the Okura Act City Hotel, I immediately showered and settled in for Sunday morning services. Right after the closing prayer (which happily coincided with my goal of staying up till midnight local time to help my body get acclimated to the current time zone), I tumbled into my small, hard bed that was surprisingly comfortable.

The next morning I felt fantastic (or at least a lot better than I did when I got to my room the night before). After Sunday evening services and daily Bible reading, I checked out the view of the city, mountains, and the Pacific) from my room:


While Japan is totally clean (I saw maybe two pieces of trash on the street the whole time I was there), downtown Hamamatsu is definitely prettier at night. Another thing I noticed my first day there was the bathrooms. The toilets were either porcelain holes in the ground (not the first thing you want to see when you get off a plane you've been in for 10+ hours) or highly technical machines with bidet buttons:


The shower had three knobs- one to turn on the bath faucet, one to turn on the shower head, and one to select the temperature (no guessing at the perfect temp there). And the mirror had an area above the sink that wouldn't fog when you took a shower (love it).

After meeting my advisor for breakfast, I went across the street to the hotel conference center where all the presentations were being given:


Every day from about 8:30-6:00 someone was lecturing about something- I heard about A LOT of different research projects going on...so much in fact that I realized how much I miss going to class. One of the most interesting presentations was about the vortices formed by the flapping of butterfly wings. My presentation went alright; although, I wish I would've done a better job answering the few questions that were asked about my work.

Lunches were provided for us each day as well:


We received green tea in a juice-box and a box with 6-9 compartments containing various Japanese delicacies. Each lunch box came with a guide to what was in each compartment; some of the descriptions on this guide were quite interesting, for example:

"food boiled and seasoned"

"boiled rice with assorted ingredients"

"Shizuoka Oden - Japanese dish containing all kinds of ingredients cooked in a special broth of soy sauce, sugar, sake, etc."

Tuesday night I spent going to a Technical Committee meeting and working on my presentation (which I gave Wednesday at noon). Wednesday night there was a banquet for all the conference participants- it was opened with the smashing of a Sake barrel by the leaders of each society, closed with a Japanese word and a clap from the crowd, and filled in between with Japanese culture. There were Japanese style dishes (both sweet and savory), green tea, and music on Japanese harps from a group called the Harp Queens:


Since the purpose for my trip was the conference, I didn't get to do much sightseeing; however, Monday and Thursday nights I did get out of the hotel complex for a bit. The first night out it was me and a map (with the locations all in Japanese). I struck out to find Hamamatsu Castle, but I didn't make it there before dark (at about 7:00 pm). Since the castle was in a less populated area of town, I decided to go back to the hotel (Japan has a low crime rate, but I didn't want to take my chances). On the way back, I got lost for about 20 minutes before finding a sign that said "Hamamatsu Station"...then I followed the train station signs home.

Thursday night was less adventurous; my advisor and I went to try and get souvenirs for our families. While wandering around the city, we ran into another conference attendee with his Japanese "sister" (who had been an exchange student in his home when he was younger). We went to a Japanese BBQ place with them, where the sister ordered various items (from a Japanese Mr. Robinson) that were brought to our table along with what was essentially a mini charcoal grill. The food was wonderful- especially the beef- and I can now say that I have tried cow tongue. Here some random pictures from my wanderings:


And that was my trip to the land of the Samurai in a nutshell. It was a great experience that I was so thankful to have had, and if I can ever go back, I will (but I am definitely taking Mr. Poe with me next time)!

MrsDrPoe: Biblical Definitions

It's another Theology Thursday, folks! Please open up your Bibles with me as we look at a few passages from God's word. Today's topic stems from one of the things that our friend, Ms. Long, loves about language- the fact that it's a living organism, constantly growing and changing. Because of this, there are several Bible words in the current vernacular that may bring different ideas to mind than the ideas the Biblical contexts present. We'll look at two for now: profane and visit.


PROFANE
1) not connected with religion or religion matters; secular 2) not initiated into the inner mysteries or esoteric knowledge of something 3) not hallowed or consecrated 4) showing disrespect or contempt for sacred things; irreverent*

bebelos - permitted to be trodden, accessible (related to koinos - common)**

Typically when we think of the word profane, we think of the related word profanity, which then leads to the thought of trash or filth. Even the phrasing of the dictionary definition above brings to mind that to profane something means to drag it through the mud. But examining the Biblical definition, we see profaning something doesn't just mean heaping trash on it, but also simply making it accessible or common.

So if we consider what it means to "profane the name of [our] God" (Lev 18:21, etc.), we need to realize that it doesn't just mean pairing "God" with curse words. Any time we use His name other than when we are consciously speaking of Him or to Him, we are profaning His name by making it common. We need to be mindful of flippantly using phrases such as "Oh, Lord" and "Oh my God," realizing that there is a context in which these phrases should be used and a context in which they should not. We must take great care to not make common anything that is holy.

VISIT
1) to go or come to see out of friendship or for social reasons 2) to stay with as a guest for a time 3) to go or come to see in a professional or business capacity 4) to go or come to in order to inspect or investigate 5) to go or come to for a time so as to make use of , look at, etc. 6) to occur or come to 7) to bring suffering, trouble, etc. 8) to inflict (punishment, etc.) upon someone; to afflict (with punishment, etc.); to avenge*

episkeptomai - to inspect (a late form of episkopeo - to look upon, care for, exercise oversight)**

When I say something like: "I'm going to go visit ___," I am usually employing one of the first six dictionary definitions of the word, meaning I'm visiting someone for social or business reasons. But these definitions don't encompass the full Biblical meaning of the word. Take Ruth 1:6 for example: "Then she arose with her daughters-in-law that she might return from the country of Moab, for she had heard in the country of Moab that the LORD had visited His people by giving them bread." Prior to this visit by God, there was a famine in the land of Israel (Ruth 1:1), and this verse tells us that God visited the children of Israel by giving them bread. Here we can see the Biblical definition of "visit"- to supply a need.

So when we are told in Jas 1:27, "Pure and undefiled religion before God and the Father is this: to visit orphans and widows in their trouble, and to keep oneself unspotted from the world," we know this doesn't necessarily mean stop by and say hi (although social interaction is important and can be a valid need- especially for shut-ins). To truly visit orphans and widows in their trouble, we must help supply their needs in whatever area their lives are lacking; this is pleasing to God (Matt 25:36-46).

Another verse that talks about visiting is Ex 32:34, "...Nevertheless, in the day when I visit for punishment, I will visit punishment upon them for their sin." In this verse we see God planning to visit to supply another need- the need for justice and punishment for sin. We should remind ourselves daily of this need and strive daily to remove sin from our lives, seeking the grace of God when we stumble. Ironically, in a world full of sin, visiting to supply the specific need of punishment has remained a valid dictionary definition for the word "visit."


I hope these thoughts have been helpful to you, and until next time...happy studying!

*From Webster's New World College Dictionary, Fourth Edition
**From Vine's Complete Expository Dictionary of Old and New Testament Words

MrsDrPoe: Corn Fritters

Today's What's for Dinner post could actually be an appetizer or side dish: Grandmama Wolgemuth's corn fritters. When I visited the great state of PA a few weeks ago, my uncle mentioned these in passing, and I knew I needed to get the recipe because 1) everything my grandmother makes is superb and 2) Papa Poe loved the corn fritters we ate in Gatlinburg last year. So without further ado...


Ingredients: 2 large ears of corn (as dry as possible), 1 egg, 0-4 tablespoons of flour, and oil for frying (not pictured).


Remove the corn from the cob by grating each ear; you should have approximately one cup of corn when you finish.


Beat the egg in a small bowl, and add the corn. If the corn wasn't very dry, add a few teaspoons of batter to stiffen the mixture slightly; the drier the corn, the less flour that you need to add. Drop by spoonfuls into hot oil.


After a minute or so, flip the fritters. After the fritters are cooked through and golden brown, remove them from the oil and let them drain on a papertowel. Serve with ketchup or maple syrup (Papa Wolgemuth's and my favorite fritter-dip).


Notes: This recipe (which makes about 10 half-dollar sized fritters) is not exact; try to stick to the 1 egg to 1 cup corn ratio and to add as little flour as possible when trying to obtain the thicker consistency that holds together when dropped into the oil. To dry my corn, I leave shucked ears in the refrigerator (uncovered) for several days. In the future I'd like to try this recipe with other produce (apples, etc.); I'll be sure to post my results!

MrsDrPoe: Ms. Ledbury

Good morning all! For today's edition of Poes' Pals, I introduce you to...Ms. Ledbury:


Although we have not known Ms. Ledbury as long as we have known most of the friends that have been featured so far in this segment, it truly seems like we have. We first met her when she visited the land of the Bulldogs to check out the mechanical engineering PhD program. Ms. Ledbury had graduated at the top of her class from the University of Memphis a few years prior and was debating whether or not to return to the wonderful world of college.

When Ms. Ledbury decided that she would indeed join our ranks at State, we were exceedingly happy. Since that time, she has successfully completed her first year of the direct-to-PhD program, scoring amazingly well on her qualifying exams. We have been particularly impressed with her drive, especially having been out of school for a while.

During the overlap of our years in Starkville, we had the privilege of not only visiting with Ms. Ledbury on campus, but also visiting in her home and worshiping with her regularly. Her hospitality and kindness are truly obvious, even to those who know her even a short while. She is always quick to offer whatever service she can provide, and we certainly do miss her!

MrsDrPoe: Conservation of Momentum, Part I

It's another Thesis Tuesday on the blog! Today we'll be looking at the second conservation equation that governs fluid mechanics: Conservation of Momentum (AKA Newton's 2nd Law or the Linear Momentum Equation).

In Lagrangian terms, this equation simply states that the sum of the forces acting on an object is equal to the mass of the object times its acceleration (or the time rate of change of its linear momentum). Recall that we wish to employ an Eulerian methodology; therefore, we must use Reynolds Transport Theorem to convert this equation.

For this case, our extensive (mass dependent) property is linear momentum, and our intensive (mass independent) property is linear momentum per unit mass, or density times velocity. Combining the result from the Reynolds Transport Theorem with the Lagrangian form of the conservation of momentum equation, we get the sum of the forces acting on the control volume is equal to:

sum(F) = d/dt(int(rho*V)dV) + int(rho*V*(V.n))dA

Here, F is a force, rho is the density, V is the velocity, and n is the unit outward normal vector.

The first thing we should notice about this equation is that it is a vector equation and can thus be written as 1, 2, or 3 equations depending on how many dimensions our problem has. For a 3D problem:

sum(Fx) = d/dt(int(rho*u)dV) + int(rho*u*(V.n))dA

sum(Fy) = d/dt(int(rho*v)dV) + int(rho*v*(V.n))dA

sum(Fz) = d/dt(int(rho*w)dV) + int(rho*w*(V.n))dA

The second thing we should notice is the similarity between these equations and the conservation of mass equation. Each one has something equal to a term tracking how our intensive property changes with time in the control volume plus a term tracking how much of the intensive property is crossing the control surface (into or out of the control volume).

We will employ the following methodology to a fixed, non-deforming control volume:

1) Choose the best CV, establishing all bounds and known conditions
2) Apply the conservation of mass equation
3) Determine all forces acting on the CV
4) Evaluate the right side of the conservation of momentum equation in terms of unknown and known variables
5) Combine both sides of the conservation of momentum equation and solve for the unknowns

Now, let that stew, and tune in next Tuesday for some fun examples.

MrsDrPoe: Happy Anniversary, Baby!

Three years ago today, Mr. Poe and I were wed. In my humble opinion, I would argue that Mr. Poe is the best husband ever, and I have thoroughly enjoyed the past three years of companionship and encouragement that our marriage has provided me with. We have grown together in faith and love- qualities that have better developed our relationship with each other and with God. I am blessed beyond measure and thus extremely thankful! In the words of Rick and Bubba:

"Happy anniversary, Baby! I got you on my mind!"

MrsDrPoe: Drug Store Deals, 7/31

Happy Money Monday to all! Due to some technical difficulties at "Poe Central Station," I don't have any pictures of the great deals this week. I did, however, wish to share my scenarios with you:

CVS
1 Gillette Fusion Proglide Razor ($4/1 PG 7/31)
2 Skinny Cow Candies (B1G1 RP 7/31)

Total Sale Price: $11.97
Total Coupons: $4.99
ECBs Used: $1.00
Total OOP: $7.46
ECBs Back: $5.99

Wags*
Transaction 1
1 Goody Hair Clips
1 Allegra Allergy 5ct. (Mail-in-Rebate RP 7/31)

Total Regular Price: $10.61
Total Sale: $0.99
Total OOP: $9.62
RR and MiR back: $8.99

Transaction 2
1 Complete Contact Solution ($1/1 SS 7/31)
1 Folder

Total Regular Price: $10.15
Total Sale and Coupons: $2.47
RR Used: $2.00
Total OOP: $5.68
RR Back: $8.00

*You could probably split these two transactions up differently to spend less OOP, but the Allegra MiR says it won't pay you back for coupons, so I didn't want to use RR for this item since they appear on the receipt as "Manufacturer Coupons." Am I just being paranoid? Perhaps.

Until next week...happy saving!

MrsDrPoe: Sascha's Story

Good morning all! Since we talked about our youngest "daughter" a few weeks ago, I thought it would be only fair to talk about our oldest one on this Foto Friday:


Sascha's story starts several semesters ago. Mr. Poe and I had been dating for nearly two years, and, while we weren't engaged at that time, we were planning to get married. One of the things that we often talked about was having a dog; I really wanted a Dachshund of my own (I love the ones my parents had/have very much), and Mr. Poe thought that starting off small was a sensible option. Although we decided we wouldn't get one until we said "I do," I spent some of my spare time looking through local animal shelter websites for a pup. It was during a random search of the Corinth Alcorn County Humane Society's website that I saw this pitiful picture:


It was love at first sight. I showed Ryan, my parents, my siblings, my current roommate, my future roommate...basically anyone who would look at it. After several days of looking, talking, and praying, Mr. Poe decided to adopt Sascha for me as an anniversary present. We drove up to Corinth to pick her up. She was "on the mend" from heart worm treatments, with tremendously sad, lifeless eyes; on the way home she would duck like she was about to get hit every time we went under an overpass. We didn't know much about the (approximately) two-year old's history, but the folks at the shelter thought she might have been involved in some sort of puppy mill.

She spent the first few months of her life as a Wolgemuth/Poe with Mama and Papa Wolgemuth (I was interning at Penn State). Mama Wolgemuth gave her lots of loving and treats, and when I returned, she was a changed pup...full of life and very happy:


Although she has a very cat-like personality (i.e. an attitude of "I'll come see you if I want to"), Sascha is a loving dog. She's sweet and playful, and she has brought tremendous joy to our lives. Her antics are crazy, and she always makes me laugh:


We love our little Snoosh, and we are so thankful we adopted her! Feel free to share some of your pet adoption stories!

MrsDrPoe: Examining Modern Media

Well friends, another Theology Thursday is upon us! As always, I invite you to open your Bibles as we once again examine a portion of God's word.

Sometime in the past year, Mr. Poe and I heard a lesson by our friend Mr. Ellis titled "Glorifying God in Gray Areas." In essence, the lesson pointed out that if you try to look in the Bible for a specific verse about getting a tattoo, what to look at on the internet, etc., you won't find one; however, that doesn't mean that the Bible is out-dated or non-applicable to us. Based on study of the basic New Testament principles and guidelines presented in the Bible, any specific 'modern-day' question we have can be answered. Using this concept, today we will look at the side note from last weeks post about current media.

Mr. Poe and I have tried to be even more diligent recently about screening the music we listen to, the articles and books we read, and the movies and TV show that we watch. In order to do that, we look at reviews of movies, shows, books, and articles and read lyrics to determine which movies, songs, etc. have bad language, inappropriate themes/scenes, or any other trash in them. At this point you may be thinking that we're big weirdos (which is ok with me), but before you totally blow this post off, let's look at two Biblical reasons that influenced our decision in this matter:

1: These influences can lead directly to sin.

Jas 1:14-16 says, "But each one is tempted when he is drawn away by his own desires and enticed. Then, when desire has conceived, it gives birth to sin; and sin, when it is full-grown, brings forth death. Do not be deceived, my beloved brethren.*" Inappropriate language and themes in media feed on our desire to be like the stars and other worldly people, to be popular or adventurous or loved, etc. in the way that they are. Like James says, dwelling on these desires leads to us physically committing the sin we see/hear. But it's more than that...it's our thoughts as well. Suppose you're watching an inappropriate movie or music video, which means you've got inappropriate thoughts in your head. Matt 5:28 tells us that "...whoever looks at a woman to lust for her has already committed adultery with her in his heart."

While James provides part of the solution in 4:7-8, "Therefore submit to God. Resist the devil and he will flee from you. Draw near to God and He will draw near to you. Cleanse your hands, you sinners; and purify your hearts, you double minded." In his letters to Timothy, Paul tells him to "...flee these things and pursue righteousness, godliness, faith, love, patience, gentleness," (1 Tim 6:11) and "Flee also youthful lusts; but pursue righteousness, faith, love, peace with those who call on the Lord out of a pure heart." (2 Tim 2:22) We must resist the devil and flee from lusts/temptations! And the most effective way to do that is to get rid of negative/worldly influences in our lives. As Jesus said in Matt 5:29-30, "If your right eye causes you to sin, pluck it out and cast if from you...and if your right hand causes you to sin, cut if off and cast it from you."

2: You can't hate it if you accept it.

If you think that you aren't tempted to use bad language or to lust after a woman/man by popular media, you may need to think again (see * above). But if you're fully convinced that you wouldn't sin in these ways by watching a movie or listening to a song, consider how this media affects your attitude toward the subject of the movie or song. Do you find bad language acceptable for other people to use? Do you find promiscuous acts okay for other people to perform? Now consider the Biblical attitude toward sin and evil:

"Hate evil, love good..." (Amos 5:15)

"Let none of you think evil in your heart against your neighbor; And do not love a false oath. For all these are things that I hate,' Says the LORD." (Zech 8:17)

"These six things the LORD hates, Yes, seven are an abomination to Him: A proud look, A lying tongue, Hands that shed innocent blood, A heart that devises wicked plans, Feet that are swift in running to evil, A false witness who speaks lies, And one who sows discord among brethren." (Prov. 6:16-19)

"For the LORD God of Israel says That He hates divorce, For it covers one's garment with violence..." (Mal 2:16)

If God hates it, and we are striving to be like Him, we should hate it too. But it is very hard to hate something if you don't think it's wrong. We should definitely consider how today's media can skew how we view sin; we should also consider that our acceptance of it and the sin it portrays can be a stumbling block to others...


Any way you look at it, "Evil company [or influence] corrupts good habits." (1 Cor 15:33) I've heard people say that if you wouldn't listen to/watch/etc. something with your grandmother, than you probably shouldn't be listening to/watching/etc. it...but that all depends on who your grandmother is. Instead, next time you listen to a song or watch a movie, pay attention to the content and ask yourself if you would still be listening to or watching it if Jesus was in the room with you. If the answer is no, then you should probably turn it off.

MrsDrPoe: Apricot Chicken

What's for dinner this Wednesday is a variation on the first dinner Mr. Poe made for me when we started dating: Apricot Chicken. It's got a very sweet and spicy taste to it that I'm sure you'll enjoy!

Ingredients: 8 oz french or Catalina dressing, 1 pouch dry onion soup mix, 1/4 cup diced jalapenos, 9 oz apricot jam, 6 oz diced chicken breast, 1 cup rice (cooked):


Combine the dressing, soup mix, jalapenos, and jam in a large skillet over med-high heat. Wisk constantly until the jam melts:


Add chicken and continue to cook, stirring occasionally until the chicken is fully cooked (about 25 minutes). Serve over rice (feeds 2-3):

MrsDrPoe: Solomon on Wealth

For today's reading review, I'd like to present to you...Dr. Stan Bullington's "Solomon on Wealth: Modern Financial Wisdom from an Ancient King"


Mr. Poe and I received an autographed copy of this book as a gift from the Bullington family several years ago; and I thought a review of it now would be fitting considering the topic of my last review.

This book was an easy read and covered the Bible passages in Proverbs that discuss wealth. As Dr. Bullington points out, the final two chapters in the book of Proverbs are generally thought to have been written by someone other than Solomon; however, a discussion on the wealth passages present in these chapters is included in this work. He also employs the information given to us about the "virtuous wife" in Proverbs 31 as a financial case study.

From these passages, Dr. Bullington describes the healthy view of wealth that a Christian should have. He discusses the fact that while wealth is a blessing from God, it is also a great danger. There is also information presented on the scriptural view of debt, workaholism, diversification, risk, and financial windfalls, as well as a multitude of other topics. One of the things that I greatly appreciated about this book are the suggestions that Dr. Bullington makes to help readers implement Solomon's financial wisdom in our own lives.

I really don't have any negative comments about this book; however, as always, I recommend reading it with an open Bible. Dr. B is a fantastic Bible student and teacher (Mr. Poe and I greatly respect him and his family), and I know he would agree with me that no book, no matter how well researched or written, should ever take the place of the Holy Word of God.

MrsDrPoe: Conservation of Mass, Part II

Well hello again! Today we'll be continuing last Tuesday's discussion on Conservation of Mass (i.e. the idea that mass cannot be created or destroyed). The math today may get hairy, but perseverance is the key! Think of what each term means physically as we look at it, and match the physics to your real-life experiences with fluid flow.

Example:

Let's consider the nozzle attachment on the hose of your vacuum cleaner (or your mom's vacuum cleaner). When we turn the vacuum on, air is sucked through the nozzle, as in Figure 1.A. The first step to finding a solution to the problem is to define a CV, like the one in Figure 1.D that contains all the air in the nozzle and is perpendicular to the flow into and out of the attachment. To make this example as simple as possible, we're going to make the simplifying assumptions that we are dealing with steady, laminar, incompressible, and uniform (or inviscid) flow. This means that our velocity profiles at the nozzle inlet and exit look like those in Figure 1.B.

Figure 1

Once again, the integral form of the continuity or conservation of mass equation for a control volume is:

0 = d/dt(int(rho)dV) + int(rho*(V.n))dA

If we look at the first term on the right side of the equation, we have:

d/dt(int(rho)dV)

Since our flow is steady, d/dt(anything) (how anything changes as time changes) is equal to zero because nothing is changing with time.

If we look at the second term on the right side of the equation, we have:

int(rho*(V.n))dA

Since our flow is incompressible, rho is constant and can mathematically be pulled out of the integral:

rho*int(V.n)dA

For this term, we are integrating over the entire control surface. It makes our lives easier if we divide the control surface into segments like Figure 1.D- control surface I is the disk at the nozzle inlet; control surface II is the disk at the nozzle exit; and control surface III is the "sleeve" along the inside wall of the nozzle attachment.

rho*int(VI.nI)dAI + rho*int(VII.nII)dAII + rho*int(VIII.nIII)dAIII

Remember we said that our velocity profile looks like Figure 1.B; thus, at every point on the nozzle inlet/exit, the velocity vector (VI or VII) looks like the ones in Figure 1.A. These vectors look like this:

Inlet (surface I): (0 |VI| 0) and Exit (surface II): (0 |VII| 0)

Along surface III, the air is flowing parallel to the nozzle surface (since we have assumed inviscid flow), making the velocity vector (VIII) here:

Surface III: (0 |VIII| 0)

Now what about that pesky n...the unit outward normal vector? This vector is different at every point along the control surface, as you can see in Figure 1.C. BUT this vector can always be determined because of its definition. Unit - means it always has a magnitude of 1. Outward - means that it is always pointing out of the control volume. Normal - means that it is always perpendicular to the control surface. So at every point on surfaces I and II:

nI: (0 -1 0) and nII: (0 1 0)

The unit outward normal vectors are different for different points on surface III, but we'll deal with that in a minute.

At this point we have every piece to the puzzle...I mean the continuity equation. We know all the velocity and unit outward normal vectors...we just have to put everything together. This means taking the dot product of V and n for each control surface segment:

I: VI.nI = 0*0 + |VI|*(-1) + 0*0 = -|VI|
II: VII.nII = 0*0 + |VII|*(1) + 0*0 = |VII|
III: VIII.nIII = 0 because VIII is always parallel to the surface and nIII is always perpendicular to the surface; thus VIII and nIII are perpendicular and the dot product is zero.

We now have:

rho*int(-|VI|)dAI + rho*int(|VII|)dAII

Again our assumptions that allow us to have the uniform velocity profile in Figure 1.B mean that the velocity magnitudes at I and II are constant and can be pulled out of the integral leaving us with:

rho*-|VI|*AI + rho*|VII|*AII

where AI and AII are the areas of these control surfaces. Putting allllllll of this information back into our original continuity equation, we get:

rho*|VI|*AI = rho*|VII|*AII

Density*velocity*area is known as a mass flow rate, so we can rewrite the above as:

mI = mII or min = mout

Or in words, the amount of air that enters the nozzle equals the amount of air that exits the nozzle. This makes physical sense because the nozzle itself is not expanding or contracting, and the amount of air in the nozzle remains constant.

It all boils down to this:

Mass can't be created or destroyed; therefore, if we have mass entering a control volume, either a) the amount of mass in the control volume must be changing with time (i.e. filling up a swimming pool) or b) the same amount of mass must be simultaneously exiting the control volume (i.e. our nozzle problem). The mathematical expressions presented in the continuity equation track how the amount of mass in the control volume changes with time and how much mass crosses into or out of the control volume; it is essentially an accounting equation that keeps track of mass.

I hope that this example has helped you better grasp the concept of mass conservation as well as the math in the expression. Please feel free to comment or ask questions, and until next time...happy trails!

MrsDrPoe: A Beginners Guide to Couponing, Part 8

Today we will resume the series on couponing for beginners with another grocery store that has some fantastic deals:

Publix
Initiation
Unlike Kroger, you will not need to obtain any kind of store loyalty card to partake in the deals at Publix.

Preparation
As before any shopping trip, I look to Jenny to tell me what sales are going on and what coupons I can match with them. Occasionally, sale prices that Jenny lists differ slightly from those at my store due to different pricing in different regions; however, I use Jenny's prices as a guide for any items not listed in the weekly sales flyer on the Publix website.

In addition to the typical coupons I get in the Sunday paper, Publix will often include inserts with their store coupons:


I believe you can use one manufacturer and one store coupon on a single item. Also, manufacturer coupons up to $0.50 will be doubled at Publix. Furthermore, Publix stores will accept store coupons from whatever store it considers to be its competitor in a certain area. Here, we are allowed to use Kroger coupons; however, there is a limit of one use per person of a specific store coupon per day. For example: if I had 2 Kroger dog food coupons and 1 Kroger tuna fish coupon, I can only use 1 dog food coupon and the tuna fish coupon on my purchase at Publix today.

B1G1 free sales at Publix can be misleading; these items are simply reduced in price by half. You do not need to purchase two items to see the savings (at most stores)...but you can if you want to. Often there are no limit to the number of items you purchase at Publix; however, you should always pay attention to the fine print to be sure, especially with products like milk and soft drinks.

Publix also has a "penny item" promotion, where on either Wednesdays or Thursdays (depending on your store), you can get a certain item for a penny with any purchase of $10 or more (before coupons). A penny item coupon is required at many stores and can be found in the newspaper on Wednesday or Thursday. Another different sale that Publix often holds is a "buy theirs get ours" deal. To take advantage of this, you must buy a specified name brand item and you will get the same type of item (but the Publix brand, of course) for free. Unlike a typical B1G1 sale, you must get both items to see savings.

Implementation
When I get to the store, I shop like normal. When I've gathered all the items I wanted, I'll double check the items and the coupons I had planned to use for my trip, and then I head to the checkout line. Publix has a very nice method of showing you the prices/discounts of items as they are rung up, which I always try to watch to triple check the prices. After all my items are scanned, I hand the cashier my coupons.

As with any store, a receipt prints out after your purchase detailing the purchase and providing a savings breakdown for your shopping trip. Of course, since there is no Publix card, these savings are not tracked for any previous trips to the store.

Notes: 1) Publix Stores in Florida have different policies, which are not described here. 2) Because the regular priced items at Publix are often way more expensive than those at Kroger and because the cost of gas is so high, I typically forgo these sales at Publix unless every item I need for the next week is on sale there.

What's your favorite grocery store to shop at?