It's Money Monday, and I'd like to start things off today with the surprise I mentioned last week. As you know, today is September 5, Labor Day, and 3 months and 20 days away from CHRISTMAS! I absolutely love Christmas. In fact, I listen to Christmas music and watch Christmas movies year-round. While I realize this is pretty weird, I'm going to suggest to you today that you start thinking about the holidays year-round as well (although perhaps not to the extent that I do) and before you stop reading, let me tell you why.
Christmas is a time of giving, but giving can be hard if you're: a student, unemployed, living on one income, etc. As you can imagine, planning and thinking more often about Christmas gifts will greatly help you stick to your budget (no matter how small) around the holidays. It's for this reason that I've decided to focus September's Money Monday posts about giving gifts without going broke. Of course the tips and tricks discussed will be applicable to any gifts you give throughout the year, but I hope that it'll definitely help out this holiday season. Please feel free to comment with more thoughts/suggestions!
The future topics I have planned for the rest of the month are: how to afford more lavish gifts on a budget (for everyone on your list), how to have a homemade holiday, and how to make sure you're a responsible receiver. This first post in the series will be a brief introduction on how to give without going broke.
Evaluating your situation
Keeping a budget and knowing where you stand with your income, debt, investments, etc. is as important to giving without going broke as it is to any subject of purchasing. If you don't have a working budget, you need to make one. Right now. And I suggest you read this to help you do so. Make sure that when you're creating yours that you include a gift giving category- Mr. Poe and I decided how much we could to spend on parents, siblings, etc. for birthdays and holidays, added everything up, and divided it by 12 to see how much we needed to save each month to spend what we could* on everyone throughout the year. Each time I make a gift purchase, I deduct it from our gift savings.
*Keep in mind that what you want to spend on family and friends might not be fiscally possible for you. If you want to save $30 a month, but you can only save $20 because the remainder of your monthly budget is going toward bills, debt, etc. that's alright. A thought: if you get into financial trouble trying to give your family their 'dream Christmas,' you're not doing them any favors because they'll probably be the ones you go to for help...or the ones who will inherit your debt.Having said that, we need to keep in mind that "it is more blessed to give than to receive" (Acts 20:35). If the reason you can only save $20 a month to give to others (family or otherwise) is because you have 3 car payments in a two-driver house, a boat payment, and you're saving $300 to go skiing next winter, you might want to rethink your priorities (and maybe sell a few things). It's good for us to enjoy the fruit of our labor, because it's a gift from God (Ecc 2:24, 3:13, 5:18) but not at the expense of our service to others (remember Jas 1:27).
Being honest
Once you've looked over your finances and established a gift budget, you need to be honest with yourself and with the people you want to give to. If people on your list usually spend mega bucks on you, and you can't reciprocate this year like usual, put your pride aside and tell them. It'll be much less awkward to have this discussion now before most people have purchased presents than waiting till these folks open a manual can opener after giving you a 60" flat screen.
Don't feel bad if you can't give your loved ones the world right now. It really is okay to be 'cheap'- especially if you're not hording what you have for your own enjoyment.
Jumping into action
So now you've figured out how much you can afford to give and you've had some possibly difficult conversations...what next? The answer is one of things I'm best known for: planning. Start by visiting your list of people you'll be shopping for and brainstorm about these people's hobbies, careers, likes, needs, wants, etc. A second brainstorming session should immediately follow producing a list of gift ideas.
Just because you write something down doesn't mean that's definitely what you'll end up purchasing, but having ideas will greatly aid you in your deal scouting. For instance, if Uncle Jimmy loves golf, I know that I'll want to keep my eye on daily deal sites that may get him a free game at his favorite course and/or sporting goods store sales. Who knows...I may find a fantastic deal on golf balls and tees next month that will allow me to get him something he'd like at a price that's in my budget. (FYI I don't have an Uncle Jimmy.)
I'm sure you can see how planning ahead and scouting for deals can quickly become a year-long task. One of my favorite times to spot fantastic prices on gifts is black Friday. In years past I've been able to get kitchen appliances like waffle makers and crockpots for $10-$15, dvd players for $10.00, dvds for $3, and the list goes on and on. Great deals are definitely there to be found on the most wonderful shopping day of the year; however, not every sale that goes on during black Friday is the best sale...or even a good sale. Again by keeping your eye out, you'll become aware of what constitutes a 'good' sale on the gifts you're looking for.
However you find your deals, I hope that these tips on budgeting and planning ahead will help you give gifts without going broke. Stay tuned next week for some lavish but thrifty gift ideas!
As a Christian, wife, mother of a little girl and two fur-babies, Mississippi State Bulldog, and PhD, I lead a very busy life. If you add on top of that my obsession for organization and loves for couponing, sewing, knitting, cooking, reading, gardening, and a host of other random hobbies, you've got the recipe for...well...variety. And variety is the spice of life!
Monday, September 5, 2011
Friday, September 2, 2011
MrsDrPoe: How to Change a Flat
The inspiration of this Foto Friday post* came from a lone trip a few weeks ago. I found my mind wandering to several things that could go wrong on the road, which lead to the possibility of a flat tire...without Mr. Poe or any friends in the area to aid me. As I mentally went through the steps in the process of changing a flat, I thought that this subject would definitely make a helpful post for myself, and I hope that you agree!
Step 1: Pull over.
If you get a flat, your car will try to veer to the side that the flat is on. When this happens, stay calm, firmly grasp the wheel, turn on your hazard lights, and carefully make your way to the shoulder. Don't freak out if you can't immediately pull over- a ruined wheel is a lot easier to replace than a life. If you're on a one-way stretch of road like the interstate, try to pull off on the shoulder that allows you to have your vehicle as a barrier between you and traffic as you work (ex: flat is on the left side, pull off on the left shoulder). Be sure to pull off the road as far as you can while keeping the car on relatively flat ground.
Step 2: Take precautions.
When you're safely pulled over, turn on your hazard lights if you've forgotten; turn off the car; and put on the parking break to help stabilize the vehicle during the tire changing process. Text or call a friend to let someone know where you are and when you stopped- be sure to tell them to check on you if you don't touch base again in 30 minutes.
Step 3: Get out your gear.
Your spare tire/doughnut, lug wrench, and jack will be in different locations depending on what type of vehicle you have. For our car, all the stuff is in the trunk underneath a section of carpet:
Make sure you've located the necessary equipment before the time comes that you actually need it. You'll also want to periodically check your spare/doughnut to ensure that the tire is at its proper pressure (this pressure can be found in your car manual or on the tire).
Step 4: Remove the hubcap.
Most newer vehicles have a lovely cover over the center of the actual wheel; this must be removed before you can get to the lug nuts. The decorative covers over the lugs will probably be plastic, so be careful with them (you may not need the wrench at this point). After these covers are loosened (A), remove the cap (B), exposing the lugs (C):
Next, you'll want to use the lug wrench to loosen the lug nuts at this point (it's ok to kick or stand on the wrench...see A in the figure in Step 6); if you don't loosen the lugs before you raise the car, you'll literally just be spinning your wheels when you try with the tire in the air.
Step 5: Set up the jack.
There should be a long, thin metal piece on the underside of your vehicle (like Mr. Poe is pointing to in A). This piece should fit in the groove of your jack (B). To ensure that this happens, set the jack up and start raising it; when the top of the jack nears the underside of the car, line up the groove with the metal strip (C):
Continue to raise the jack (and the car at this point) until the wheel is entirely off the ground and can spin freely.
Step 6: Remove the tire.
Hopefully you loosened your lugs (A) in Step 4 (if not, lower the car, loosen them, and then repeat Step 5). Once all the lug nuts are removed (B), place the lugs in the hubcap (C) or some other place where you don't loose them:
Carefully grasp the tire with both hands and remove it from the vehicle, pulling out and then down to the ground. As an additional safety precaution, you can lay this tire with its tread perpendicular to the ground under the car beside the jack. That way, if something crazy should happen and the jack fails, the car will land on the tire and not your foot.
Step 7: Put on the spare.
There are two sides to a doughnut (if that's what you have). One side (A) has an extruded flat piece in the center of the wheel; the other side has a concave flat piece (B). The extruded flat piece is the back of the wheel; this side should face the car when you're putting the doughnut on:
If you have little to no upper body strength (like me), you can set the spare on your foot/feet and use it/them to help you lift the new wheel (A). You'll want to first line up the top hole in the spare wheel with the top screw; prop the wheel on this screw and then rotate it until the other screws and holes line up (B). Place the lugs back on with your fingers in a star pattern (bottom left, top, bottom right, top left, top right) (C); then use the lug wrench to tighten each lug nut down as much as possible (until the tire spins...again using the star pattern). You'll need to go over the first ones that you tighten a second time (D):
Step 8: Finish up.
Remove the old tire from under the car and slowly lower the car to the ground. Using the wrench, tighten the lug nuts one final time, ensuring they're as tight as you possibly can get them:
Pack your equipment back into your car and wipe up if you have some napkins (unless you have gloves, you're going to get a little dirty). Call or text your friend to give him/her an update; turn on the car; take off the parking break; and carefully merge back into traffic. Once you're up to speed, turn off your hazard lights.
So that's it! I hope this has been as useful for you as it has been for me, and until next time...happy motoring!
*A special thanks to Mr. Poe for some additional safety tips, reviewing this post, and being my photographer and an all-around great husband.
Step 1: Pull over.
If you get a flat, your car will try to veer to the side that the flat is on. When this happens, stay calm, firmly grasp the wheel, turn on your hazard lights, and carefully make your way to the shoulder. Don't freak out if you can't immediately pull over- a ruined wheel is a lot easier to replace than a life. If you're on a one-way stretch of road like the interstate, try to pull off on the shoulder that allows you to have your vehicle as a barrier between you and traffic as you work (ex: flat is on the left side, pull off on the left shoulder). Be sure to pull off the road as far as you can while keeping the car on relatively flat ground.
Step 2: Take precautions.
When you're safely pulled over, turn on your hazard lights if you've forgotten; turn off the car; and put on the parking break to help stabilize the vehicle during the tire changing process. Text or call a friend to let someone know where you are and when you stopped- be sure to tell them to check on you if you don't touch base again in 30 minutes.
Step 3: Get out your gear.
Your spare tire/doughnut, lug wrench, and jack will be in different locations depending on what type of vehicle you have. For our car, all the stuff is in the trunk underneath a section of carpet:
Make sure you've located the necessary equipment before the time comes that you actually need it. You'll also want to periodically check your spare/doughnut to ensure that the tire is at its proper pressure (this pressure can be found in your car manual or on the tire).
Step 4: Remove the hubcap.
Most newer vehicles have a lovely cover over the center of the actual wheel; this must be removed before you can get to the lug nuts. The decorative covers over the lugs will probably be plastic, so be careful with them (you may not need the wrench at this point). After these covers are loosened (A), remove the cap (B), exposing the lugs (C):
Next, you'll want to use the lug wrench to loosen the lug nuts at this point (it's ok to kick or stand on the wrench...see A in the figure in Step 6); if you don't loosen the lugs before you raise the car, you'll literally just be spinning your wheels when you try with the tire in the air.
Step 5: Set up the jack.
There should be a long, thin metal piece on the underside of your vehicle (like Mr. Poe is pointing to in A). This piece should fit in the groove of your jack (B). To ensure that this happens, set the jack up and start raising it; when the top of the jack nears the underside of the car, line up the groove with the metal strip (C):
Continue to raise the jack (and the car at this point) until the wheel is entirely off the ground and can spin freely.
Step 6: Remove the tire.
Hopefully you loosened your lugs (A) in Step 4 (if not, lower the car, loosen them, and then repeat Step 5). Once all the lug nuts are removed (B), place the lugs in the hubcap (C) or some other place where you don't loose them:
Carefully grasp the tire with both hands and remove it from the vehicle, pulling out and then down to the ground. As an additional safety precaution, you can lay this tire with its tread perpendicular to the ground under the car beside the jack. That way, if something crazy should happen and the jack fails, the car will land on the tire and not your foot.
Step 7: Put on the spare.
There are two sides to a doughnut (if that's what you have). One side (A) has an extruded flat piece in the center of the wheel; the other side has a concave flat piece (B). The extruded flat piece is the back of the wheel; this side should face the car when you're putting the doughnut on:
If you have little to no upper body strength (like me), you can set the spare on your foot/feet and use it/them to help you lift the new wheel (A). You'll want to first line up the top hole in the spare wheel with the top screw; prop the wheel on this screw and then rotate it until the other screws and holes line up (B). Place the lugs back on with your fingers in a star pattern (bottom left, top, bottom right, top left, top right) (C); then use the lug wrench to tighten each lug nut down as much as possible (until the tire spins...again using the star pattern). You'll need to go over the first ones that you tighten a second time (D):
Step 8: Finish up.
Remove the old tire from under the car and slowly lower the car to the ground. Using the wrench, tighten the lug nuts one final time, ensuring they're as tight as you possibly can get them:
Pack your equipment back into your car and wipe up if you have some napkins (unless you have gloves, you're going to get a little dirty). Call or text your friend to give him/her an update; turn on the car; take off the parking break; and carefully merge back into traffic. Once you're up to speed, turn off your hazard lights.
So that's it! I hope this has been as useful for you as it has been for me, and until next time...happy motoring!
*A special thanks to Mr. Poe for some additional safety tips, reviewing this post, and being my photographer and an all-around great husband.
Thursday, September 1, 2011
MrsDrPoe: The Key to Singing
Once again Theology Thursday is upon us, and as always, I invite you to open your Bibles with me as we examine a portion of God's word. Today we will take a brief look at one aspect of our worship to the Lord- singing.
In several places in the new testament, we are instructed to sing to the Lord:
James 5:13 - Is anyone among you suffering? Let him pray. Is anyone cheerful? Let him sing psalms.
Eph 5:18-21 - And do not be drunk with wine, in which is dissipation; but be filled with the Spirit, speaking to one another in psalms and hymns and spiritual songs, singing and making melody in your heart to the Lord, giving thanks always for all things to God the Father in the name of our Lord Jesus Christ, submitting to one another in the fear of God.
Col 3:16 - Let the word of Christ dwell in you richly in all wisdom, teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord.
1 Cor 14:26 - How is it then, brethren? Whenever you come together, each of you has a psalm, has a teaching, has a tongue, has a revelation, has an interpretation. Let all things be done for edification.
1 Cor 14:15 - ...I will sing with the spirit, and I will also sing with the understanding.
Based on these verses, it seems pretty obvious that we should sing to the Lord. We can also see some of the purposes of our singing- it shows we're cheerful; it shows we're filled with the Spirit; it can teach, admonish, and edify us and our fellow brethren. These verses also show us one important instruction that we must keep in mind when singing to the Lord: we should sing with understanding.
This instruction should make sense to us in the context of teaching, admonishing, and edifying one another and of glorifying God in song. If you were teaching a child to add fractions, would you expect him/her to get anything from your lesson if you didn't know what you were talking about? If I told you, "If you need anything, call me. I'll be praying for you." in Italian, would that be of any comfort to you? If you wanted to get your mother a card for Mother's Day, wouldn't you try to understand what a card was saying to make sure that it conveyed to her the exact sentiments that you wanted to? In these everyday examples, we can see that understanding is crucial to teaching, admonishing, edifying, comforting, glorifying, etc. Italian may sound pretty, but if you don't know what I'm saying it means nothing- just like singing "ye that labor and are heavy laden, lean upon your dear Lord's breast*" is not a comfort unless it is sung (and heard) with understanding. We must take great care to focus on the words of the songs that we sing while we are singing them.
Mr. Poe and I were in a Bible study of sorts several weeks ago, when he brought up his favorite hymn, "It Is Well with My Soul." The song is a beautiful one, due to both the musical notes and the fantastic lyrics. Let's look at a couple of verses as another example:
"My sin, oh, the bliss of this glorious thought! My sin, not in part but the whole, Is nailed to the cross, and I bear it no more, Praise the Lord, praise the Lord, O my soul!"
How encouraging and comforting! Every time we sing this verse, we are reminding ourselves and those around us that Jesus Christ died on the cross in order to redeem us! "He poured out His soul unto death, and He was numbered with the transgressors, and He bore the sin of many and made intercession for the transgressors." (Isaiah 53:12) We are no longer slaves to sin because Christ bore ALL our sins on the cross for us!
"And Lord, haste the day when my faith shall be sight, The clouds be rolled back as a scroll; The trump shall resound, and the Lord shall descend, Even so, it is well with my soul."
How we Christians do long for this day! Christ's glorious second coming... But think about this: suppose you've never become a Christian or suppose you are a Christian who's returned to living in sin AND you're singing along with this 'beautiful song.' By singing these lyrics, you are asking God to "haste the day" of His return...you're asking for your own condemnation to come quickly!
Do you see why we need to sing with understanding?
On a related note, if any of you will be in the Atlanta area during the next several weeks, one of our adult classes will be focused on this topic to help us better praise God in song.
*From "Hark! The Gentle Voice"
In several places in the new testament, we are instructed to sing to the Lord:
James 5:13 - Is anyone among you suffering? Let him pray. Is anyone cheerful? Let him sing psalms.
Eph 5:18-21 - And do not be drunk with wine, in which is dissipation; but be filled with the Spirit, speaking to one another in psalms and hymns and spiritual songs, singing and making melody in your heart to the Lord, giving thanks always for all things to God the Father in the name of our Lord Jesus Christ, submitting to one another in the fear of God.
Col 3:16 - Let the word of Christ dwell in you richly in all wisdom, teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord.
1 Cor 14:26 - How is it then, brethren? Whenever you come together, each of you has a psalm, has a teaching, has a tongue, has a revelation, has an interpretation. Let all things be done for edification.
1 Cor 14:15 - ...I will sing with the spirit, and I will also sing with the understanding.
Based on these verses, it seems pretty obvious that we should sing to the Lord. We can also see some of the purposes of our singing- it shows we're cheerful; it shows we're filled with the Spirit; it can teach, admonish, and edify us and our fellow brethren. These verses also show us one important instruction that we must keep in mind when singing to the Lord: we should sing with understanding.
This instruction should make sense to us in the context of teaching, admonishing, and edifying one another and of glorifying God in song. If you were teaching a child to add fractions, would you expect him/her to get anything from your lesson if you didn't know what you were talking about? If I told you, "If you need anything, call me. I'll be praying for you." in Italian, would that be of any comfort to you? If you wanted to get your mother a card for Mother's Day, wouldn't you try to understand what a card was saying to make sure that it conveyed to her the exact sentiments that you wanted to? In these everyday examples, we can see that understanding is crucial to teaching, admonishing, edifying, comforting, glorifying, etc. Italian may sound pretty, but if you don't know what I'm saying it means nothing- just like singing "ye that labor and are heavy laden, lean upon your dear Lord's breast*" is not a comfort unless it is sung (and heard) with understanding. We must take great care to focus on the words of the songs that we sing while we are singing them.
Mr. Poe and I were in a Bible study of sorts several weeks ago, when he brought up his favorite hymn, "It Is Well with My Soul." The song is a beautiful one, due to both the musical notes and the fantastic lyrics. Let's look at a couple of verses as another example:
"My sin, oh, the bliss of this glorious thought! My sin, not in part but the whole, Is nailed to the cross, and I bear it no more, Praise the Lord, praise the Lord, O my soul!"
How encouraging and comforting! Every time we sing this verse, we are reminding ourselves and those around us that Jesus Christ died on the cross in order to redeem us! "He poured out His soul unto death, and He was numbered with the transgressors, and He bore the sin of many and made intercession for the transgressors." (Isaiah 53:12) We are no longer slaves to sin because Christ bore ALL our sins on the cross for us!
"And Lord, haste the day when my faith shall be sight, The clouds be rolled back as a scroll; The trump shall resound, and the Lord shall descend, Even so, it is well with my soul."
How we Christians do long for this day! Christ's glorious second coming... But think about this: suppose you've never become a Christian or suppose you are a Christian who's returned to living in sin AND you're singing along with this 'beautiful song.' By singing these lyrics, you are asking God to "haste the day" of His return...you're asking for your own condemnation to come quickly!
Do you see why we need to sing with understanding?
On a related note, if any of you will be in the Atlanta area during the next several weeks, one of our adult classes will be focused on this topic to help us better praise God in song.
*From "Hark! The Gentle Voice"
Wednesday, August 31, 2011
MrsDrPoe: Tuna Salad
It's another What's for Dinner Wednesday on the blog. Tonight I'd like to share with you a meal that's quick, easy, and great for lunch or dinner any day of the week (unless you're pregnant): Tuna Salad. I typically serve this on bread or buns, but it is equally tasty on your favorite cracker.
Ingredients (per serving): 1 5-6 oz can of tuna in water (drained), 1 tablespoon lite mayo, 2 tablespoons dill pickle relish:
Combine ingredients in an appropriately sized bowl with a fork. Serve immediately or refrigerate for up to one week:
There are a multitude of alternate methods for making tuna salad. Two examples are: using sweet relish instead of dill or adding an additional 1-2 tablespoons finely chopped apple to the mix (Mrs. Holland's favorite).
How do you typically make your tuna?
Ingredients (per serving): 1 5-6 oz can of tuna in water (drained), 1 tablespoon lite mayo, 2 tablespoons dill pickle relish:
Combine ingredients in an appropriately sized bowl with a fork. Serve immediately or refrigerate for up to one week:
There are a multitude of alternate methods for making tuna salad. Two examples are: using sweet relish instead of dill or adding an additional 1-2 tablespoons finely chopped apple to the mix (Mrs. Holland's favorite).
How do you typically make your tuna?
MrsDrPoe: Ms. Nowell
For the latest edition of Poes' Pals, I present to you Ms. Nowell:
Ms. Nowell is another friend from Mississippi that Mr. Poe and I have known for several years; we first met her shortly after she moved from the great state of Texas. She is a joy to be around, and we greatly admire her desire to serve the Lord and her drive to work hard at any task she begins.
Often Ms. Nowell invites her classmates to Bible studies and shows hospitality by gathering fellow students to the home she shares with her grandfather- I remember many an enjoyable evening of Rock Band and karaoke there. She has also had to make some difficult choices in order to better align her life with the patterns found in Biblical examples and teaching, which is a great encouragement to all who are around her. Currently, Ms. Nowell is participating in a nursing program in which she is doing quite well. When she finishes, I know she will be such a blessing to the babies and families she'll work with wherever she chooses to get a job!
If I've said it before, I've said it a million times, Mr. Poe and I miss Ms. Nowell and all of our Starkville family very much!
Special thanks to Ms. K. Davis for use of her fabulous photography skills.
Ms. Nowell is another friend from Mississippi that Mr. Poe and I have known for several years; we first met her shortly after she moved from the great state of Texas. She is a joy to be around, and we greatly admire her desire to serve the Lord and her drive to work hard at any task she begins.
Often Ms. Nowell invites her classmates to Bible studies and shows hospitality by gathering fellow students to the home she shares with her grandfather- I remember many an enjoyable evening of Rock Band and karaoke there. She has also had to make some difficult choices in order to better align her life with the patterns found in Biblical examples and teaching, which is a great encouragement to all who are around her. Currently, Ms. Nowell is participating in a nursing program in which she is doing quite well. When she finishes, I know she will be such a blessing to the babies and families she'll work with wherever she chooses to get a job!
If I've said it before, I've said it a million times, Mr. Poe and I miss Ms. Nowell and all of our Starkville family very much!
Special thanks to Ms. K. Davis for use of her fabulous photography skills.
Tuesday, August 30, 2011
MrsDrPoe: Conservation of Momentum, Part V
It's Thesis Tuesday on the blog, and today we'll be continuing our examination of the Conservation of Momentum equation, this time focusing on the inviscid reduction of its differential form.
If you recall, the difficulty with the differential momentum equation is that we need to define the stress terms. Previously, we obtained the following results:
If we examine the case of inviscid flow, this means we are looking at an area where viscous effects are negligible (mu = 0). Generally this occurs in the far-field, i.e. in a region of the fluid far away from any walls or boundaries. This leaves us with:
So our stress tensor terms are ONLY related to changes in pressure. If we replace these new equalities in the differential form of the equation, we end up with a set of equations known as Euler's Equations. It is important to note, however, that this set is only valid for inviscid flows.
If we apply the assumptions of steady, incompressible flow with no outside forces acting on the fluid to Euler's Equations, we get:
Using a vector identity (which we won't discuss in further detail), and applying along a streamline (lines always parallel or tangent to the flow), we can further reduce this equation to:
This is Bernoulli's Equation, and it is written for two specific points along a streamline.
Restrictions:
Remember that this equation is only applicable to flows of fluids where the assumptions we made to derive the equation (steady, incompressible, inviscid, along a streamline, no outside forces) hold. It is CRUCIAL to realize that if the flow does not meet these qualifications, this simplified equation CANNOT be used!
If our flow cannot be treated as incompressible, but the other assumptions hold, we can modify the Bernoulli Equation so that it can still be used. For compressible gases, we can apply the ideal gas law to obtain:
For unsteady flows, we can modify the equation by the addition of a single term integrating the acceleration over a streamline:
Physical Meaning:
The Bernoulli Equation is simply the mathematical statement of the principle "the work done on a particle by all forces acting on the particle is equal to the change of the kinetic energy of the particle." We can better see that if we look at each of the terms in the equation. As the particle moves, we see forces of pressure and gravity acting on it (the z*g and p/rho terms). This is directly connected to the amount of kinetic energy that the particle has (0.5*V*V).
If we multiply each term in the Bernoulli Equation by the density, rho:
we obtain the pressure form of the equation. Here p represents the thermodynamic pressure of the fluid as it flows (this pressure determines the state of a fluid, i.e. whether it is a gas or a liquid). This value is typically termed the static pressure of the fluid, since it could be measured by moving along with the fluid or being static in relation to the fluid. The third term is the hydrostatic pressure, which is associated with the hydrostatic pressure condition. The second term is called the dynamic pressure since it is associated with the velocity of the fluid.
The combination of the first two terms in the equation is the stagnation pressure. This pressure represents the conversion of all the kinetic energy into a pressure rise, which occurs at a stagnation point where the velocity is equal to zero. The streamline leading to a stagnation point is called a stagnation streamline. The sum of all three terms in this form of the Bernoulli Equation is known as the total pressure, which is constant along a streamline.
Often in Mechanical Engineering, the Bernoulli Equation will be written in head form; this form of the equation is particularly useful for pipe flow and can be derived by dividing each term in the original equation by the gravitational constant, g:
If you recall, the difficulty with the differential momentum equation is that we need to define the stress terms. Previously, we obtained the following results:
d/dx(Sxx) + d/dy(Txy) + d/dz(Txz) = -d/dx(p) + mu*(d/dx(d/dx(u))+d/dy(d/dy(u)) + d/dz(d/dz(u)))
d/dx(Tyx) + d/dy(Syy) + d/dz(Tyz) = -d/dy(p) + mu*(d/dx(d/dx(v))+d/dy(d/dy(v)) + d/dz(d/dz(v)))
d/dx(Tzx) + d/dy(Tzy) + d/dz(Szz) = -d/dz(p) + mu*(d/dx(d/dx(w))+d/dy(d/dy(w)) + d/dz(d/dz(w)))
d/dx(Tyx) + d/dy(Syy) + d/dz(Tyz) = -d/dy(p) + mu*(d/dx(d/dx(v))+d/dy(d/dy(v)) + d/dz(d/dz(v)))
d/dx(Tzx) + d/dy(Tzy) + d/dz(Szz) = -d/dz(p) + mu*(d/dx(d/dx(w))+d/dy(d/dy(w)) + d/dz(d/dz(w)))
If we examine the case of inviscid flow, this means we are looking at an area where viscous effects are negligible (mu = 0). Generally this occurs in the far-field, i.e. in a region of the fluid far away from any walls or boundaries. This leaves us with:
d/dx(Sxx) + d/dy(Txy) + d/dz(Txz) = -d/dx(p)
d/dx(Tyx) + d/dy(Syy) + d/dz(Tyz) = -d/dy(p)
d/dx(Tzx) + d/dy(Tzy) + d/dz(Szz) = -d/dz(p)
d/dx(Tyx) + d/dy(Syy) + d/dz(Tyz) = -d/dy(p)
d/dx(Tzx) + d/dy(Tzy) + d/dz(Szz) = -d/dz(p)
So our stress tensor terms are ONLY related to changes in pressure. If we replace these new equalities in the differential form of the equation, we end up with a set of equations known as Euler's Equations. It is important to note, however, that this set is only valid for inviscid flows.
If we apply the assumptions of steady, incompressible flow with no outside forces acting on the fluid to Euler's Equations, we get:
u*d/dx(u) + v*d/dy(u) + w*d/dz(u) = gx - (1/rho)*d/dx(p)
u*d/dx(v) + v*d/dy(v) + w*d/dz(v) = gy - (1/rho)*d/dy(p)
u*d/dx(w) + v*d/dy(w) + w*d/dz(w) = gz - (1/rho)*d/dz(p)
u*d/dx(v) + v*d/dy(v) + w*d/dz(v) = gy - (1/rho)*d/dy(p)
u*d/dx(w) + v*d/dy(w) + w*d/dz(w) = gz - (1/rho)*d/dz(p)
Using a vector identity (which we won't discuss in further detail), and applying along a streamline (lines always parallel or tangent to the flow), we can further reduce this equation to:
0.5*V*V + (p/rho) + g*y = constant (along a streamline)
or: 0.5*V1*V1 + (p1/rho) + g*y1 = 0.5*V2*V2 + (p2/rho) + g*y2
This is Bernoulli's Equation, and it is written for two specific points along a streamline.
Restrictions:
Remember that this equation is only applicable to flows of fluids where the assumptions we made to derive the equation (steady, incompressible, inviscid, along a streamline, no outside forces) hold. It is CRUCIAL to realize that if the flow does not meet these qualifications, this simplified equation CANNOT be used!
If our flow cannot be treated as incompressible, but the other assumptions hold, we can modify the Bernoulli Equation so that it can still be used. For compressible gases, we can apply the ideal gas law to obtain:
0.5*V*V + y*g + R*T*ln(p) = constant (along a streamline)
For unsteady flows, we can modify the equation by the addition of a single term integrating the acceleration over a streamline:
0.5*rho*V1*V1 + p1 + rho*g*y1 = rho*int(d/dt(V))ds + 0.5*rho*V2*V2 + p2 + rho*g*y2
Physical Meaning:
The Bernoulli Equation is simply the mathematical statement of the principle "the work done on a particle by all forces acting on the particle is equal to the change of the kinetic energy of the particle." We can better see that if we look at each of the terms in the equation. As the particle moves, we see forces of pressure and gravity acting on it (the z*g and p/rho terms). This is directly connected to the amount of kinetic energy that the particle has (0.5*V*V).
If we multiply each term in the Bernoulli Equation by the density, rho:
0.5*rho*V*V + p + g*rho*y = constant (along a streamline)
we obtain the pressure form of the equation. Here p represents the thermodynamic pressure of the fluid as it flows (this pressure determines the state of a fluid, i.e. whether it is a gas or a liquid). This value is typically termed the static pressure of the fluid, since it could be measured by moving along with the fluid or being static in relation to the fluid. The third term is the hydrostatic pressure, which is associated with the hydrostatic pressure condition. The second term is called the dynamic pressure since it is associated with the velocity of the fluid.
The combination of the first two terms in the equation is the stagnation pressure. This pressure represents the conversion of all the kinetic energy into a pressure rise, which occurs at a stagnation point where the velocity is equal to zero. The streamline leading to a stagnation point is called a stagnation streamline. The sum of all three terms in this form of the Bernoulli Equation is known as the total pressure, which is constant along a streamline.
Often in Mechanical Engineering, the Bernoulli Equation will be written in head form; this form of the equation is particularly useful for pipe flow and can be derived by dividing each term in the original equation by the gravitational constant, g:
(p/gamma) + (0.5*V*V/g) + y = constant (along a streamline)
In this form, the pressure term is called the pressure head, which represents the height of a column of fluid needed to produce the pressure p. The velocity term is called the velocity head, which represents the vertical distance needed for the fluid to fall freely to reach the velocity V from rest. The height term is the elevation head, and it represents the potential energy of the fluid.
Next week we'll look at some very simple examples of how to employ the Bernoulli Equation. Stay tuned!
Next week we'll look at some very simple examples of how to employ the Bernoulli Equation. Stay tuned!
Monday, August 29, 2011
MrsDrPoe: Deals Deals Everywhere! 8/28
It's the start of another week, and that means Money Monday has arrived! I'd like to share with you guys some great deals I've taken advantage of this week at CVS, Walgreens, Advanced Auto Parts, and PetSmart:
CVS
St. Joseph Asprin ($2/36 ct.) - $1/1 SS 8/07; $2 back in RR (you make $1!)
Pringles ($1.50/can) - $1/4 PG 7/31, 8/31
Charmin ($5.44/12 rolls) - $0.25/1 PG 7/31, 8/31
Dawn ($0.99/10.4 oz) - $0.50/1 PG 7/31, 8/31
Orbit ($1.37/pack) - $1/1 CVS coupon printing at price checker
I bought: 8 cans of Pringles, 3 packages of Charmin, 2 bottles of Dawn, 1 bottle of St. Joseph Asprin, 1 pack of Orbit for...
Total Regular Price: $52.46
Total Sale and Coupons: $21.46
ECBs Used: $5.00
Total OOP: $26.00
ECBs Back: $2.00, plus $10 gas card
Wags
Carmex Moist Lip Balm (Vanilla or Lime Twist, 0.15 oz)
Total Regular Price: $2.10
Total Sale and Coupons: $0.49
ECBs Used: $1.00
Total OOP: $0.61
ECBs Back: $1.50
Advanced Auto Parts
5 quarts (individual or jug) or Havoline oil + 1 Drive Works filter: $15.99
5 quarts (individual) Quaker State oil + 1 Purolator Classic filter: $15.49
We took advantage of both of these deals (there weren't any Drive Works filters to fit our car), paying $35.29 OOP and saving $20.94. They also had a deal on oil changing gear (pan, etc.) like Mr. Poe previously discussed if you're in need of it.
PetSmart
I bought Layla a 40 lb bag of Iams for...
Total Regular Price: $41.44
Total Sale and Coupons: $5
Total OOP: $36.44
A great deal, plus there's $55 in Iams and PetSmart coupons in the bag!
Stay tuned next Monday for more deals and a special surprise!
CVS
St. Joseph Asprin ($2/36 ct.) - $1/1 SS 8/07; $2 back in RR (you make $1!)
Pringles ($1.50/can) - $1/4 PG 7/31, 8/31
Charmin ($5.44/12 rolls) - $0.25/1 PG 7/31, 8/31
Dawn ($0.99/10.4 oz) - $0.50/1 PG 7/31, 8/31
Orbit ($1.37/pack) - $1/1 CVS coupon printing at price checker
I bought: 8 cans of Pringles, 3 packages of Charmin, 2 bottles of Dawn, 1 bottle of St. Joseph Asprin, 1 pack of Orbit for...
Total Regular Price: $52.46
Total Sale and Coupons: $21.46
ECBs Used: $5.00
Total OOP: $26.00
ECBs Back: $2.00, plus $10 gas card
Wags
Carmex Moist Lip Balm (Vanilla or Lime Twist, 0.15 oz)
Total Regular Price: $2.10
Total Sale and Coupons: $0.49
ECBs Used: $1.00
Total OOP: $0.61
ECBs Back: $1.50
Advanced Auto Parts
5 quarts (individual or jug) or Havoline oil + 1 Drive Works filter: $15.99
5 quarts (individual) Quaker State oil + 1 Purolator Classic filter: $15.49
We took advantage of both of these deals (there weren't any Drive Works filters to fit our car), paying $35.29 OOP and saving $20.94. They also had a deal on oil changing gear (pan, etc.) like Mr. Poe previously discussed if you're in need of it.
PetSmart
I bought Layla a 40 lb bag of Iams for...
Total Regular Price: $41.44
Total Sale and Coupons: $5
Total OOP: $36.44
A great deal, plus there's $55 in Iams and PetSmart coupons in the bag!
Stay tuned next Monday for more deals and a special surprise!
Friday, August 26, 2011
MrsDrPoe: Braves Trivia
Good evening all! Since today's main post was about Atlanta's home team, I thought you might enjoy a bit of Braves trivia. Here's a timed quiz that will definitely test your team knowledge...be sure to share with us how you do!
This quiz and others can be found on at Sporcle- a site truly full of "mentally stimulating diversions." Mr. Poe and I love Sporcle quizzes- especially the daily word ladders. Definitely check out the rest of the site when you get a chance; you may just find your new favorite hobby!
This quiz and others can be found on at Sporcle- a site truly full of "mentally stimulating diversions." Mr. Poe and I love Sporcle quizzes- especially the daily word ladders. Definitely check out the rest of the site when you get a chance; you may just find your new favorite hobby!
MrsDrPoe: So We'll Root, Root, Root for the Bravos...
This Foto Friday I have something for you sports fans out there! We recently went to (my first) Braves game at Turner Field with our friends, the Granthams:
We parked at the CNN building:
And then walked through downtown Atlanta, past the capitol building:
And across the sea of swirly twirly gumdrops (just kidding) to the stadium. I've been to two other baseball stadiums in my lifetime (Minute Maid Park and Busch Stadium), and I don't remember the view from either of them being as lovely as the one from Turner Field...but I'm probably just partial to my new hometown:
That night the Bravos beat the Arizona Diamondbacks, 4-2 with 3 homers; although, I must confess that I yacked more than I watched the game:
The whole experience was quite relaxing, with the exception of parts of the walk back through downtown to the cars. Mr. Poe and I had a ton of fun, and we were so happy that we could go!
We parked at the CNN building:
And then walked through downtown Atlanta, past the capitol building:
And across the sea of swirly twirly gumdrops (just kidding) to the stadium. I've been to two other baseball stadiums in my lifetime (Minute Maid Park and Busch Stadium), and I don't remember the view from either of them being as lovely as the one from Turner Field...but I'm probably just partial to my new hometown:
That night the Bravos beat the Arizona Diamondbacks, 4-2 with 3 homers; although, I must confess that I yacked more than I watched the game:
The whole experience was quite relaxing, with the exception of parts of the walk back through downtown to the cars. Mr. Poe and I had a ton of fun, and we were so happy that we could go!
Thursday, August 25, 2011
MrsDrPoe: True Friendship
Welcome to Theology Thursday here at the blog! I invite you all to open your Bibles with me today as well examine what true friendship looks like according to the word of God.
At any given time in our lives, each of us has had one or more persons that could be called a friend; these people are definitely blessings from God and a great encouragement through life's trials. Although we form these friendships in various places and through various circumstances, each of these relationships shares that we have something in common with and enjoy the company of our friend. We must ask ourselves, however, do our friends exhibit the qualities that true friends should? And do we exhibit these qualities toward our friends? To determine what a true friend should be, we should examine some Biblical examples of friendship.
If we look in 1 Kings 12:1-15, we see the children of Israel requesting of King Rehoboam to reduce the heavy burdens that his father (King Solomon) had placed on them. Before making a decision, Rehoboam sought counsel from the elders who served his father; they told him to grant the people's request. Rehoboam didn't like this answer; however, so he further sought the counsel of his friends that he had grown up with. These friends advised him to not only deny the people's request but to further increase their burden. Rehoboam approved of this answer and, as a result, later lost the majority of his kingdom to Jeroboam (as was prophesied).
If we go back a little further in the Old Testament to 2 Sam 13, we see one of King David's sons, Amnon, who lusted after his half-sister, Tamar. Just like Rehoboam, Amnon had a friend named Jonadab who told him exactly what he wanted to hear. Jonadab helped Amnon devise a plan that allowed Amnon to physically take advantage of Tamar, humbling her, disgracing the royal family, and eventually leading to the murder of Amnon.
Were the friends of Rehoboam and Amnon good friends? The world would say, "Of course! They helped give them what they wanted. They helped make them happy (at least for a little while)." Solomon would disagree in Proverbs 1, however. In this passage, the wise old king tells his son to avoid the companionship of those who would entice and encourage sinful behavior, contrasting their calls for friendship with the call of wisdom to be holy and seek the Lord.
We must conclude then that true friendship should be anchored by more than a common workplace/sports team/hobby. To be a good friend, one must keep another's spiritual well-being in mind. If we have a friend who is lusting after a woman/man not his/her wife/husband, the 'friendly' thing to do is to help them overcome these sinful thoughts through prayer, Bible study, counseling, etc. The 'unfriendly' thing to do is outlined in the 2 Samuel passage we just examined. Similarly, if we are the ones lusting, a true friend would help us overcome this sin NOT encourage us to continue in it.
Look with me at 2 Samuel 12. In this passage, the prophet, Nathan, comes before King David to tell him a parable about a rich man who steals a lamb from a poor man who loved the lamb as his family; outraged at the injustice, David vows to kill the rich man. Nathan then tells David that he is the rich man and that the parable is a parallel to what he had done to Uriah and Bathsheba. Even though he was speaking to the king, Nathan had the courage to point out his sin as God had sent him to do. Unlike the friends of Rehoboam and Amnon, Nathan was a true friend to David.
So what's the best way to be a good friend? If our friend is not a Christian, we can invite him/her to Bible study, introducing him/her to Jesus and allowing His teaching throughout the New Testament to point out the sin in their lives. If our friend is a Christian, Matt 18, 1 Cor 5, and 2 Thess 3 tell us that sin in the church must be addressed; and if it is not remedied, withdrawal is required.
It's really hard to be a true friend. I've never known anyone who particularly enjoys confrontations, and telling someone what he/she wants to hear is a lot less confrontational that telling that same person that what he/she is doing or wants to do is wrong. No one desires the social stigma associated with one who's labeled as "nosy," "rude," or "intolerant." And of course it's always difficult to determine the best way to approach a sinful situation- we don't want to hurt or embarrass our friends. But we must remember that our friends' souls are more important than an awkward moment or temporary strain on/loss of a friendship.
At any given time in our lives, each of us has had one or more persons that could be called a friend; these people are definitely blessings from God and a great encouragement through life's trials. Although we form these friendships in various places and through various circumstances, each of these relationships shares that we have something in common with and enjoy the company of our friend. We must ask ourselves, however, do our friends exhibit the qualities that true friends should? And do we exhibit these qualities toward our friends? To determine what a true friend should be, we should examine some Biblical examples of friendship.
If we look in 1 Kings 12:1-15, we see the children of Israel requesting of King Rehoboam to reduce the heavy burdens that his father (King Solomon) had placed on them. Before making a decision, Rehoboam sought counsel from the elders who served his father; they told him to grant the people's request. Rehoboam didn't like this answer; however, so he further sought the counsel of his friends that he had grown up with. These friends advised him to not only deny the people's request but to further increase their burden. Rehoboam approved of this answer and, as a result, later lost the majority of his kingdom to Jeroboam (as was prophesied).
If we go back a little further in the Old Testament to 2 Sam 13, we see one of King David's sons, Amnon, who lusted after his half-sister, Tamar. Just like Rehoboam, Amnon had a friend named Jonadab who told him exactly what he wanted to hear. Jonadab helped Amnon devise a plan that allowed Amnon to physically take advantage of Tamar, humbling her, disgracing the royal family, and eventually leading to the murder of Amnon.
Were the friends of Rehoboam and Amnon good friends? The world would say, "Of course! They helped give them what they wanted. They helped make them happy (at least for a little while)." Solomon would disagree in Proverbs 1, however. In this passage, the wise old king tells his son to avoid the companionship of those who would entice and encourage sinful behavior, contrasting their calls for friendship with the call of wisdom to be holy and seek the Lord.
We must conclude then that true friendship should be anchored by more than a common workplace/sports team/hobby. To be a good friend, one must keep another's spiritual well-being in mind. If we have a friend who is lusting after a woman/man not his/her wife/husband, the 'friendly' thing to do is to help them overcome these sinful thoughts through prayer, Bible study, counseling, etc. The 'unfriendly' thing to do is outlined in the 2 Samuel passage we just examined. Similarly, if we are the ones lusting, a true friend would help us overcome this sin NOT encourage us to continue in it.
Look with me at 2 Samuel 12. In this passage, the prophet, Nathan, comes before King David to tell him a parable about a rich man who steals a lamb from a poor man who loved the lamb as his family; outraged at the injustice, David vows to kill the rich man. Nathan then tells David that he is the rich man and that the parable is a parallel to what he had done to Uriah and Bathsheba. Even though he was speaking to the king, Nathan had the courage to point out his sin as God had sent him to do. Unlike the friends of Rehoboam and Amnon, Nathan was a true friend to David.
So what's the best way to be a good friend? If our friend is not a Christian, we can invite him/her to Bible study, introducing him/her to Jesus and allowing His teaching throughout the New Testament to point out the sin in their lives. If our friend is a Christian, Matt 18, 1 Cor 5, and 2 Thess 3 tell us that sin in the church must be addressed; and if it is not remedied, withdrawal is required.
It's really hard to be a true friend. I've never known anyone who particularly enjoys confrontations, and telling someone what he/she wants to hear is a lot less confrontational that telling that same person that what he/she is doing or wants to do is wrong. No one desires the social stigma associated with one who's labeled as "nosy," "rude," or "intolerant." And of course it's always difficult to determine the best way to approach a sinful situation- we don't want to hurt or embarrass our friends. But we must remember that our friends' souls are more important than an awkward moment or temporary strain on/loss of a friendship.
Wednesday, August 24, 2011
MrsDrPoe: Sliders
It's another What's for Dinner Wednesday, and tonight I'll actually be sharing a main course recipe for two- old school sliders. Technically, we prepare regular sized hamburgers this way too, but mini-burgers are cuter. The breadcrumbs and Worcestershire make for a super moist and delicious burger, no matter the size!
Ingredients: 1/2 pound lean ground beef, 2 Tablespoons Worcestershire sauce, 1/4 cup Italian breadcrumbs, small buns or rolls (not pictured), your favorite burger toppings (not pictured).
In a small bowl, combine the beef, Worcestershire sauce, and breadcrumbs with your hands. After the mixture is thoroughly combined, divide in fourths, forming a small bun-shaped patty out of each fourth. Place the patties on a hot grill (or electric grill or grill pan if you're cooking inside):
Cook the burgers to your desired doneness (15-20 minutes till well-done on a grill pan, depending on patty shape and pan temp), flipping once about half-way through the cooking time. Place on the buns (we love potato rolls) and top with your favorite flavors (we like mustard, ketchup, dill pickles, bacon, lettuce, tomato, and cheese; the Lukes love BBQ sauce, ranch, bacon, cheese, lettuce, and tomato). Bon Appetit!!
Ingredients: 1/2 pound lean ground beef, 2 Tablespoons Worcestershire sauce, 1/4 cup Italian breadcrumbs, small buns or rolls (not pictured), your favorite burger toppings (not pictured).
In a small bowl, combine the beef, Worcestershire sauce, and breadcrumbs with your hands. After the mixture is thoroughly combined, divide in fourths, forming a small bun-shaped patty out of each fourth. Place the patties on a hot grill (or electric grill or grill pan if you're cooking inside):
Cook the burgers to your desired doneness (15-20 minutes till well-done on a grill pan, depending on patty shape and pan temp), flipping once about half-way through the cooking time. Place on the buns (we love potato rolls) and top with your favorite flavors (we like mustard, ketchup, dill pickles, bacon, lettuce, tomato, and cheese; the Lukes love BBQ sauce, ranch, bacon, cheese, lettuce, and tomato). Bon Appetit!!
MrsDrPoe: Gone with the Wind
For the next reading review, I'll be examining some fiction for a change. I present to you "Gone with the Wind" by Margaret Mitchell.
I had read this ginormous book (over 1000 pages!) once before in high school and had seen the movie at least once, so I knew all about Scarlett, Rhett, Ashley, and Melanie, and the major events in the story. While it was nice to fill in the blanks that were lacking in my memory bank, I was a little disturbed by the amount of profane language used by the characters, especially considering the negative publicity associated with the single word present in the 1939 making of the movie of the same title. All the characters except for Melanie and Ellen (Scarlett's mother) were also very disappointing, as selfishness, deceit, lust, gossip, and countless other sinful actions and attitudes were prevalent and even justified throughout the pages. I read the last few chapters through tear-filled eyes, severely affected at the mess the characters had made of their lives. I don't think this will be a book I read again in my lifetime.
Having said all that, there were several things that I did enjoy about this book. The first is the fact that because I now live in the metro-Atlanta area, I was super-excited every time I saw the name of a city that I knew of- Marietta, Atlanta, Kennesaw, Jonesboro, etc. The story really came alive for me since I am now familiar with its setting. Secondly, it was nice to review tidbits of history since I haven't had a true history class in years. It has never been a favorite subject of mine, but I do enjoy learning about certain past events when I know there's not going to be a test afterward. The thing I was most intrigued about, however, was that for a book about very worldly (and mostly ungodly) people, there were several Biblical references in the text that I was excited to find- the hanging of Haman, baptism washing away sins, carrying your cross (although, I think this was misused), gaining the world and loosing your soul, etc.
Those are my thoughts on this monster of a novel. Have you ever read Gone with the Wind? What parts did you like/dislike?
I had read this ginormous book (over 1000 pages!) once before in high school and had seen the movie at least once, so I knew all about Scarlett, Rhett, Ashley, and Melanie, and the major events in the story. While it was nice to fill in the blanks that were lacking in my memory bank, I was a little disturbed by the amount of profane language used by the characters, especially considering the negative publicity associated with the single word present in the 1939 making of the movie of the same title. All the characters except for Melanie and Ellen (Scarlett's mother) were also very disappointing, as selfishness, deceit, lust, gossip, and countless other sinful actions and attitudes were prevalent and even justified throughout the pages. I read the last few chapters through tear-filled eyes, severely affected at the mess the characters had made of their lives. I don't think this will be a book I read again in my lifetime.
Having said all that, there were several things that I did enjoy about this book. The first is the fact that because I now live in the metro-Atlanta area, I was super-excited every time I saw the name of a city that I knew of- Marietta, Atlanta, Kennesaw, Jonesboro, etc. The story really came alive for me since I am now familiar with its setting. Secondly, it was nice to review tidbits of history since I haven't had a true history class in years. It has never been a favorite subject of mine, but I do enjoy learning about certain past events when I know there's not going to be a test afterward. The thing I was most intrigued about, however, was that for a book about very worldly (and mostly ungodly) people, there were several Biblical references in the text that I was excited to find- the hanging of Haman, baptism washing away sins, carrying your cross (although, I think this was misused), gaining the world and loosing your soul, etc.
Those are my thoughts on this monster of a novel. Have you ever read Gone with the Wind? What parts did you like/dislike?
Tuesday, August 23, 2011
MrsDrPoe: Conservation of Momentum, Part IV
Thesis Tuesday is upon us yet again, ladies and gents! As promised, today we will be continuing our discussion of the Conservation of Momentum Equation with an example of how to solve the Navier Stokes equations.
We'll start with fluid flowing between two parallel plates, separated by H meters and infinite in the z-direction. (Note: infinite plates do not exist, but this consideration allows us to approximate the flow as 2D instead of 3D). We will consider the pressure driven flow case where both plates are stationary (I), as well as the Couette Flow case where the upper plate moves in the +x-direction with some velocity U m/s (II).
Given: gap height = H meters
Find: the flow field description (u, v, w, and p)
Assumptions: steady, laminar, incompressible, infinite plates (w = 0, d/dz(...) = 0), constant properties, ignore edge effects, Newtonian fluid, fully developed (d/dx(...) = 0)
Solution:
Step 1: We must first apply the continuity equation.
Since the flow is steady (or because it's incompressible), the first term is equal to zero. For fully developed, laminar flow, d/dx(rho*u) = 0; for infinite plates, d/dz(rho*w) = 0. Because the fluid is incompressible, rho can be pulled out of the derivative in the remaining term. Thus, we are left with:
x-momentum:
d/dt(u) = 0 since the flow is steady; d/dx(u) = 0 since the flow is fully developed; d/dy(u) = d/dz(u) = 0 because the flow is laminar; thus, the entire left side of the equation equals zero for this case. On the right-hand side, rho*gx = 0 because gravity only acts in the downward (-y) direction; d/dx(d/dx(u)) = 0 also because the flow is fully developed; d/dz(d/dz(u)) = 0 since we are dealing with infinite plates. Rearranging the two terms that are left, we have:
y-momentum:
From the result of our continuity equation examination, we know that all the terms containing a v must be equal to zero. We can quickly see that we are only left with two terms:
When both sides of this equation are integrated, we obtain the hydrostatic pressure distribution.
z-momentum:
Because our flow is laminar, all terms containing a w or d/dz(...) are equal to zero. Also, we know that the term rho*gz = 0, since gravity is only acting in the downward (-y) direction. This equation quickly reduces to:
Step 3: Then we integrate the reduced Navier-Stokes equations and solve for the unknowns.
z-momentum:
y-momentum:
x-momentum:
We now have an expression for each of the variables necessary for a full flow field description (v = 0, w = 0, p = ..., u = ...). To completely finish the problem, we must examine our given boundary conditions to determine
Step 4 (I): We need two boundary conditions since there are two constants of integration that need to be determined. For this case, both plates are stationary; therefore, the no-slip condition tells us that u = 0 at y = 0 and u = 0 at y = H (if we consider the bottom plate to be located at y = 0). Applying the first yields:
Applying the second gives:
So: u = (0.5/mu)*d/dx(p)*(y*y - H*y)
Step 4 (II): We again need two boundary conditions since there are two constants of integration that need to be determined. For this case, the bottom plate is stationary and the top plate is moving with constant velocity, U; therefore, the no-slip condition tells us that u = 0 at y = 0 and u = U at y = H (if we consider the bottom plate to be located at y = 0). Applying the first yields:
Applying the second gives:
So: u = (0.5/mu)*d/dx(p)*(y*y - H*y) + (U*y)/H
We can plot the velocity for both of these cases verses y for specified values of d/dx(p), U, mu, and H; this will give us the velocity distribution of the flow between the plates. Here you can see an animation of velocity profiles for various values of U and d/dx(p). If you'd like to play with this program yourself, you can download it (for free I think) from Wolfram Mathematics.
And that's the Navier Stokes equations in a nutshell! Like I mentioned last week, a lot of assumptions need to be made in order to obtain a version of these equations that we can work with; however, once these have been made, the resulting forms of the equations can be solved rather simply.
If you're feeling extra adventurous, try to go through the procedure again by yourself, examining what the velocity profile looks like for the case where the top plate is moving and bottom one is stationary or one plate is moving in the +x-direction and one is moving in the -x-direction or both plates are moving in the +x-direction at the same speed and at different speeds.
We'll start with fluid flowing between two parallel plates, separated by H meters and infinite in the z-direction. (Note: infinite plates do not exist, but this consideration allows us to approximate the flow as 2D instead of 3D). We will consider the pressure driven flow case where both plates are stationary (I), as well as the Couette Flow case where the upper plate moves in the +x-direction with some velocity U m/s (II).
Given: gap height = H meters
Find: the flow field description (u, v, w, and p)
Assumptions: steady, laminar, incompressible, infinite plates (w = 0, d/dz(...) = 0), constant properties, ignore edge effects, Newtonian fluid, fully developed (d/dx(...) = 0)
Solution:
Step 1: We must first apply the continuity equation.
d/dt(rho) + d/dx(rho*u) + d/dy(rho*v) + d/dz(rho*w) = 0
Since the flow is steady (or because it's incompressible), the first term is equal to zero. For fully developed, laminar flow, d/dx(rho*u) = 0; for infinite plates, d/dz(rho*w) = 0. Because the fluid is incompressible, rho can be pulled out of the derivative in the remaining term. Thus, we are left with:
rho*d/dy(v) = 0 or d/dy(v) = 0
Step 2: Next, we simplify the Navier Stokes equations.
Since the derivative of v is equal to zero, that means that v must be constant (found by integrating both sides of the above equation):
But we know that because we are dealing with a viscous fluid, the no-slip condition holds. This tells us that the fluid adjacent to either plate has the same velocity as the plate; therefore, since the bottom plate is fixed in both cases, u = v = w = 0 at this location. Putting this boundary information with the result from the continuity equation, v = 0 throughout the domain.
v = const
But we know that because we are dealing with a viscous fluid, the no-slip condition holds. This tells us that the fluid adjacent to either plate has the same velocity as the plate; therefore, since the bottom plate is fixed in both cases, u = v = w = 0 at this location. Putting this boundary information with the result from the continuity equation, v = 0 throughout the domain.
x-momentum:
rho*[d/dt(u) + u*d/dx(u) + v*d/dy(u) + w*d/dz(u)] = -d/dx(p) + rho*gx + mu*[d/dx(d/dx(u)) + d/dy(d/dy(u)) + d/dz(d/dz(u))]
d/dt(u) = 0 since the flow is steady; d/dx(u) = 0 since the flow is fully developed; d/dy(u) = d/dz(u) = 0 because the flow is laminar; thus, the entire left side of the equation equals zero for this case. On the right-hand side, rho*gx = 0 because gravity only acts in the downward (-y) direction; d/dx(d/dx(u)) = 0 also because the flow is fully developed; d/dz(d/dz(u)) = 0 since we are dealing with infinite plates. Rearranging the two terms that are left, we have:
d/dx(p) = mu*d/dy(d/dy(u))
y-momentum:
rho*[d/dt(v) + u*d/dx(v) + v*d/dy(v) + w*d/dz(v)] = -d/dy(p) + rho*gy + mu*[d/dx(d/dx(v)) + d/dy(d/dy(v)) + d/dz(d/dz(v))]
From the result of our continuity equation examination, we know that all the terms containing a v must be equal to zero. We can quickly see that we are only left with two terms:
d/dy(p) = rho*gy
When both sides of this equation are integrated, we obtain the hydrostatic pressure distribution.
z-momentum:
rho*[d/dt(w) + u*d/dx(w) + v*d/dy(w) + w*d/dz(w)] = -d/dz(p) + rho*gz + mu*[d/dx(d/dx(w)) + d/dy(d/dy(w)) + d/dz(d/dz(w))]
Because our flow is laminar, all terms containing a w or d/dz(...) are equal to zero. Also, we know that the term rho*gz = 0, since gravity is only acting in the downward (-y) direction. This equation quickly reduces to:
0 = 0
Step 3: Then we integrate the reduced Navier-Stokes equations and solve for the unknowns.
z-momentum:
0 = 0 tells us nothing
y-momentum:
p = -rho*gy*y + fp(x)
essentially the hydrostatic pressure distribution, the integration constant in this case, fp(x), is constant in the y direction, but may be a function of x
essentially the hydrostatic pressure distribution, the integration constant in this case, fp(x), is constant in the y direction, but may be a function of x
x-momentum:
(1/mu)*d/dx(p) = d/dy(d/dy(u)) rearranging
(1/mu)*d/dx(p)*y + const1 = d/dy(u) integrating once
(0.5/mu)*d/dx(p)*y*y + const2 = u integrating twice
(1/mu)*d/dx(p)*y + const1 = d/dy(u) integrating once
(0.5/mu)*d/dx(p)*y*y + const2 = u integrating twice
We now have an expression for each of the variables necessary for a full flow field description (v = 0, w = 0, p = ..., u = ...). To completely finish the problem, we must examine our given boundary conditions to determine
Step 4 (I): We need two boundary conditions since there are two constants of integration that need to be determined. For this case, both plates are stationary; therefore, the no-slip condition tells us that u = 0 at y = 0 and u = 0 at y = H (if we consider the bottom plate to be located at y = 0). Applying the first yields:
const2 = 0
Applying the second gives:
const1 = -(0.5/mu)*d/dx(p)*H
So: u = (0.5/mu)*d/dx(p)*(y*y - H*y)
Step 4 (II): We again need two boundary conditions since there are two constants of integration that need to be determined. For this case, the bottom plate is stationary and the top plate is moving with constant velocity, U; therefore, the no-slip condition tells us that u = 0 at y = 0 and u = U at y = H (if we consider the bottom plate to be located at y = 0). Applying the first yields:
const2 = 0
Applying the second gives:
const1 = -(0.5/mu)*d/dx(p)*H + U/H
So: u = (0.5/mu)*d/dx(p)*(y*y - H*y) + (U*y)/H
We can plot the velocity for both of these cases verses y for specified values of d/dx(p), U, mu, and H; this will give us the velocity distribution of the flow between the plates. Here you can see an animation of velocity profiles for various values of U and d/dx(p). If you'd like to play with this program yourself, you can download it (for free I think) from Wolfram Mathematics.
And that's the Navier Stokes equations in a nutshell! Like I mentioned last week, a lot of assumptions need to be made in order to obtain a version of these equations that we can work with; however, once these have been made, the resulting forms of the equations can be solved rather simply.
If you're feeling extra adventurous, try to go through the procedure again by yourself, examining what the velocity profile looks like for the case where the top plate is moving and bottom one is stationary or one plate is moving in the +x-direction and one is moving in the -x-direction or both plates are moving in the +x-direction at the same speed and at different speeds.
Monday, August 22, 2011
MrsDrPoe: JCPenny Deal, 8/21
Another exciting tidbit of information I have for you today involves one of my favorite department stores: JCPenny.
Since we've moved to Atlanta, I've gotten four coupons for $10 off a purchase of $10 or more at Penny's. Needless to say, I've been stoked about it. For my latest purchase, I bought a shirt to go with a hand-me-up skirt a friend passed on to me:
Grand Total OOP: $0.21
While at the store, the clerk told me about JCP Rewards, the rewards program for JCPenny shoppers. Without applying for the store credit card, you can earn rewards points by registering up to three credit cards with JCP online. For each dollar you spend in store or online using one of your registered cards, you earn one point. When you reach 250 points each month, you will get a $10 reward. Plus, by providing your email address, you will be notified about giveaways, discounts, and various other store offers. I'm not sure how much this rewards program will help us, since we don't spend that much at department stores, but I'm hoping we'll see some great deals come out of it around black Friday.
Do any of you have experience with this program? Have you seen significant savings?
Since we've moved to Atlanta, I've gotten four coupons for $10 off a purchase of $10 or more at Penny's. Needless to say, I've been stoked about it. For my latest purchase, I bought a shirt to go with a hand-me-up skirt a friend passed on to me:
Grand Total OOP: $0.21
While at the store, the clerk told me about JCP Rewards, the rewards program for JCPenny shoppers. Without applying for the store credit card, you can earn rewards points by registering up to three credit cards with JCP online. For each dollar you spend in store or online using one of your registered cards, you earn one point. When you reach 250 points each month, you will get a $10 reward. Plus, by providing your email address, you will be notified about giveaways, discounts, and various other store offers. I'm not sure how much this rewards program will help us, since we don't spend that much at department stores, but I'm hoping we'll see some great deals come out of it around black Friday.
Do any of you have experience with this program? Have you seen significant savings?
MrsDrPoe: Wags and Kroger Deals, 8/21
Happy Money Monday to all! It'd like to share some deals at Walgreens and Kroger that are going on this week:
Wags
Degree Deo: 2/$4, $1 back in ECBs, $1/2 RP 7/31
Dial Body Wash: $3.99, $3.00 back in ECBs
Candles: $1.49 clearance
Extra Dessert Delights gum: $0.65 clearance
Transaction 1
Total Regular Price: $12.36
Total Savings and Coupons: $6.50
ECBs Used: $5.00
Total OOP: $0.86
ECBs Back: $3.00
Transaction 2
Total Regular Price: $7.57
Total Savings and Coupons: $3.62
ECBs Used: $3.00
Total OOP: $0.95
ECBs Back: $1.00
Kroger
Boneless, skinless chicken breasts $1.99/lb
Fresh corn $0.38/ear
Kroger Shredded Cheese B1G1
Check out Mega Event deals here.
Wags
Degree Deo: 2/$4, $1 back in ECBs, $1/2 RP 7/31
Dial Body Wash: $3.99, $3.00 back in ECBs
Candles: $1.49 clearance
Extra Dessert Delights gum: $0.65 clearance
Transaction 1
Total Regular Price: $12.36
Total Savings and Coupons: $6.50
ECBs Used: $5.00
Total OOP: $0.86
ECBs Back: $3.00
Transaction 2
Total Regular Price: $7.57
Total Savings and Coupons: $3.62
ECBs Used: $3.00
Total OOP: $0.95
ECBs Back: $1.00
Kroger
Boneless, skinless chicken breasts $1.99/lb
Fresh corn $0.38/ear
Kroger Shredded Cheese B1G1
Check out Mega Event deals here.
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