MrsDrPoe: Monster's Christmas Vacation

Happy Foto Friday on the blog!  Today I'll share with you some pictures of Monster's Christmas vacation.

She spent most of her times sleeping:

And loving on Mama and Papa Poe:

Because she's had problems with her tail:
 

 

Poor Monster!  We're taking good care of her, and hope that she can be her playful tail-swinging self again soon!

MrsDrPoe: 2012 Challenge

It's the last Theology Thursday of 2011!  Once again, I'd like to encourage you all to join me with adopting a book and reading through the Bible in a year in 2012.

"How can a young man cleanse his way?  By taking heed according to Your word.  With my whole heart I have sought You; oh, let me not wander from Your commandments!  Your word I have hidden in my heart, that I might not sin against You.  Blessed are You, O LORD!  Teach me Your statutes.  With my lips I have declared all the judgements of Your mouth.  I have rejoiced in the way of Your testimonies, as much as in all riches.  I will meditate on Your precepts, and contemplate Your ways.  I will delight myself in Your statutes; I will not forget Your word." - Psalm 119 9-16

MrsDrPoe: Fall Harvest Pasta

What's for Dinner this Wednesday is another original recipe that reminds me of fall but really makes a tasty dinner any time of year- Fall Harvest Pasta.

Ingredients: 4 oz chicken breast, 1 tsp ground cinnamon, 1 tsp ground nutmeg, 1 tsp ground ginger, 1 tsp garlic powder, 1 tsp onion powder, 1/2 an apple, 1/2 cup of grapes, 1/4 cup of pecans, 1 Tbs olive oil (not pictured), pasta.

Dice the chicken, fruit, and nuts, then saute in olive oil with all the spices on med-high heat until the chicken is cooked and the fruit is soft (15-20 minutes).

Serve over your favorite pasta (Note: I would recommend a thicker noodle than angel-hair), and enjoy!

MrsDrPoe: What To Expect When You're Expecting

For today's Reading Review, I present to you "What To Expect When You're Expecting" by Heidi Murkoff and Sharon Mazel*:

This book was an easy read with lots of information mixed with humor and encouragement.  Since I've never been pregnant, I don't know about all the questions or symptoms a pregnant woman would have, but this work seemed to cover the gamut.  The main section of the book was broken up into 9 month-by-month chapters that detailed what the baby was growing or practicing each week in the month, symptoms you may be having, and what you may be concerned about (food, physical activity, pains, intimacy, etc).  It also covered pre-pregnancy topics, post-pregnancy topics, and information on miscarriages and stillbirths.

The only pseudo-negative thing about this book is that it truly was written for every woman; while even those with STDs, drug problems, who would consider abortion, etc. need information about pregnancy I didn't particularly enjoy reading those sections of the book.  Having said that, I would definitely recommend this book to any woman who is pregnant or desiring to become pregnant, and I plan to purchase my own copy when we (Lord willing!) are blessed with news of the first non-furry-Poe-baby.  I also look forward to reading the other books in the "What to Expect" series!

*Mr. Poe and I are not pregnant, but we would like to have children one day, so I'm reading about it now before it's upon me and I have no time to read.

MrsDrPoe: Blasius Boundary Layer Example

It's another Thesis Tuesday on the blog, and as promised, I'll be giving you an example of the Blasius Boundary Layer Solution.

Problem: A viscous fluid with a known density (rho = 1300 kg/m^3) flows past a flat plate such that the boundary layer thickness at a distance 1.3 m from the leading edge is 12 mm.  Determine the boundary layer thickenss, shear stress and friction coefficient at a distance of 0.2 m from the leading edge if the free stream velocity is 1.5 m/s.

Given: xk = 1.3 m, deltak = 12 mm, rho = 1300 kg/m^3, U = 1.5 m/s
Find: delta, tauw, and Cf at 0.2 m
Solution:

Rek = (5*xk/deltak)^2 = 2.934x10^5

nu = U*xk/Rek = 6.646x10^-6 m*m/s

mu = nu*rho = 8.64x10^-3 N*s/m*m

Rex = U*x/nu =  45,140

delta = 5*x/sqrt(Rex) =4.707 mm

tauw = 0.3332*U^(3/2)*sqrt(rho*mu/x) = 4.571 Pa

Cf = 0.664/sqrt(Rex) = 3.125x10^-3

Pretty simple, huh?  Until next time...keep studying!

MrsDrPoe: Deals 12/26

Happy Money Monday to you all!  There aren't that many fantabulous deals out there this week- except of course Christmas decor, which is currently 50% off.  But here are a few things that I've got my eye on:

Wags
Red Baron Pizza - $2.99 with in-add coupon

CVS
Zyrtec 5ct. - $5.99, get $5.99 back in ECBs
Folgers Country Roast Coffee 43.5 oz - $6.99, plus Q in RP 12/04




What deals have you guys come across this week?
 

MrsDrPoe: "Merry Christmas, Harry!" "Happy Hanukka, Marv!"

Merry Christmas Eve Eve and Foto Friday to you all!  Today I'd like to share with you our Christmas present this year*:

That's right...Mr. Poe and I are now HOMEOWNERS!  We are so thankful for such a tremendous blessing and pray that we will always use it to glorify God.  

Hope your holiday is merry and bright!

*Photo credit to zillow.com

MrsDrPoe: Wise Words for the Holiday Season

For this Theology Thursday on the blog, I'd like to leave you with a few words to remember this holiday season:

"I have shown you in every way, by laboring like this, that you must support the weak. And remember the words of the Lord Jesus, that He said, 'It is more blessed to give than to receive.' " -Acts 20:35

MrsDrPoe: Curried Chicken and Apple Pie Two Ways

Another What's For Dinner Wednesday is upon us, and tonight I'd like to share with you another result from my kitchen experiments while Mr. Poe was traveling a few months ago.  I was in the mood for chicken curry and was contemplating apple pie for dessert, so I combined the two and added in some cheddar cheese (I've always been strangely curious about the combo of apple pie and cheese) to make...curried chicken and apple pie, two ways.

Ingredients: 4 oz chicken breast (chopped), 1/2 an apple (chopped), 2 tablespoons olive oil, 2 tablespoons flour (not pictured), 1-2 cups milk, 2 teaspoons cinnamon, 1 teaspoon onion powder, 1 teaspoon garlic powder, 1 1/2 tablespoons curry powder, 1 package saffron yellow rice (cooked), 1/2 cup shredded cheddar cheese.

Saute the chicken, apple, and spices in the olive oil, using a medium skillet on med heat.  When the chicken is cooked and the apple has softened, add flour to the skillet, and continue to cook for a minute longer.  Add milk, stir, and continue to heat until the sauce thickens.  Once thickened, reduce the heat and stir in the cheese until melted:

To serve...

1) For a traditional chicken curry look, pour the sauce over rice and accompany with grilled nann: 

2) For a more 'apple pie' look, spread some uncooked naan dough in the bottom of a casserole dish.  Combine the sauce with the rice, and layer it over the dough.  Cover with another layer of dough, then bake at 350 degrees for 15 to 20 minutes until the naan is light brown and crispy:

 

Enjoy!

MrsDrPoe: Ms. Long

For the next edition of Poes Pals, I'd like you to meet another friend of ours from Starkville, Ms. Long*:

We've known Ms. Long for many years and have had many adventures with her.  A recent graduate of MSU, she is currently teaching English and working on a masters degree.  Ms. Long loves everything about English- words and spooky stories in particular, and H.P. Lovecraft is one of her favorite authors.  We wouldn't be surprised if her own work was published one of these days; she's a great writer, even though she tends to keep her stories to herself.

Ms. Long also has a goofy side that makes for a barrel of laughs.  She loves the Lord and her family, and is very close to her mother and sister.  We look forward to the opportunity to visit Ms. Long and the rest of our Starkville family soon!

*Picture taken by Ms. Long's cousin, Ms. K. Davis.

MrsDrPoe: The Blasius Boundary Layer Solution

It's Thesis Tuesday on the blog, and today we'll be looking at the Blasius Boundary Layer solution.

Often when discussing boundary layer flow over a flat plate, the Blasius boundary layer solution is examined.  This solution is based on the fact that, even though the boundary layer profile changes along the plate, its general shape remains the same.  To capture this relationship, Blasius defined a similarity variable, eta = y*sqrt(Uinfinity/(2*nu*x)).  We can define a stream function for the flow based on the volumetric flow rate between streamlines: psi = sqrt(2*nu*Uinfinity*x)*f(eta).  Using our stream function/velocity relations and the product rule, we can see that:

u = d/dy(psi) = Uinfinity*f'(eta)

v = -d/dx(psi) = sqrt((nu*Uinfinity)/(4*x))*(eta*f'(eta) - f(eta)).

Since we now have our velocity components in terms of x and y, we can plug these expressions into the boundary layer momentum equation to obtain (with MUCH manipulation): 

f''' + f*f'' = 0.

The boundary conditions for this differential equation are f = f' = 0 at eta = 0 and f' -> 1 as eta -> infinity.  Check out the figure here.

From the computed solution, it can be seen that u = 0.99*Uinfinity when eta = 5.0.  This gives us: delta = 5*sqrt(nu*x/Uinfinity) = 5*x/sqrt(Rex), where Rex is the local Reynolds number at any x-location along the plate (Rex = Uinfinity*x/nu).  Furthermore, since we now know the velocity profile in the boundary layer, we can calculate the shear stress at any x-location along the plate by tauw = 0.332*Uinfinity^(3/2)*sqrt(rho*mu/x).  We can also determine the friction coefficient at a particular x-location Cf = 0.664/sqrt(Rex).

Next week we'll look at an example problem involving these equations.  Happy studying!

MrsDrPoe: Twas the Week Before Christmas...

Happy Money Monday here on the blog!  It's the last week to buy Christmas presents or materials for them.  There isn't a whole lot going on at the drugstores this week, but other retailers are hoping to help you save on those last minute purchases.  Be sure to check here and here for up-to-the-minute deals as they're published.  

I don't have anything to report, since all my shopping is done, but I hope you find the deals you're looking for!  Have a great holiday season!

MrsDrPoe: "And Above All The Bustle You'll Hear..."

Happy Foto Friday to you all!  The past weeks have been busy for Mr. Poe and me (more on that next FF); although, since my computer had to be sent off for repair, I had actually had some spare time...

When Mr. Poe and I were planning our wedding (years ago), we decided that I would make my bridesmaids dresses as my gift to them and I would make vests and ties for Mr. Poe and his groomsmen as gifts to them.  I finished the dresses and had started Mr. Poe's vest (from the leftover satin from my gown) when we found out that vests and ties came free with the tuxes we had chosen to rent for the gents in our bridal party.  Needless to say, since there were a million other wedding details to be working on (not to mention setting up a new apartment, graduating, and starting grad school), the vest went on the back burner...until now.  I finally finished and made a tie to go along with it:

So now if you see Mr. Poe with a little more swag than usual, you'll know why.  I also had time to add some length to one of my favorite dresses that hasn't been out of the closet in years:

And in case you didn't know, Mr. Poe loves to build things.  Since we didn't have finals to cram for this year, he designed a gingerbread mansion for us to build:

I think he did a great job...even without using as much of my dough as he wanted to.  We plan to make this a new holiday tradition, so be on the lookout for next year's design!

MrsDrPoe: Psalm 1

It's Theology Thursday on the blog, and as always, I invite you to open up your Bibles as we look into another portion of God's word.

Psalm 1

Blessed is the man who walks not in the counsel of the ungodly,

Nor stands in the path of sinners,

Nor sits in the seat of the scornful;

But his delight is in the law of the LORD,

And in His law he meditates day and night.

He shall be like a tree Planted by the rivers of water,

That brings forth its fruit in its season, whose leafe also shall not wither;

And whatever he does shall prosper.

The ungodly are not so, but ar like the chaff which the wind drives away.

Therefore the ungodly shall not stand in the judgment,

Nor sinners in the congregation of the righteous.

For the LORD knows the way of the righteous,

But the way of the ungodly shall perish.

A couple of thoughts from this psalm:


First, we can see the progression of sin in the first few lines- we begin by asking ungodly people for advice then by carrying through with sinful actions (Jas 1:13-16).


We also see that there are ONLY two choices- we follow the way of the LORD and are righteous in His sight, or we refuse to and perish as the ungodly.




We must be very careful of the company we keep, the desire of our hearts, and the actions that we take.  I hope these thoughts have been helpful to you on this very lovely Thursday!

MrsDrPoe: Mocha Latte

What's for Dinner Wednesday?  How about a nice, snuggly Mocha Latte!  Avoid Starbucks and save some cash for Christmas presents with this quick and easy drink.

Ingredients: 4 oz chocolate milk, 8 oz coffee or espresso.

Make the foam by pouring the chocolate milk in a jar with a lid, and shake till frothy and doubled in size (about 30 seconds):

Pour the coffee into your favorite mug, and gently pour the milk and foam in the coffee:

Enjoy!

MrsDrPoe: The Dwelling Place

One of the ladies from my book club was kind enough to let me borrow the sequel to The Swan House, so for the next Reading Review, I present to you Elizabeth Musser's The Dwelling Place:

This story is set in Atlanta and Hilton Head and is about the youngest daughter (Ellie) of the main character in The Swan House (Mary Swan).  As in the first work of the series, the plot focuses on a daughter "discovering" both her mother and what living for Jesus means.  It definitely has it's sad parts (as well as happy ones) and gives a myriad of examples of how we can use our trials to glorify God.

I enjoyed reading this book (maybe not as much as The Swan House), and I found it very hard to put down.  As with the first book, it is very clean with very clear spiritual overtones.  It also made me think a lot about how little I know about what my mother and grandmothers went through that shaped them into what they are/were.  All too often I look at those around me who I haven't known their whole lives and take for granted that they are who they are; I don't take the time to learn more about them and to appreciate things they may have overcome to get where they are today.  I think this type of knowledge would help me to have a deeper love and appreciation for people.

While I appreciated that The Dwelling Place encouraged thought, it did seem like some of the things that happened to the characters in this work were too fictional and too "perfect" (even though they weren't necessarily good things).  This is probably because there are so many years between the first and second books that it was hard for me to imagine the end of the first one leading to the events in the second; I found myself somewhat glad that there isn't a third book in the series for this reason.

I would definitely recommend this book to anyone, especially those who enjoyed The Swan House; however, I would caution readers that some of the religious ideas presented in the work are not in accordance with what the Bible teaches.    

MrsDrPoe: Boundary Layer Equations

It's once again Thesis Tuesday on the blog, and today we'll look some more at external flow.

One of the most important considerations of external flow is this region around the body in the flow that is affected by viscous stresses.  This region, called a boundary layer, possesses a large velocity gradient as the velocity transitions from 0 at the wall (from the no-slip condition) to 0.99*Uinfinity at the top of the boundary layer.  Since tau = mu*d/dy(u), we know that it is because of this velocity gradient that viscous stresses are important!  Typically, the height (distance from the surface to the top of the boundary layer) is denoted delta.

Fluid flow in the boundary layer is governed by a special reduced form of the governing equations.  We can find these equations using simple scaling analysis.  We will begin with the continuity equation for flow over a flat plate:

d/dt(rho) + d/dx(rho*u) + d/dy(rho*v) + d/dz(rho*w) = 0

Reducing for incompressible, 2D flow:

d/dx(u) + d/dy(v) = 0

We can say that du scales with Uinfinity (Uinfinity is a representative x-velocity), dx scales with L, dv scales with vs, and dy scales with delta.   For continuity to be satisfied, these two scaled terms must be of the same magnitude.  Thus, setting them equal, we find that vs = U*delta/L.

Next we will look at the Navier-Stokes y-momentum equation (so we've made assumptions of Newtonian Fluid, steady, constant properties, laminar, incompressible) for 2D flow:

rho*(u*d/dx(v) + v*d/dy(v)) = -d/dy(p) + v*(d/dx(d/dx(v)) + d/dy(d/dy(v)))

Applying our scaling arguments as before with the exception of p scaling with rho*U*U: rho*U*vs/L, rho*vs*vs/delta, rho*U*U/delta, v*vs/(L*L), v*vs/(delta*delta).  If we substitute in the value for vs that we found from the continuity equation:

rho*U*(1/L)*(U*delta/L), rho*(U*delta/L)*(1/delta)*(U*delta/L), rho*U*U/delta, v*(1/(L*L))*(U*delta/L), v*(1/delta)*(U*delta/L)

We can make these terms dimensionless by multiplying both sides by delta/(U*U*rho): (delta*deta)/(L*L), (delta*delta)/(L*L), 1, (delta*delta)/(L*L), 1/Re, 1/Re.  If we then take the limit as delta/L (the boundary layer is VERY thin) -> 0 and Re -> infinity, we see that the only term that does not go to zero is the pressure term, d/dy(p).  From these arguments, we can see that d/dy(p) = 0, or the pressure does not vary significantly in the direction normal to the wall.

Finally, we will apply scaling arguments to the Navier-Stokes x-momentum equation (again already reduced for 2D flow): rho*(u*d/dx(u) + v*d/dy(u)) = -d/dx(p) + v*(d/dx(d/dx(u)) + d/dy(d/dy(u))).  The terms become: rho*U*U/L, rho*vs*U/delta, rho*U*U/L, v*U/L, v*U/delta.  Substituting our expression for vs: rho*U*U/L, rho*(U*delta/L)*U/delta, rho*U*U/L, v*U/L, v*U/delta and non-dimensionalizing by multiplying by L/(U*U*rho): 1, 1, 1, 1/Re, (L*L/delta*delta), 1/Re.  If we again take the limit as delta/L -> 0 and Re -> infinity, we can see that the fourth term goes to zero; however, it is unclear what the last term becomes.  We can examine three possibilities: a) it's less that 1, b) it's greater than 1, or c) it's equal to 1.  

For case (a), scaling allows us to eliminate this term (since it is insignificant compared to the terms that reduced to 1) leaving: rho*(u*d/dx(v) + v*d/dy(v)) = -d/dx(p).  This equation is true for potential flow (irrotational, no viscous stresses), but since we definitely have these stresses present in the boundary layer, this option cannot be true.  

For case (b), the fifth term is the most significant term in the momentum equation so it would become: 0 = v*d/dy(d/dy(u)).  While this equation accounts for viscous stresses, it is purely diffusive and incorrect (we can see that d/dy(u) changes along the plate in the x-direction and is not constant).  

So case (c) must be correct, which means our boundary layer x-momentum equation can be written: rho*(u*d/dx(u) + v*d/dy(u)) = -d/dx(p) + v*d/dy(d/dy(u)).

A few miscellaneous notes:

Our full set of boundary layer equations consists of: 

d/dx(u) + d/dx(v) = 0

 

rho*(u*d/dx(u) + v*d/dy(u)) = -d/dx(p) + v*d/dy(d/dy(u))

 

0 = d/dy(p)

The boundary conditions for these equations are: u(x,0) = 0 (no-slip), v(x,0) = 0 (no-slip), u(x,delta) = Uinfinity, and u(x0,y) = uin(y) (starting velocity profile).

Incidentally, for our scaling: delta/L scales with 1/sqrt(Re).  Also, just outside the boundary layer, Bernoulli's equation applies.

MrsDrPoe: Deals 12/11

Happy Money Monday to you all!  Here are a few deals going on this week:

Christmas Cards:

Order at American Greetings - you can get 60 percent off and they'll ship them for free to all your recipients (if you type in their addresses)

Buy 3 $0.99 American Greetings Christmas cards at CVS, get $3 back in ECBs

Freebees:

Buy Goodies mini hair clips or hair pins ($2) at Walgreens, get $2 back in RRs


Buy Salonpas Pain Patch ($1) at Walgreens, get $1 back in RRs


Buy a bag of Combos ($2) at CVS, get $2 back in ECBs

MrsDrPoe: The Weather Outside is Frightful...

As you know, it's been cold recently.  This Foto Friday, I'd like to show you how the girls deal with the 'frightful weather'...

aren't they so cute in their scarves and hats?  Hope you all are staying warm!

MrsDrPoe: The Offense of Familiarity

It's another Theology Thursday on the blog, and I'd like to once again invite you to open your Bibles with me as we look at a portion of God's word.

In Mark 6:1-6, Jesus goes to His hometown of Nazareth to continue His earthly teaching ministry.  We see Him in v. 2 preaching in the Synagogue on the Sabbath as was His typical M.O.  The folks in the city regard the fact that He is teaching "wisdom" and performing "mighty works"; however, instead of heeding the wisdom of His word, they are offended at Him because they knew Him as "the carpenter" and desire to kill Him (Luke 4:29).  Because of their unbelief, Jesus provides them with no further signs of His person but instead continues teaching in other villages.

It seems so ironic to read of people who basically say, "Jesus has so much wisdom!  But lets totally ignore it."  But isn't that what we do sometimes?  Jesus says in v. 4, "A prophet is not without honor except in his own country, among his own relatives, and in his own house."  Examining the prophets in the old testament, nearly all were ill-received and mistreated by the very people they were trying to warn.  Again I ask, isn't that what we do sometimes?

If your mom or brother or friend tells you that you should be going to Bible study, you have been very unkind lately, you have a lot of anger, the people you are hanging around with are not helping you spiritually, or any number of other things, don't we often get offended?  But if someone we didn't know quite so well told us the same thing, would we be more inclined to listen?  Just like the people of Nazareth were so familiar with Jesus the carpenter whose family they knew, they were offended by the things that he taught and did.

Not wanting to listen to advice is a pride issue that we all must struggle against.  Although every piece of advice we are given (solicited or not) may not be the best course of action to take, we must humble ourselves to truthfully examine what we are told- especially from those who know us best and truly have our best spiritual interests at heart.  And we must also humble ourselves before the word of God.  While we read the teachings of Jesus, we must examine ourselves and try to correct where we are lacking.  We must be careful not to be offended by or take lightly the instruction of "the Carpenter" or the godly wisdom of those who follow Him.

MrsDrPoe: Maple Syrup Pasta

It's another What's for Dinner Wednesday, and since it's the holiday season, tonight I'd like to share with you my original, Elf inspired dessert- Maple Syrup Pasta.

Ingredients: 1/2 an apple, 1/2 cup grapes, 2 tablespoons pecans, 1 teaspoon nutmeg, 1 teaspoon ginger, 2 teaspoons cinnamon, 1 tablespoon butter, 1/4 cup maple syrup, cooked pasta.

Chop up the fruit and nuts, and saute in butter and spices till the fruit is soft:

Stir in the syrup to warm it.  Poor the sauce over cooked pasta, and enjoy!

 
This may sound a bit odd, but trust me- Buddy the Elf knew what he was doing when he combined maple syrup and pasta!

MrsDrPoe: The Goins Family

Welcome to the next edition of Poes' Pals here on the blog.  Today I'd like you to meet some of our new friends from Atlanta, the Goins Family:

We first met the Mr. and Mrs. Goins when we moved to the big city a few months ago, right before they were wed.  They are such a sweet couple, and they very cute together!  Mrs. Goins brought a furry 'child' into the family- a fluffy bunny named Rascal; he does something to make us laugh every time we visit their place.

Mr. Goins enjoys trivia games and UGA football.  Mrs. Goins currently works for a local insurance company.  In her spare time, she loves to experiment in the kitchen (which she does very well) and to look at pictures of puppies.  They are both very hospitable and eager to serve the Lord.  We consider ourselves blessed to have them in our lives!

MrsDrPoe: Characteristics of Flow Past an Object

Happy Thesis Tuesday to you all!  Today we'll be starting a series on external flow by examining some of this flow's general characteristics.

Flows in which an object is completely submerged in a fluid are termed external flows; however, flows such as those around buildings are also considered external flows, even though buildings aren't completely submerged.  We can consider cases where the object or body is stationary and fluid is flowing around it, where the object is moving through a stationary fluid, or some combination of the two.  For all of these situations, if we fix our coordinate system with the body, we can analyze these scenarios as if fluid were flowing over a stationary body.  We will consider the velocity upstream of the body (Uinfinity) to be constant with respect to time and space.  The bodies in the flow can be classified using one of two systems:

1a) 2D object extending infinitely in a third direction
1b) axi-symmetric bodies formed by rotating a cross-section about an axis of symmetry
1c) 3D bodies

2a) streamlined bodies
2b) blunt bodies

As you can imagine, flow past an object is influenced by both the fluid properties and the size and shape of the object.  These characteristics are typically grouped in dimensionless parameters; those used most often for external flows are Reynolds number, Mach number, and the Froude number.

We can examine some general differences in flows for a range of Reynolds number values by taking a closer look at flows over a flat plate.  Here we consider a plate of length, l, in the same fluid with the same viscosity and density, but we will continue to increase the upstream velocity, Uinfinity, so that Re = 0.1, 10, and 10^7.  As the Reynolds number increases, the region around the plate where the viscous forces/stresses are important shrinks considerably, causing outer streamlines to be deflected from the plate less and less.  The wake region behind the plate also shrinks as the Reynolds number increases.  It should be noted that flows with Re < 1 are dominated by viscous effects while flows with Re > 1 are dominated by inertia.

If we look at flow over a cylinder, we can make some more generalizations about how flow over blunt bodies is affected by changes in Reynolds number.  For low Reynolds number flows (0.1), again we see large deflection of the streamlines far away from the body.  These streamlines appear to be symmetric about the center of the cylinder (the stagnation streamline) as we saw when we investigated the velocity potential function.  As the Reynolds number increases (50, 10^5), we see this area affected by the viscous stresses again shrinking.  We can also see that the flow separates from the surface of the clyinder, creating a recirculation bubble or wake behind the cylinder.

Next week we'll continue looking at external flows, focusing on the region affected by the viscous forces.  Until then, happy studying!

MrsDrPoe: Drugstore Deals 12/04

Happy Money Monday to you all!  There are a few good deals going on at the drugstores this week that I wanted to share with you today...

CVS

Candy Canes - $1.27, get $1.27 back in ECB (double check that your ECBs printed before you leave the store)
American Greeting cards - $0.99 ea. (selected), get $3 ECB WYB 3, coupon printing at kiosk for $1/2 (you make a dollar!)
Buy $20 in Schick/Playtex, get $10 ECB - buy 2 packs of Schick disposible razors and 1 shave gel, use B1G1 SS 11/06, $2/1 SS 12/04, and $1 SS 12/04 to make it all free!

Wags

W by Duck Packaging Tape - $0.99 with in-add coupon, $1/1 in SS 11/20 makes it free
Revlon Top Speed Nail Enamel - $3.99, get $3 back in RR
Holiday Goody Containers - $0.99


AND...for those of you who live in the Metro-Atlanta Area, the Forum is offering free horse carriage rides Saturday evenings and Sunday afternoons; pick-up is in front of Belk.

MrsDrPoe: "It's Beginning to Look a Lot Like Christmas"

Happy Foto Friday everyone!  Mr. Poe has a rule that we cannot decorate for Christmas or listen to Christmas music before December 1st.  As you know, today is December 2nd, so last night we continued our annual tradition of picking out a tree, eating a sackful of Krystals, and putting up the decorations while watching Elf.  Check it out:

What holiday decoration traditions do you have?

MrsDrPoe: "How Is It That You Have No Faith?"

Welcome to another Theology Thursday on the blog!  As usual, I invite you to open up your Bibles with me as we look into another portion of God's word.

One of the threads running through the book of Mark is that fear causes faith to grow or shrink.  If we look at Jesus' calming of the storm in 4:35-41, we see one particular example.  In this passage, Jesus and some of His disciples are on a boat crossing the sea of Galilee when a "great windstorm" comes up.  The disciples are frantic, thinking they are about to die while Jesus is asleep on a pillow.  (Note: Many of these men were fishermen by trade who had grown up on these waters; this must have been some storm to have seasoned seamen so shaken up.)  They wake Jesus, who calms the storm with three words and then asks, "Why are you so fearful?  How is it that you have no faith?"

We may think to ourselves, "Isn't that a little harsh?  These people left everything they had to follow Him!"  Indeed they had a great enough faith to leave their old lives; however, when their faith was tested by their fear of the storm, it failed.

This example should be an important one for us- it shows that we cannot be stagnant in our faith.  We can't assume that we have "great faith" because once several years ago we believed in the risen Savior.  If our faith isn't growing, it's shrinking.

Just like we grow in bodily strength through weight-resistance, we grow in faith through resisting temptations.  When we fear ridicule for speaking up about our faith, speaking up anyway builds our faith.  When we don't have time to read our Bibles or pray, making time anyway builds our faith.  As we continue to grow our faith through these challenges, it makes it easier to grow when more difficulties are presented.  And because we are imperfect, we should take comfort in the fact that if we do shrink in our faith at one time, through the grace of God, we can overcome the next time we are tested, just like the disciples did.

I hope these thoughts have been helpful for you, and I hope you have a blessed day!

MrsDrPoe: Turkey Panini

It's another What's for Dinner Wednesday on the blog!  For those of you who have a few turkey scraps left over, here's a great way to polish them off...Turkey Paninis.

Ingredients: turkey, bacon, crescent rolls, provolone cheese, jam, sweet potato casserole.

Cut the crescent roll in half, and spread jam on one side and sweet potato casserole on the other.  Layer turkey, bacon, and cheese on the bottom roll half:

Place the remaining half of the roll on the top of the sandwich, and put the whole thing in a panini press (or George Foreman grill or on a skillet on the stove).  Cook till cheese is melted and turkey is warm.  Enjoy!

MrsDrPoe: The Swan House

For the next Reading Review here on the blog, I present to you another work of fiction, "The Swan House" by Elizabeth Musser:

"The Swan House" is a tale of a young girl growing up in Atlanta in the early sixties, revolving around the real-life Orly plane crash, racial tension, and faith.  The book has something for everyone- romance, suspense, football*, laughter, sadness, life, death...and the list goes on and on.

I really enjoyed reading this work.  I thought it was very well written, and I greatly appreciated the Mrs. Musser's subtleties (simply saying "he cursed" instead of providing full dialog, etc.) which adequately conveyed certain character's personalities without being crude.  I also appreciated the theme that Jesus can comfort all our pains and His truth sets us free.  This story was very fascinating and really pulled me into the story. 

On a negative note, I think that the prologue and epilogue are virtually unnecessary and almost detract a bit from the main story.  I would also caution readers to examine the various forms of Christianity presented in the book in light of the Bible, as many of the ideas portrayed are not in accordance with scripture.  While it is most refreshing to read a novel that places so much emphasis on faith in Christ, we must keep in mind that Christians are to worship "in Spirit and in truth."  


All in all, I would definitely recommend reading "The Swan House" (with a box of tissues handy), and I look forward to the chance to read the sequel.

*Mr. Poe and I learned that John Heisman used to coach at Tech from this book...cool huh?

MrsDrPoe: Dimensional Analysis, Part III

Welcome to the final Thesis Tuesday on Dimensional Analysis.  As promised last week, we're going to go through an example problem today so you can see the Buckingham Pi Theorem in action.

Example: Water sloshes back and forth in a tank as shown in the figure.  The frequency of the sloshing, f, is assumed to be a function of the acceleration of gravity, g, the average depth of the water, h, and the length of the tank, l.  Develop a suitable set of dimensionless parameter for this problem using g and l as repeating variables.

Given: f = F(g, h, l)
Find: suitable set of dimensionless parameters for the given problem
Solution:

Step 1: The variables in the problem are: 

frequency, f

tank length, l

gravity, g

water height, h

Step 2: Expressing these variables in basic dimensions:

f = 1/T

l = L

g = L/(T*T)

h = L

Step 3: Determining the number of pi terms:

k = 4 (f, g, l, h) and r = 2 (L, T) so k-r = 2

Step 4: We will choose g and l as our repeating variables because the problem statement told us to; however, we could work the problem using g and h as well.  Note: we cannot use f at all because it is the dependent variable, and we cannot use both h and l because the combination of repeating variables must contain all the basic dimensions.

Step 5: We will find the first pi term:

Pi1 = f*g^(a1)*l^(b1)

(1/T)*(L/T*T)^(a1)*L^(b1) = T^(0)*L^(0)

for L to cancel: a1 + b1 = 0

for T to cancel: -1 -2*a1 = 0

So: a1 = -1/2 and b1 = 1/2

Pi1 = f*sqrt(l/g)

Step 6: We will find the second pi term:

Pi2 = h*g^(a2)*l^(b2)

(L)*(L/T*T)^(a2)*L^(b2) = T^(0)*L^(0)

for L to cancel: 1 + a2 + b2 = 0

for T to cancel: -2*a2 = 0

So: a2 = 0 and b2 =-1

Pi2 =h/l

Step 7: Since it's easy to make a mistake, we need to check the pi terms:

Pi1 = f*sqrt(l/g) = (1/T)*sqrt((L*T*T)/L) = 1

Pi2 = h/l = L/L = 1

Step 8: Next, we will write the pi term containing the dependent variable as a function of the remaining pi terms:

Pi1 = F(Pi2) or f*sqrt(l/g) = F(h/l)

Not too bad, huh?

Additional Considerations

Our variables that we deal with in this process can be classified into three broad categories: those dealing with geometry (lengths, angles), material properties (viscosity, density), or external effects (velocities, external forces).

It is important to note that there is not a unique set of pi terms that arises from a dimensional analysis; however, the required number of pi terms is fixed.

Common Non-dimensional Numbers

Reynolds Number - (rho*V*l)/mu = inertial forces/viscous forces; applicable to all types of fluid dynamics problems

Froude Number - V/sqrt(g*l) = inertial forces/gravitational forces; applicable to flow with a free surface

Euler Number - p/(rho*V*V) = pressure forces/inertial forces; applicable to problems where pressure or pressure difference are important

Mach Number - V/c = inertial forces/compressibility forces; applicable to problems where compressibility of a fluid must be considered

MrsDrPoe: Cyber Monday

Welcome to the Cyber Monday edition of Money Monday on the blog.  There are all kinds of deals available online today at every store imaginable!  You can check out some of the best deals here.

There are also some drug store freebees (no coupons required)...

CVS has free bottles of Complete contact solution,

and Wags has free cold sore treatment, lip balm, muscle rub, and foot cream.  So get out there (or stay in) and save some money!

MrsDrPoe: Black Friday

Welcome to the Black Friday edition of Foto Friday here on the blog!  Mr. Poe and I went out at 3:30 this morning- we finished our Christmas shopping and found great deals on items we'll be needing in the near future.  After that we took a quick nap, and I joined Papa Wolgemuth in cutting down a Christmas tree at the Merry Christmas Tree Farm:

Later that night Papa Wolgemuth, Mama Wolgemuth, Mr. Poe, and I went to see White Christmas at the Orpheum:

It was a long, wonderful Black Friday!