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