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