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I am glad you enjoyed the video. It is the first of a whole series. Note that you can download the notes that I generated while creating the videos. This may save you some writing time. Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

No, I have about 2 more weeks of material. I am working on them - Christmas break and getting ready for classes (start tomorrow) has slowed me down. Also, my "A Professor Skeptic Christmas Carol" took a LONG time to create and edit, as you can imagine if you have watched it. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala sure! got it! thanks!

Glad you found my videos helpful. Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you. And thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@johncimbala Sure, I'm actually doing that with everyone. This channel is an absolute treasure and many of my friends who so much liked your textbook with Prof Cengel liked to know about it too. I just can't describe how grateful we are. May God bless you for this amazing work that you granted us for free. Thank you so much

Ha! I don't consider myself to be great. If you want to accomplish something, put your heart and soul into it and work hard. Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

I am not sure where you mean. Please point out where, as I am unaware of any errors in that lesson Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it..

One book where it is used is the book I use when I teach this course, namely, Fluid Mechanics by Kundu, Cohen, and Dowling by Academic Press. Tensor notation is used a lot in the study of fluid mechanics, especially turbulence. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for your comment. I am glad that my videos were helpful to you. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for your kind comment. I am glad that you enjoy my videos. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for your kind comment. I am glad that you find these videos useful. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala sure, I will definitely do that.

No reason you can't. Either send me a link or send the actual picture to jmc6@psu.edu Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

I am planning to created a playlist for my entire compressible flow course - hopefully starting this semester after I complete my graduate fluids video series. The compressible flow lessons may or may not be ready in time for your compressible flow course (which sounds like you will take in the fall). Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for your comment. Note that "no stately form or majesty" does not imply that he had defects. We don't know for sure, but I believe that Jesus had no physical defects since he was the God-man. But this is debatable and many others hold to your belief. Note that most of Isaiah 53 discusses his appearance from the crucifixion. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Yes, Jesus is talking about fulfilling the law and the prophets, many (if not most) being about Jesus himself. In my Dramatic Bible Reading videos, I do not do any commentary, just a straight Bible reading. In my playlist called Two-Minute Bible Videos, I analyze a Bible verse or passage in more detail and comment about it - you may enjoy some of those. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala Thank you Prof.

Thanks, Jean. I appreciate your kind comment!

I respectfully disagree with you. I take the Bible to be the truth, literally, and I stand by what I concluded in my video. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala My brother in Christ, I recognize why you would perceive your perception to be true. As soon as you stated "literally", the Holy Spirit guided me to refer you to these scriptures. In regards to referring people to your TH-cam channel, I also have a channel with 356 videos covering the same items you have list. But my videos make the connect of the Holy Spirit that can be found within all religious doctrines. We must be Empowered by the Spirit. Jesus says as Luke quotes him: "And while staying with them he ordered them not to depart from Jerusalem, but to wait for the promise of the Father, which, he said, “you heard from me; for John baptized with water, but you will be baptized with the Holy Spirit not many days from now.” The problem that is developed by "literally interpreting" the scriptures is, you are perceiving them from a physical perspective, ignoring the message to be received by the Holy Spirit. This is why Jesus speaks in parables as explained in (Matthew 13:10-13) where his disciples ask him why he speaks to people in parables, and he replies that it is to "hide the mysteries of the kingdom of heaven from those who are not ready to understand" and to reveal them to those who are receptive; essentially, to separate those with open hearts from those with hardened hearts. One more key message you might have missed is in (John 4:24), "God is spirit, and his worshipers must worship in the Spirit and in truth". I follow Jesus Christ by worshiping within the Holy Spirit. If you would like to know more, you can reach me at th-cam.com/channels/PG2BSyFRIOQSRsmC-gxv6Q.html My channel is where I give my 100% raw and truthful transition of giving up my life, bearing my own cross, and I have "literally" travelling around the world giving my money to the poor. This is how I perceive the scriptures "literally" and live my life through the Holy Spirit's prospective. I never ask anyone to subscribe or like my videos. I know that one must be drawn to the "Absolute Truth" within the Holy Spirit organically, otherwise we are merely seeking popularity of our channel. In this way we become the two olive trees and the two lamp stands. We do not know the Holy Spirit unless we find the "Spiritual whole" within all religious doctrines. The Holy Spirit is unity not division. We must listen to others perceptions out of empathy and find how the Holy Spirit within us, aligns with others. Have no fear and my peace be with you.

Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@johncimbala sure

I agree with you that a Y chromosome doesn't just "pop" into existence. That is why it had to be a miracle of God!

Mostly correct. System and Lagrangian are pretty much the same. Control volume and integral are pretty much the same. Differential can be either. In fluid mechanics, Eulerian is typically preferred over Lagrangian and that is why we use the material derivative, as covered in a different video to transform from system (Lagrangian) to Eulerian differential equations. In an integral analysis, we use the Reynolds Transport Theorem to do the same - go from a system to a control volume. Hope this helps. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala Thank you, John, for the explanation. I will certainly recommend it to my colleagues and friends. Following up on the query above, what about moving or deforming control volumes? This concept may not be analogous to the Eulerian description.

@@suryatejaananth5724 Deforming CVs get a little more complicated. However, you must sill start with the system equations (like conservation of mass) and then transform to the CV equations using the more general Reynolds Transport Theorem for CVs. This is covered in my fluid mechanics textbook and to a lesser extent in some of my lesson videos.

Perhaps so... Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thanks, Ed! Glad you liked it!

Ha Ha! Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@daveclipper6617 Thank you!

Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@jt4998 Thank you J T!

Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Sure😊

Thank you for your comment. I am glad that you find my videos useful. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Yes, my video series should certainly help you learn the basics of fluid mechanics. That's why I created them! Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@ Absolutely, Prof. Cimbala!!! Thank you again for your kind response. (:

Yes, indeed.

Glad you found my video helpful. Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Glad you found my video helpful. Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Glad you found my videos helpful. Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

​@johncimbala I'm making sure everyone I know (who likes math) knows about this. Looking forward to watching your Bible series also. Many thanks.

Glad it was helpful to you. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

I pray that he does. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

PI 3 is simple because it is just a length over a length. All the other repeating variables drop out. You are welcome to go through the step by step procedure to calculate this PI and you get the exponents I mention in the video for PI 3, which turns out to be epsilon divided by D. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@johncimbala sure sir

Well, there is only so much material we can discuss. In Mechanical Engineering, we typically don't encounter baroclinic situations. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala Thanks! just wanted to make sure :)

The signs are correct. The force of the bucket on the wheel is opposite in sign of the force of the wheel on the bucket. And you need to think in terms of the control volume, not what you think physically, since you can treat the control volume as a "black box" meaning that you can solve the problem without even knowing what is inside. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for your very kind comment! I am glad that my videos were helpful to you. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

That is what I say in my video. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you for watching my video and for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

All human beings have the same number of chromosomes (except for Down Syndrome), so I don't follow your line of reasoning about Adam. I obviously take a more literal view of the Bible than you do. Finally, Jesus did go back to heaven but with a resurrected body that was changed from his old body yet still recognizable (still had the scars, for example). We who believe will also receive new bodies that are like that of Jesus. Thank you for watching my video and for your comment. Please tell your friends and colleagues about my TH-cam channel where there are over 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.