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Thank you for your comment. Note that I respect, but do not hold to, the Roman Catholic doctrine of Mary's Immaculate Conception. My video is an analysis of where Jesus' DNA came from without invoking the sinlessness of Mary. Please tell your friends and colleagues about my TH-cam channel where there are more than 480 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 more than 480 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

We can respectfully disagree about Mary's sinlessness. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 480 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

I usually pick a point in the flow, like (x,y) = (1,1) or something easy like that and calculate u and/or v. That gives you the direction of one streamline. The rest easily follow once you know the direction of one. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 480 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala Thank your, will do

hank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 480 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

PDF files of all my lesson videos are available for download. See the TH-cam description of the video and click "...more." There is a link to an Excel file that has all of the pdf files for the lessons (plus equation sheets and other resources). Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 480 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Yes, that could happen if it is a compressible ball. Then you would have to use the density of the smaller, compressed ball to calculate the buoyancy force. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 480 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

n is a vector that is the unit outward normal. It has magnitude one and points in the direction perpendicular to the plane or face (area) being considered.

Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 480 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 more than 480 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Gamma_a determines the lift on the airfoil, so it is set by how much lift the airplane needs to generate. Later on in the course, we will have more detail about this. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 480 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 how to answer - at what point in the video are you referring to? Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 480 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 more than 480 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

I agree. The point of my video, however, is that the Bible never says that the lion will lie down with the lamb. It says instead that the wolf will lie down with the lamb. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you and thanks for your helpful suggestions!

Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you. I appreciate that. I do hope to continue the compressible flow videos, but probably not within the next month. We'll see.

Please do not call me Lord - that title is reserved for Jesus Christ. If you back up one episode you will see where I introduce and explain potential flow theory, also called irrotational flow because it applies to irrotational regions of flow. The video lesson is Fluid Mechanics Lesson 12E: The Irrotational Flow Approximation th-cam.com/video/NY_KYh6UagI/w-d-xo.html Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

Think of the surface of a liquid as the skin of a balloon - there is a tension force, and that force is between fluid molecules, yes. But when the surface touches a solid, that tension is felt between the fluid and the solid as well. For capillary tubes, for example, the surface tension force of the wall acting on the liquid pulls it up until gravity (hydrostatic pressure) force and surface tension force balance. Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

​@@johncimbala Thanks Is this related to young's equation at interface?

@@ahammedafzal7797 Yes, very much so, although I do not mention Young's equation in my video.

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A normal shock, by definition, is perpendicular to the flow. So, any shock at an angle, even a small deflection angle, is NOT a normal shock - it is an oblique shock. Thank you for your kind comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 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 more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala I will Prof.

Good points. Thank you. My main point was that the contrails (especially far downstream) are not smoke but condensed water droplets. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 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 more than 470 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 more than 470 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 more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

1) Yes. 2) Yes, but less than the total even across a shock wave. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 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 more than 470 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 more than 470 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 more than 470 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 more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala Done. Sir I have few queries regarding hydraulic machines. How to ask?

@@gauravshakrawal4336 You can ask here. I try to answer questions as I am able but cannot spend too much time if they are detailed questions about specific machines - just general questions. There are also Facebook groups for just about any topic where people ask and answer questions.

Civil engineers use a different friction factor than do mechanical engineers. MEs use the Darcy friction factor while CEs use the Fanning friction factor. The Darcy friction factor is four times the Fanning friction factor. CEs also use a different hydraulic radius than do MEs, by the way. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala Thankyou Prof!!

Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 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 more than 470 free videos about the Bible, fluid mechanics, science, math, statistics, Excel, air pollution, and other topics. I would greatly appreciate it.

Ha ha!

Yes, but it does work.

Yes, I provide all the needed equations on the equation sheet that you can download. However, it takes some iteration to determine the shock location. I discuss this in detail in my compressible flow course (a technical elective), for which I do not yet have many youtube videos. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 400 free videos about the Bible, fluid mechanics, science, math, statistics, air pollution, and other topics. I would greatly appreciate it.

Thank you. I appreciate that.

Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 400 free videos about the Bible, fluid mechanics, science, math, statistics, air pollution, and other topics. I would greatly appreciate it.

By the way, my name is Cimbala, not Ximbala.

​@@johncimbala Sorry, x and c keys are so close on my cellphone.. 😅

Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 400 free videos about the Bible, fluid mechanics, science, math, 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 more than 400 free videos about the Bible, fluid mechanics, science, math, statistics, air pollution, and other topics. I would greatly appreciate it.

If you watch closely (or better yet, look at the annotated notes PDF file), you will see that I never say that Pvac is negative. Pvac is never negative. Rather, I said in that example that -Pvac is negative. Pvac is the negative of Pgage. As for watching the videos, yes, the entire series represents the full 3-credit fluid mechanics course that I teach at Penn State. It should indeed prepare you well for your course. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala ohhhh yeah I do remember you saying that. Thank you very much. Love your videos and the effort. If any of my peers have trouble I’ll refer them to your videos.

Interesting thought, but I have no idea how to respond. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.

@@johncimbala I would but all my colleagues work in IT (including myself). I did graduate aeronautics somewhere in eastern EU some 33 years ago but worked only 2 years in the field. Moved to IT because it pays much better and I had 2 kids I needed to raise. From time to time I'm coming back to youtube movies to remember what I learned in college. But mostly my interests are related on how some of these phenomenon in electro magnetism are happening. For instance we have Faraday law of induction which is great for a quantitative analysis but there is no explanation how or why is happening. And I did read Maxwell original book and I'm sure it's all fluid dynamics, the fluid being the aether or what we call nowadays space time. So was always wondered if some of these phenomenon can be explained with fluid dynamics. Take the magnetic field. Experiences prove there is no magnetic monopole (only south or only north pole). But a simple explanation is the magnetic field line is a vortex closing on itself so that alone explains why there are no monopoles.

It would climb up to the top and for the most part maintain its meniscus. It could not bulge outward because that would make the pressure in the liquid greater than atmospheric pressure across the meniscus. It also could not just flow out the top because that would be a perpetual motion machine that would violate the second law of thermodynamics. Thank you for your comment. Please tell your friends and colleagues about my TH-cam channel where there are more than 470 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 more than 470 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.