@@johncimbala hello professor, lovely to see you on youtube.. your books in fluid mechanics and thermodynamics are the best things, I have had in my life...glad to hear your voice..now when I read ur books, your voice will ring in my ears
Thank you for your kind comment. Please tell your friends and colleagues about my RUclips 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 RUclips channel where there are 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 RUclips 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 kind comment. Please tell your friends and colleagues about my RUclips 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.
I can't seem to understand the purpose of the Taylor expansion. All I remember from my calculus courses was it being used to approximate functions as polynomials...how does that relate to what we are doing here?
We are using it to generate a differential equation. We examine how properties change across a small volume. Then, when that volume shrinks to infinitesimal size, we end up with a differential equation.
Same differential equation since I did not treat density as constant in the derivation. Near the end of the video and near the end of the annotated notes I show an integral that includes the density within the integral since it may not be constant. Thank you for your comment. I am glad that my videos have been useful to you! Please tell your friends and colleagues about my RUclips channel where there are almost 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.
truncated Taylor series for single variable in this case would be f(x)=f(a)+f'(a) ∆x considering this case for multivariable scalar function P, the series would be P(x,y,z)(at centre)= P(x,y,z+dz/2)(at top) +(dP(x,y,z+dz/2)/dz)*dz/2 but how does dP(x,y,z+dz/2)/dz)*dz/2= dP(x,y,z)/dz*dz/2 is it because z+dz/2=z because dz tends to zero? and if dz tends to zero then taking center, upper and bottom face would be meaningless, the fluid element would just be a point
This is extremely underrated it is Cimbala himself the guy who write the book of fluid mechanics why aren't more people watching
I don't know why. Please get the word out for me!
@@johncimbala hello professor, lovely to see you on youtube.. your books in fluid mechanics and thermodynamics are the best things, I have had in my life...glad to hear your voice..now when I read ur books, your voice will ring in my ears
Great explanation sir
Thank you for your kind comment. Please tell your friends and colleagues about my RUclips 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 professor! I understand it!!!!!!
Thank you for your kind comment. Please tell your friends and colleagues about my RUclips channel where there are 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.
Explained so well!
Thank you for your comment. Please tell your friends and colleagues about my RUclips 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 so much professor
Thank you for your kind comment. Please tell your friends and colleagues about my RUclips 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.
@@johncimbala Of course professor. We are watching and learning from your videos from Turkiye. Thank you so much for these great books and lectures.
I can't seem to understand the purpose of the Taylor expansion.
All I remember from my calculus courses was it being used to approximate functions as polynomials...how does that relate to what we are doing here?
We are using it to generate a differential equation. We examine how properties change across a small volume. Then, when that volume shrinks to infinitesimal size, we end up with a differential equation.
GOD DAMN ITS SO GOOD ~ THX
Thanks for the comment - except for the cursing.
how about compressible case teacher
Same differential equation since I did not treat density as constant in the derivation. Near the end of the video and near the end of the annotated notes I show an integral that includes the density within the integral since it may not be constant.
Thank you for your comment. I am glad that my videos have been useful to you! Please tell your friends and colleagues about my RUclips channel where there are almost 500 free videos about the Bible, fluid mechanics, science, math, Excel, statistics, air pollution, and other topics. I would greatly appreciate it.
truncated Taylor series for single variable in this case would be
f(x)=f(a)+f'(a) ∆x
considering this case for multivariable scalar function P, the series would be
P(x,y,z)(at centre)= P(x,y,z+dz/2)(at top) +(dP(x,y,z+dz/2)/dz)*dz/2
but how does dP(x,y,z+dz/2)/dz)*dz/2= dP(x,y,z)/dz*dz/2
is it because z+dz/2=z because dz tends to zero?
and if dz tends to zero then
taking center, upper and bottom face would be meaningless, the fluid element would just be a point
It shrinks to a point which is why we can truncate the Taylor series in the first place.