Fluid Mechanics Lesson 02C: Equation of Fluid Statics
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- เผยแพร่เมื่อ 5 ก.พ. 2025
- Fluid Mechanics Lesson Series - Lesson 02C: Equation of Fluid Statics
In this 11-minute video, Professor Cimbala derives the equation of fluid statics, also called hydrostatics, by using Taylor series expansions on a small fluid element. The equation is then simplified for the case of an incompressible fluid.
This video incorporates material from Section 3-1 of the Fluid Mechanics textbook by Cengel and Cimbala.
An Excel file listing of all the videos in this series can be found at
www.me.psu.edu... .
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Dr. John M. Cimbala is Professor of Mechanical Engineering at Penn State. He is an educator, textbook author, Christian author, husband, father, and grandfather. He also created and maintains a website for helping people grow in their faith called Christian Faith Grower at www.christianf... His TH-cam channel is at / @johncimbala
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
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.
Great explanation sir
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Thank you professor! I understand it!!!!!!
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Explained so well!
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Thank you so much professor
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@@johncimbala Of course professor. We are watching and learning from your videos from Turkiye. Thank you so much for these great books and lectures.
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.
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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.