B Pressure gradient causes conservative force?

Is the force that accelerates afluid betwen two points of different pressure conservative?
 

Charles Link

Homework Helper
Insights Author
Gold Member
2018 Award
4,216
1,754
A very interesting question. Since the force per unit volume is ## \vec{f}_v=-\nabla P ## , and ## \nabla \times \nabla P=0 ##, (a vector identity that is commonly known from E&M theory), you might think that could be possible. In a real fluid however, there will also be viscous damping forces on the volume that are part of the total force equation that are often left out of the equation ## \vec{f}_v=-\nabla P ##. ## \\ ## So that the answer is the forces in a liquid are non-conservative, even though the part that comes from the minus of the pressure gradient could be considered to be conservative. ## \\ ## Note: This is my own analysis=others may agree or disagree=this is the first time I have encountered this question. ## \\ ## Additional note: You could think of these forces as acting on a small object of finite volume that is placed in the fluid. (And of course gravity will also act on the object, which is a conservative force).
 
Last edited:
Thank you so much for your answer
It is clear
 

Charles Link

Homework Helper
Insights Author
Gold Member
2018 Award
4,216
1,754
Thank you so much for your answer
It is clear
I added one more part above, about the force of gravity on an object in the fluid=be sure and see that. ## \\ ## Additional item: There is a vector identity, ## \int \nabla P \, d^3 x=\int P \, \hat{n} dA ##, (where ## \hat{n} ## is the outward pointing normal), and to have equilibrium, ## -\delta g \, \hat{z}+-\nabla P= 0 ##, (where ## \delta ## is the density (mass per unit volume)), so that you can actually derive Archimedes' principle from the pressure gradient force.
 

Want to reply to this thread?

"Pressure gradient causes conservative force?" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Top Threads

Top