Fluids: Bernoulli's Equation Derivation Question

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Discussion Overview

The discussion revolves around the derivation of Bernoulli's equation, specifically focusing on the forces acting on a fluid element and the direction of these forces in relation to fluid flow. Participants explore concepts related to pressure forces, Newton's laws, and the implications of these forces on fluid behavior.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question why the second force (F2) is applied in the opposite direction to the flow, suggesting it may be due to resistance.
  • There are inquiries about how pressure can be converted to energy and its relation to the direction of F2.
  • Several participants assert that the pressure force should act to the right, based on the direction of fluid velocity and pressure application.
  • Newton's second and third laws are referenced to explain the interactions between the fluid in the control volume and the fluid ahead of it, with emphasis on the forces exerted by and on the fluid.
  • One participant mentions that the direction of arrows in diagrams can be confusing, but believes that following the sums leads to consistent results.
  • There is a reflection on the nature of free body diagrams, noting that they typically only show forces exerted on a body, not those it exerts on others.

Areas of Agreement / Disagreement

Participants express differing views on the direction of the pressure force and the implications of Newton's laws, indicating that multiple competing interpretations exist without a clear consensus.

Contextual Notes

Participants acknowledge the complexity of the forces involved and the potential for confusion regarding the directionality of forces in diagrams. There is also mention of assumptions related to the ideal behavior of fluids, such as neglecting viscous forces.

Sbee
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TL;DR
Hi,
Studying Bernoulli's equation derivation and am not understanding WHY is the second Force for the larger distance applied in the direction OPPOSITE to the flow of the velocity?

I am using this textbook figure:
https://openstax.org/books/university-physics-volume-1/pages/14-6-bernoullis-equation

The derivation starts at "We also assume that there are no viscous forces in the fluid, so the energy of any part of the fluid will be conserved. "
I figure that either the Force F2 is applied in the opposite direction because of some kind of resistance, but I'm not sure.
Thanks!
 
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Sbee said:
Summary:: Hi,
Studying Bernoulli's equation derivation and am not understanding WHY is the second Force for the larger distance applied in the direction OPPOSITE to the flow of the velocity?

I am using this textbook figure:
https://openstax.org/books/university-physics-volume-1/pages/14-6-bernoullis-equation

The derivation starts at "We also assume that there are no viscous forces in the fluid, so the energy of any part of the fluid will be conserved. "

I figure that either the Force F2 is applied in the opposite direction because of some kind of resistance, but I'm not sure.
Thanks!
What direction do you think the pressure force exerted on the portion of the fluid under consideration by the fluid ahead of it should be acting?
 
F2 means the outlet pressure of the system converted to energy
 
horacio torres said:
F2 means the outlet pressure of the system converted to energy
What does this mean? How can pressure be converted to energy? How does it relate to the direction of F2?
 
Chestermiller said:
What direction do you think the pressure force exerted on the portion of the fluid under consideration by the fluid ahead of it should be acting?
It should be acting to the right, because the pressure is coming from the left side of the fluid and because the velocity is to the right!
 
Sbee said:
It should be acting to the right, because the pressure is coming from the left side of the fluid and because the velocity is to the right!
You're looking at the forces exerted by the surrounding materials on the fluid in the picture. Does pressure exert a pushing force or a pulling force? When you do a force balance on a body, do you include the forces it exerts on surrounding bodies, or only the forces the they exert on it?
 
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Sbee said:
It should be acting to the right, because the pressure is coming from the left side of the fluid and because the velocity is to the right!
Think about Newton's 2nd Law. If the gas is traveling slower, which direction must the force be acting, to make this happen? (It may not feel right, intuitively but Newton tells you what really happens.)
 
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sophiecentaur said:
Think about Newton's 2nd Law. If the gas is traveling slower, which direction must the force be acting, to make this happen? (It may not feel right, intuitively but Newton tells you what really happens.)
I was thinking about Newton's 3rd law. The fluid in the control volume exerts a force of magnitude F2 on the fluid ahead of it, and the fluid ahead of it exerts an equal and opposite force of magnitude F2 on the fluid in the control volume. The latter is the force shown in the OP's diagram.
 
Chestermiller said:
I was thinking about Newton's 3rd law. The fluid in the control volume exerts a force of magnitude F2 on the fluid ahead of it, and the fluid ahead of it exerts an equal and opposite force of magnitude F2 on the fluid in the control volume. The latter is the force shown in the OP's diagram.
The directions of arrows is always difficult but if we follow the sums, the answer comes out either way. My way of explaining the increase in pressure in the wide section is that ‘something’ must be slowing the emerging fluid. Hence the direction of that something, in my head.
 
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sophiecentaur said:
The directions of arrows is always difficult but if we follow the sums, the answer comes out either way. My way of explaining the increase in pressure in the wide section is that ‘something’ must be slowing the emerging fluid. Hence the direction of that something, in my head.
I was just thinking that, when we do a free body diagram force balance on a body, we only show the forces that other bodies exert on it, not the forces that it exerts on other bodies.
 
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  • #11
I'm not sure, I think I have to move on but if I understand it later I'll let you know
 
  • #12
Sbee said:
I'm not sure, I think I have to move on but if I understand it later I'll let you know
Good luck.
 
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