How are force and pressure related in a hydraulic system?

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    Force Pressure Puzzle
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Discussion Overview

The discussion revolves around the relationship between force and pressure in a hydraulic system, particularly focusing on the behavior of syringes filled with water. Participants explore theoretical aspects, practical implications, and potential paradoxes related to pressure and force dynamics in such systems.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants suggest that the handle of a larger syringe will push the handle of a smaller syringe, causing water to flow from the small syringe to the big syringe.
  • One participant expresses initial confusion regarding whether to consider equal pressures or equal forces on the handles, indicating a perceived paradox in the problem.
  • Another participant states that forces must be equal and opposite, leading to higher pressure in the narrower syringe, which would cause water to move away from that region.
  • It is proposed that if pressures are assumed equal, the water would exert a greater force on the handle of the larger syringe compared to the smaller one, resulting in similar conclusions about fluid movement.
  • One participant raises the importance of considering frictional forces of the pistons and head loss through fittings, suggesting that these factors could balance out differences in applied pressures and complicate the problem.
  • A later reply introduces a perspective that statically the pressures are equal while dynamically the forces are equal, proposing a stepwise understanding of the phenomena but expressing a desire for a clearer justification of this viewpoint.

Areas of Agreement / Disagreement

Participants express differing views on whether to prioritize pressure or force in their analysis, indicating that multiple competing perspectives remain without a clear consensus on the relationship between force and pressure in this context.

Contextual Notes

Participants note the influence of frictional forces and head loss, which may affect the outcomes of their reasoning. There is also an acknowledgment of the complexity involved in balancing static and dynamic considerations in hydraulic systems.

matonski
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What do you think?
 
I think the handle of the big syringe will push in the handle of the small syringe. In other words, water will flow from the small syringe to the big syringe.
 
I agree.
 
However, I was initially confused because it seemed like a paradox. Do you take the pressures inside to be equal or the force on the handles to be equal? I think I have it sorted out now. I just wanted to post it since I thought it was a neat problem that I found on the Dot Physics blog.
 
The forces must be equal and opposite. Therefore, the pressure will be higher in the narrower syringe, and thus water will move away from this region.
 
Also, if you assume the pressures are equal, then the water will exert a bigger force on the handle of the big syringe than on the handle of the small syringe, again leading to the same result.
 
That all depends on the frictional forces of the pistons and the head loss of the water through the fittings. Those forces may balance out the difference in applied pressures. Without knowing those factors and with how much force the syringes are pushed together, you can't solve this problem.
 
matonski said:
Also, if you assume the pressures are equal, then the water will exert a bigger force on the handle of the big syringe than on the handle of the small syringe, again leading to the same result.

IMO It seems correct to say that statically the pressures are equal while dynamically the forces are equal. So, if you think we are proceding by steps, each one being composed by one state (static) and one process (dynamic) then you have a picture of the phenomena.

I just feel the absence of a nice justification for this manouvre.

Best wishes

DaTario
 

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