How are force and pressure related in a hydraulic system?

[matonski]

What's going to happen?

 

[Mapes]

What do you think?

 

[matonski]

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.

 

[Mapes]

I agree.

 

[matonski]

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.

 

[Mapes]

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.

 

[matonski]

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.

 

[Skrambles]

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.

 

[DaTario]

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