Master and Slave Cylinder at different heights

nmsurobert

Homework Statement
Suppose the master cylinder in a hydraulic system is at a greater height than the slave cylinder. Explain how this will affect the force produced at the slave cylinder.
Homework Equations
P = F/A
F[SUB]1[/SUB]/A[SUB]1[/SUB] = F[SUB]2[/SUB]/A[SUB]2[/SUB]
P = ρgh
I think I've made sense of this.

m: master, s:slave

Fm/Am = Fs/As

Fs = As(Fm/Am)

Fs = (As)ρghm

So with that said, if the height of the master cylinder increases then the F produced by the slave will also increase. Anyone see any problems here?

My concern is that P = ρgh isn't applicable here. Thanks.

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hutchphd

Problem Statement: Suppose the master cylinder in a hydraulic system is at a greater height than the slave cylinder. Explain how this will affect the force produced at the slave cylinder.
Relevant Equations: P = F/A
F1/A1 = F2/A2
P = ρgh

I think I've made sense of this.

m: master, s:slave

Fm/Am = Fs/As

Fs = As(Fm/Am)

Fs = (As)ρghm

So with that said, if the height of the master cylinder increases then the F produced by the slave will also increase. Anyone see any problems here?

My concern is that P = ρgh isn't applicable here. Thanks.
Your concern is correct and the equations need to reflect this. If Fm is zero there is nonzero Fs from the gravitational head. If Fm is nonzero then it adds to it.

nmsurobert

Your concern is correct and the equations need to reflect this. If Fm is zero there is nonzero Fs from the gravitational head. If Fm is nonzero then it adds to it.
I think I understand what you’re saying. Can I compensate for that by just doing this?
Fs = (As)ρghm + Fm

Or something like this. Or add mg?

Last edited:

hutchphd

I think I understand what you’re saying. Can I compensate for that by just doing this?
Fs = (As)ρghm + Fm

Or something like this. Or add mg?
Close but Its the pressure that gets added to.
In particular in the limit of ρ=zero you should recover the previous result.

nmsurobert

Close but Its the pressure that gets added to.
In particular in the limit of ρ=zero you should recover the previous result.
Fs = (As)Fm/Am + ρghm

This way the force applied to the master cylinder can be zero but the force applied to the slave cannot be zero because of the pressure created by the difference in height.

hutchphd

Fs = (As)Fm/Am + ρghm

This way the force applied to the master cylinder can be zero but the force applied to the slave cannot be zero because of the pressure created by the difference in height.
Your idea is correct but ρghm is a pressure. You now have it equated to a force.

nmsurobert

Your idea is correct but ρghm is a pressure. You now have it equated to a force.
Ahh that makes sense. The only thing that makes sense to me is to use weight. If the fluid is on top of the slave cylinder then it’s weight applies a constant force to the slave cylinder always keeping that force nonzero.

"Master and Slave Cylinder at different heights"

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