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.

Relevant 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

F_m/A_m = F_s/A_s

F_s = A_s(F_m/A_m)

F_s = (A_s)ρgh_m

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.

 

[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

F_m/A_m = F_s/A_s

F_s = A_s(F_m/A_m)

F_s = (A_s)ρgh_m

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?
F_s = (A_s)ρgh_m + F_m

Or something like this. Or add mg?

 

[hutchphd]

I think I understand what you’re saying. Can I compensate for that by just doing this?
F_s = (A_s)ρgh_m + F_m

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.

F_s = (A_s)F_m/A_m + ρgh_m

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]

F_s = (A_s)F_m/A_m + ρgh_m

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 ρgh_m is a pressure. You now have it equated to a force.

 

[nmsurobert]

Your idea is correct but ρgh_m 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.