# Master and Slave Cylinder at different heights

• nmsurobert
In summary, the conversation discusses the impact of the height difference between a master and slave cylinder in a hydraulic system on the force produced at the slave cylinder. The equations Fm/Am = Fs/As and Fs = (As)ρghm are used to demonstrate that as the height of the master cylinder increases, the force produced at the slave cylinder also increases. However, there is a concern that the equation P = ρgh may not be applicable in this situation. A possible solution is to add the weight of the fluid to the equation to account for the pressure created by the height difference. This ensures that the force applied to the slave cylinder is never zero.
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

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.

nmsurobert said:
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.

hutchphd said:
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:
nmsurobert said:
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.

hutchphd said:
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.

nmsurobert said:
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.

hutchphd said:
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.

## 1. What is the purpose of a master and slave cylinder?

The master and slave cylinder work together to transfer hydraulic pressure from the brake pedal to the brakes on a vehicle. The master cylinder is responsible for creating the pressure, while the slave cylinder uses that pressure to engage and disengage the brakes.

## 2. Why are the master and slave cylinder placed at different heights?

The master cylinder is typically placed at a higher position than the slave cylinder in order to take advantage of gravity. This allows for easier bleeding of the brake system and helps prevent air pockets from forming in the lines.

## 3. What happens if the master and slave cylinder are not at different heights?

If the master and slave cylinder are not at different heights, it can cause issues with the brake system. Air pockets may form in the lines, leading to a decrease in braking performance. Additionally, the brake pedal may feel spongy or unresponsive.

## 4. Can the master and slave cylinder heights be adjusted?

Yes, the master and slave cylinder heights can be adjusted, but it is not recommended to do so without proper knowledge and tools. If the heights are adjusted incorrectly, it can lead to brake system malfunctions and potential accidents.

## 5. Are there any other factors to consider when installing the master and slave cylinder at different heights?

Yes, it is important to also consider the angle and orientation of the cylinders. They should be positioned in a way that allows for smooth and efficient transfer of hydraulic pressure. Additionally, the cylinders should be securely mounted and free of any leaks.

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