"but the larger cylinder will exert more force than the smaller cylinder"
This is actually not correct although on the surface it appears that it would be the case. The smaller diameter slave cylinder can lift just as much as the larger master because the pressure being applied to it is proportionally greater than that on the master (assuming they are properly sized to run in sync with each other). For example, say you have a 3.0" bore, 1.25" rod cylinder as the master and a 2.75" bore cylinder as the slave (one of numerous size combinations that play well together for master/slave systems) and a 2000 psi pump relief. If the master is raising a load with none on the slave you'd have a maximum force of 14140 lbs (2000 psi times 7.07 sq inch). Now if the slave was lifting a load by itself you need to take into account the pressure increase happening across the piston of the master cylinder. Here you'd have 2000 psi at the master base but due to the ratio of the areas on the base and rod sides of the piston you'd have 2420 psi being supplied to the base of the slave. Multiply this by the base area of the slave cylinder (5.94 sq inch) and you get essentially the same 14140 lbs maximum force as we calculated for the master. (The math is slightly different because no master/slave system using off-the-shelf cylinder diameters is perfect. In our example here the mismatch between the two cylinders is less than 2% which is close enough for most any practical usage.)
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