is provided by the equipment to which theoutput piston is attached. The force of re-sistance acts against the top of the outputpiston. The pressure created in the systemby the input piston pushes on the underside ofthe output piston with a force of 10 pounds oneach square inch.In this case, the fluid column has a uniformcross section, so the area of the output pistonis the same as the area of the input piston,or 10 square inches. Therefore, the upwardforce on the output piston is 100 pounds(10 psi x 10 sq. in.), the same as the force appliedto the input piston. All that was accomplished inthis system was to transmit the 100-pound forcearound the bend. However, this principle under-lies practically all mechanical applications of fluidpower.At this point you should note that sincePascal’s law is independent of the shape ofthe container, it is not necessary that thetube connecting the two pistons have the samecross-sectional area of the pistons. A connectionof any size, shape, or length will do, as long asan unobstructed passage is provided. Therefore,the system shown in figure 2-10, with a relativelysmall, bent pipe connecting two cylinders,will act exactly the same as the system shown infigure 2-9.MULTIPLICATION OF FORCES.— Con-sider the situation in figure 2-11, where the inputpiston is much smaller than the output piston.Assume that the area of the input piston is 2square inches. With a resistant force on the outputpiston a downward force of 20 pounds acting onthe input piston creates a pressure of or 10 psiFigure 2-10.—Transmitting force through a small pipe.Figure 2-11.—Multiplication of forces.in the fluid. Although this force is much smallerthan the force applied in figures 2-9 and 2-10, thepressure is the same. This is because the force isapplied to a smaller area.This pressure of 10 psi acts on all parts of thefluid container, including the bottom of theoutput piston. The upward force on the outputpiston is 200 pounds (10 pounds of pressure oneach square inch). In this case, the original forcehas been multiplied tenfold while using the samepressure in the fluid as before. In any system withthese dimensions, the ratio of output force toinput force is always ten to one, regardless of theapplied force. For example, if the applied forceof the input piston is 50 pounds, the pressure inthe system will be 25 psi. This will support aresistant force of 500 pounds on the output piston.The system works the same in reverse. If wechange the applied force and place a 200-poundforce on the output piston (fig. 2-11), making itthe input piston, the output force on the inputpiston will be one-tenth the input force, or 20pounds. (Sometimes such results are desired.)Therefore, if two pistons are used in a fluid powersystem, the force acting on each piston is directlyproportional to its area, and the magnitude ofeach force is the product of the pressure and thearea of each piston.Note the white arrows at the bottom of figure2-11 that indicate up and down movement. Themovement they represent will be explained laterin the discussion of volume and distance factors.2-7
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