Final answer:
The output force of a linear actuator and the output torque of a hydraulic motor in a hydraulic system are determined by system pressure, assuming no losses to friction. Work input equals work output because the fluid volume is constant, causing an inverse relationship between force increase and distance moved. Friction reduces output force and efficiency, especially when the fluid is in motion.
Step-by-step explanation:
When dealing with hydraulic systems, the output force of a linear actuator or the output torque of a hydraulic motor is predominantly determined by the system pressure. If we assume no losses to friction, work input should theoretically equal work output in a hydraulic system. This is shown by the principle that the volume of the fluid is constant and, therefore, the distance the output force moves is inversely proportional to the increase in output force.
Regarding torque, it is defined as the rotational equivalent of force. It is the tendency of a force to rotate an object about an axis, fulcrum, or pivot, and it depends on the force applied, the distance from the pivot point (lever arm), and the angle of application.
In a hypothetical frictionless scenario, if we apply a 100-N force to a hydraulic system and the output side has an area five times greater than the input side, the resulting output force would be 500 N. If friction is present, it would reduce the output force and efficiency of the system, with the effects of friction becoming more significant if the fluid is moving. Friction would cause energy to be lost as heat, and more input force would be needed to achieve the same output force.
To design a hydraulic system that increases force by 100 times, the ratio of the areas between the output cylinder (slave, wheel, or controlled cylinder) and the input cylinder (master or pedal cylinder) must be 100 to 1. The diameter ratio can be found by taking the square root of the area ratio, since the area of a circle is proportional to the square of the diameter. Thus, the output distance through which the force moves would be reduced by a factor of 100 compared to the input distance.