A hydraulic system consists of a machine with an incompressible fluid to transmit pressure, a reservoir to confine the fluid, and moving parts to perform some function. You can find hydraulic machines in elevators, auto brakes, and cranes. These machines enable operators to do significant work like lifting heavy loads and drilling precision holes with little effort. You can calculate hydraulic system pressure using an equation, which states that pressure in pounds per square inch equals force in pounds times the surface area of a piston in square inches.

Obtain the values to make the calculation. You will need to know the force in pounds (F) and surface area of the piston in square inches (A). If the problem provides “F” in Newtons, you can calculate force in Newtons times 0.225 with the aid of a calculator to obtain force in pounds. If the problem provides “A” in square meters, you can calculate “A” in square meters times 1550 with the aid of a calculator to obtain “A” in square inches.

Simplify the calculation. If you have the “F” and “A” needed to calculate hydraulic system pressure (P) directly, then you can proceed to step 3. If the problem does not provide “F” and “A” needed to calculate “P” directly, you can calculate length in inches times width in inches with the aid of a calculator to obtain “A” in square inches for a rectangular shaped piston or you can calculate pi (3.14) times square radius in square inches with the aid of a calculator to obtain “A” in square inches for a cylindrical shaped piston. You can determine “F” in pounds by calculating work done by a force acting on a piston in pounds feet divided by distance moved by that piston in feet.

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Perform the calculation. Calculate “F” divide by “A” with the aid of a calculator to obtain “P” in pounds per square inch.

#### Tip

Pressure in pounds per square feet equals Force in pounds per unit area in square inches. Hydraulic systems work on Pascal’s principle, which states “Pressure applied to a confined fluid at any point is transmitted undiminished throughout the fluid in all directions and acts upon every part of the confining vessel at right angles to its interior surfaces and equally upon equal areas.” (See Reference 3) In performing the your calculation, assume that hydraulic fluid is nearly incompressible and is able to transmit power instantaneously. Because a small force on a small area would create a proportionally large force on a large area, the only limit to the force that a machine can exert is the area to which the pressure is applied. Two factors determine the hydraulic system pressure: the surface area of the piston and the size of the force produced by the machine through that piston.

#### Warning

The value of the calculated hydraulic system pressure must equal the pressure exerted by the small force acting on the small piston and must equal the pressure exerted by the large force on the large piston. If these results do not coincide, you have to recheck your calculation and ensure that you are using the right values and the right units for the parameters, and for the right moving piston. Although the equation to calculate pressure applies to all types of hydraulic machines, the force and surface area you use to calculate pressure must be for the same moving part or piston.