In the world of engineering, the ability to lift heavy loads with precision and ease is not just an advantage; it is a necessity. Construction projects in civil engineering require the lifting of heavy beams, trusses and other structural components. Heavy machinery and equipment installation in industrial settings, aerospace and automotive industries require precise lifting and positioning of equipment, which would otherwise be impossible with only human effort.

At the heart of these lifting processes today lies one of the most efficient tools called the hydraulic jack. This seemingly simple device harnesses the power of hydrostatic pressure, allowing engineers to lift heavy objects with minimal effort. In order to design and choose hydraulic jacks for a specific application, it is important to understand the basic principles of fluid statics and hydrostatic pressure, which are fundamental to their operation.

Figure. 1. At the heart of these lifting processes in engineering today lies one of the most efficient tools called the hydraulic jack. Source: Surasak/Adobe Stock

## Basic principles of fluid statics

Fluid statics deal with the conditions under which fluids are in a state of equilibrium. This means the fluid is either at rest or moves in such a way that there is no relative motion between adjacent particles. As a result, there will be no shearing stresses in the fluid, and adjacent particles will only be affected by forces due to pressure. Engineers have shown that the pressure field in such a system can be described by:

Equ1

Which can also be written for a very small fluid element as:

Equ2

Where is the specific weight and k is the unit vector along the z-coordinate axis. This set of equations would mean that pressure does not change when we move from point to point in a horizontal plane (in the x and y directions) but would change along the z-axis according to:

By solving this equation for an incompressible fluid (a fluid with constant density or negligible variation in density, such as liquids), we obtain:

This is the hydrostatic distribution of pressure. As is shown in this equation, regardless of the size or shape of the tank holding a fluid, the pressure at any given point will vary linearly with the depth of the fluid relative to some reference plane. This equality of pressure at equal elevations throughout a system is fundamental to the operation of hydraulic jacks.

## Working principle of hydraulic jacks

Figure 2: Illustration showing the transmission of fluid pressure.

Figure 2 shows the fundamental idea behind the operation of a hydraulic jack. The figure shows a closed fluid system filled with an incompressible fluid (such as oil) with a small and large piston located at both ends of the closed system.

When force F1 is applied to the smaller piston with area A1, it creates a pressure P in the fluid beneath it. This pressure can be calculated using P = F1/A1. According to Pascal’s law, the same pressure is exerted on the large piston with area A2. As a result, the force exerted on the larger piston can be obtained using F2 = PA2.

Given that the pressure is the same at the larger piston, a mechanical advantage is obtained such that the force on the larger piston is greater than the force on the small piston. A hydraulic jack relies on this principle by amplifying a relatively small force applied to a small piston into a larger force on the smaller piston. The force is magnified by the ratio of the area of the two pistons, as shown below.

Consider the scenario where a force of 100 N is applied to a small piston with an area of 0.01 m2. The pressure applied to the small piston would be obtained as 10,000 Pa. If the area of the large piston is 0.05 m2, then the force exerted by the large piston would be obtained as 500 N. This means with an applied force of 100 N at one end, engineers can lift a load as heavy as 500 N at the other end.

## Conclusion

Hydraulic jacks are essential devices in a broad range of industries today. While this article presents the basic principle guiding their operation, engineers must consider several other essential factors (such as the lifting capacity, lifting height, type of load, size and speed of operation) before choosing one for a specific application. Therefore, it is recommended to reach out to hydraulic jack suppliers to discuss application requirements.