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Pascal’s law

Hydraulic systems like the Automotive Brake System (ABS) of a car and elevators of buildings requires incompressible fluids, such as oil, water, oxygen, gases, and other mediums that are used to transmit forces from one location to another, and this transmission of forces is made possible through the application of the Physics Principle; Pascal’s Law of fluid pressures.

Our technology today has come to depend so much on the interactions of incompressible fluid, seeing that they form the foundation for technologies like the automotive and pneumatic braking system used in cars, and the landing gears used in airplanes.

Pascal’s law explains how fluids that are compressed in a tight container transmit force from the point of application to the point where the impact is expected.

Table Content:

What Is Pascal’s Law

Pascal’s law is a principle in fluid mechanics that states that a change in pressure at any point in a confined incompressible fluid is transmitted uniformly in all directions throughout the fluid, regardless of the shape of the container, such that the same change occurs everywhere.

Pascal’s law is also known as Pascal’s Principle, or the Principle of Transmission of Fluid-Pressure. The law was put forward by French Mathematician Blaise Pascal in 1653 and was published ten years later.  

Blaise Pascal was a mathematician, physicist, inventor, theologian, and writer. A child prodigy that developed and explained the concept of pressure and vacuum in fluid. His inventions include the hydraulic press, the syringe, and the primitive ‘roulette’. 

Visualizing Pascal’s Law

The best way to imagine Pascal’s law of the force present in fluids is with the help of a glass vessel with holes all over its surface.  

When filled with water and a force is applied on the surface of the fluid through the piston, the water will rush out of the holes in the vessel in all directions with high pressure.

pascal's law
A pressured vessel

However, it’s important to note that the pressure of the rushing water is the same as the force applied to it through the piston. This is because the rushing water depends on the applied force to determine its pressure.

Another important point to note is the fact that the liquid rushing out, does so in all directions of the container as proven by the holes perforated in all directions of the container. The law holds true for both liquids, as well as gasses and fluids.

Mathematical Representation of Pascal’s Law

The Pascal’s principles can be expressed mathematically as:       

Definition of terms;

P2-P1:    Hydrostatic Pressure. It’s also the difference between two points within the fluid container due to the weight of the fluid.

p:            Fluid Density.

g:            Acceleration due to gravity.

h2-h1:     Height of the fluid, also the difference in elevation between the two points within the fluid container.

For Pascal’s principles to be achieved, the following conditions must be met.

Factors That Create Pascal’s Law

  • A change in pressure is transmitted to all points of the fluid in an enclosed system at rest without a decrease in the pressure.
  • The pressure exerted on a fluid in an enclosed container is transferred uniformly and without a decrease to all areas of the container, and works at the right angle to the enclosing walls.
  • Alternate definition: The pressure applied to any portion of the enclosed liquid shall be transmitted equally through the liquid in all directions.


Our understanding of fluids comes from the study of Fluid Mechanics, a field of physical science that enquires into the response of fluids to force exerted upon them.

Fluids can be liquids, gases, or any other materials that can’t sustain any type of force (tangential or shearing) like solids when at rest, but undergoes a continuous change in shape when subjected to stress. Fluids escaping from the force by flowing and displaying other characteristics of fluids.

Unlike solids, fluids can’t withstand shear stresses and tend to yield to them, no matter how small these stresses may be. But, they do so at different rates from one another, one that’s determined by their Fluid Viscosity. It’s on this premise that Pascal’s law stipulates the behavior of fluids under a defined pressure.


As mentioned above, one concept Blaise Pascal successfully postulated was Pressure. Pascal’s law shows that Pressure in a container is the perpendicular force per unit area of the container of the liquid. Which means that the Pressure is directly proportional to force and an increase in the force will directly result in an increase in the pressure and so will a decrease in the force also result in a decrease in pressure.

Pascal's law

They’re several types of pressure, but the pressure of interest to us is the hydrostatic pressure, the one present in fluids. The hydrostatic pressure is stress exerted equally in all directions within a fluid in a container.

Hydraulic Systems

Hydraulic systems use the power of pressurized fluid to perform tasks. Hydraulic systems are engaged in heavy equipment and perform jobs like lifting heavy loads, and other precise and repetitive tasks, which are otherwise impossible to do by mere physical strength.

Hydraulic systems include Hydraulic Circuit, Hydraulic Pumps, Hydraulic Motors, Hydraulic Cylinders, Hydraulic Energy, and safety.  

Applications of Pascal’s Law

As previously stated, hydraulic systems provide a way to use the enormous power present in fluids and use them as a channel to transfer mechanical energy that can perform several types of work across spheres of application.

Some of the more common ways Pascal’s law is applied to help engineers achieve their goals include the following:

  • Hydraulic press
  • Hydraulic Circuit
  • Hydraulic Pumps
  • Hydraulic Motors
  • Hydraulic Cylinders
  • Hydraulic Lifts
  • Hydraulic Jack
  • Hydraulic Machine
  • Hydraulic Energy and Safety

Hydraulic Press

One of the simplest forms of machine that works on Pascal’s law is the Hydraulic press. It comprises two cylinders of different cross-sectional areas that are combined as one and fitted with a piston that’s responsible for creating and feeling the force from the fluid.

Pascal's law: Hydraulic press

The object to be compressed is placed over the piston of the larger cross-sectional area, ‘A’. The Hydraulic Press starts its lifting responsibility when force, ‘F1’, is applied to the piston of the small cross-sectional area, ‘a’.

The pressure ‘P,’ created by the small piston is transmitted equally to the large piston, and a force F2 acts on A that is much larger than F1.

pascals law: hydraulic press

Therefore, the Hydraulic press works with the formula:

  • P = F1/a; which is the pressure produced by the hydraulic press on the small area.
  • P=F2/A; which is also the pressure produced by the hydraulic pressure, but this time on the bigger area.
  • F2 = F1 x A/a; which is the formula showing the forces acting on both sectional areas of the hydraulic press.

Since the ratio of the area is greater than 1, then, the force F2, acting on the larger cross-sectional area, will be larger than the force acting on the smaller area F­1.

Meaning that the hydraulic press system provides a medium for smaller forces to become greater forces, capable of doing larger work.

Hydraulic Circuit

A hydraulic circuit is a system based on Pascal’s law, and it helps regulates fluid paths (where fluid flows. It equally plays a great role in thermodynamic systems) as well as regulates the fluid pressure (such as hydraulic amplifiers), carrying liquid via a series of discrete interconnected components.

A hydraulic circuit system operates similarly to the theory of electric circuits, using linear and discrete components. Hydraulic circuits (flow systems) are also used in chemical processing.

Hydraulic Braking System

The hydraulic braking system of cars, buses, and other vehicles has their designs based on the principle of Pascal law. And the process starts when the brake pedal is pushed, the force is exerted on the master cylinder which raises the pressure of the liquid inside. The liquid pressure is transferred equally to all the pistons of the other cylinders through the liquid in the metal pipes.

Pascal's law: break system

The pistons in the cylinders shift outward by pushing the brake pads with the brake drums, because of the increased liquid pressure coming from the metal pipes. The friction force between the brake pads and the brake drums halts the wheels, what we know as braking.

Hydraulic Lift

A small cylinder ‘A’ is connected to a wider cylinder ‘B’ in a hydraulic lift and is equipped with airtight pistons and packed with incompressible fluid. Pressure can be applied to shift the piston in a downward direction in cylinder ‘A’.

hydraulic press

The pressure thus applied is transmitted to the piston of the cylinder ‘B’ according to Pascal’s principle. Therefore, the piston ‘B’ travels upward in a hydraulic lift, the piston ‘B’ is used as a platform for lifting a car or other heavier objects, such as a tractor, boats, etc.

Hydraulic Pump

Using the flow and pressure of a hydraulic pump, mechanical power is converted into hydraulic energy. This hydraulic energy is what provides the energy used in most irrigations, flood control, sewage movements, and various mining services.

Hydraulic pumps work by generating a vacuum at the inlet of a pump, pushing liquid from a reservoir into an inlet and onto the pump line. Mechanical action takes the liquid to the pump source, and drives it into the hydraulic system, as it does.

hydraulic pumps functions due to pascal's law

This is an example of Pascal’s Law that is fundamental to the hydraulics theory. According to Pascal’s Law, “Throughout the fluid, a pressure change occurring anywhere in a confined incompressible fluid is transmitted such that the same change occurs everywhere.”

Hydraulic Cylinder

A hydraulic cylinder is a mechanism that converts energy stored in the hydraulic fluid into a force that moves the cylinder linearly. Hydraulic cylinders have found application in several industries and can either be single or double-acting cylinders.

The cylinders activate the pressure of the fluid as part of the entire hydraulic system, whose flow is controlled by a hydraulic motor.

Hydraulic Motors

Hydraulic motors can be combined in a hydraulic drive system, together with hydraulic cylinders and hydraulic pumps. Conversion of hydraulic pressure and flow into torque (or twisting force) and then rotation is the function of a mechanical actuator, a hydraulic motor.

Using these is reasonably adaptable. Hydraulic motors can be connected with hydraulic cylinders and hydraulic pumps into a hydraulic drive system.

Pascal's law aid in the performance of cranes and huge machineries
Pascal’s law aid the performance of powerful machines

Other Applications of Pascal’s Law

The scientific concept of Pascal’s law has several real-life implications and applications that make them an important idea of physics. Pascal’s law has a variety of applications, as hydraulic systems are used in several large and small industrial settings and locations, construction equipment, as well as, buildings, vehicles, paper mills, logging, oil and gas, manufacturing, robotics, and even steel processing, all depend all on hydraulic equipment.

Below is how they’re applied in solving real problems:

  • Scuba divers use the know-how of Pascal’s law in preparing for the deep water diving. As Pascal’s law explains why the atmospheric pressure underwater increases by about 100kPa for every 10 meters.
  • Marine and water-related services like flood control, irrigation, Automotive braking systems depend on pascal’s law to understand the pressures of water and how to use them effectively.
  • Also, Pascal’s principle is responsible for the Hydraulic Press, and it’s very important in the design and construction of refrigerators, microwaves, stamp panels, dishwashers, laundry machines, and many other machines and home appliances.
  • Bottle jacks and hydraulic hoists are other hydraulic systems that are responsible for common machines like cranes, jacks, forklifts, pumps, etc.
  • Also, Hydraulic Lifts are fairly common in society, and can be used to lift cars, trucks, and even in building elevator.
  • Some other places where the application of Pascal’s law can be found lies in Hydroelectric dams, artesian wells, water tower, dams, torque converters, fire sprinkler systems, municipal water, and waste systems.
  • Finally, Blaise Pascal’s famous medical invention, the syringe. The syringe has a wide array of functions for medical professionals, lab operators, culinary experts, printers, and several more.

Flow Simulations

After going after the full details of Pascal’s law, it isn’t so easy to come to grab with the role of the CAD software in the manufacturing process of Pascal and hydrological abiding technology. But CAD software provides the basis for Computational Fluid Dynamics (CFD). Something only the bests CAD applications and simulating programs have access to.

CAD software like SolidFace has this extra simulation services that include flow simulations that are very relevant to Pascal’s Principle. With the SolidFace flow simulations, you’re able to subject to designs to real-world conditions and elements to raise product quality and life while reducing the cost of making prototypes and running physical testing.

With the SolidFace simulates the fluid flow, fluid force, and heat transfer involved in its functional process under real-life conditions. With the added benefit of providing an easy-to-use portfolio of analysis tools that improve its virtual testing prediction of real-life conditions of your CAD models.

Computational Fluid Dynamics (CFD) Software

CFD is a software that provides technical solutions for fluid flow fields through numerical analysis. The application provides dynamic feedback on the fluid flow, force, electronic cooling, heat exchanging, aerodynamics, flow through a manifold, and other properties of the fluid and relates them to the CAD model.

Plus, most CFD programs have parametric optimization features, so users can automate the design and analytical process to the best iteration available.

Why choose SolidFace Flow Simulation

When it comes to dealing with Pascal’s related models, SolidFace Flow Simulation provides an intuitive solution that’s capable of quick, easy, and efficient simulation of liquid and gas flows. This is made possible due to its world-class designs and ability to calculate product performance.  


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