Contributions to Science and Engineering

The mathematics on this page may not display properly in older browsers. For best results I would suggest that you view this page on a recent version of Chrome, Firefox, Edge, Safari, or Opera.

Fluids and Hydraulics

Pascal performed a number of experiments dealing with fluids and hydraulics. He determined that the hydrostatic pressure in a fluid depended on the height of the fluid above it and not on the weight of the fluid. To illustrate this he put a very long small diameter tube in a barrel and filled the barrel with water. From a high position he poured water into the narrow tube. When the water in the tube reached a sufficient height the barrel burst from the pressure.

Figure 1: Pascal's Barrel Experiment

Pascal also formulated Pascal's Law that states

In a fluid at rest in a closed container, a pressure change in one part is transmitted without loss to every portion of the fluid and to the walls of the container.

This law is the basis of the hydraulic lift pictured in Figure 2.

Figure 2: Hydraulic Lift

Here a smaller weight produces a pressure change of $F_1/A_1$ in the fluid. This produces a force of $(F_1/A_1)A_2$ on the second piston. Thus the force is multiplied by $A_2/A_1$.

He also developed a simple syringe to illustrate his law. A plunger in a cylindrical tube was attached to a sphere that had multiple holes. Both the tube and the sphere were filled with water. This syringe is pictured in Figure 3 below

Figure 3: Pascal's Syringe

Applying pressure to the plunger cause water to squirt out of the holes in the attached sphere equally in all directions. This is an illustration of Pascal's law.


In order to help his father with his tax calculations Pascal designed and developed a mechanical calculator called a Pascaline. Pascal not only designed the device, but also supervised its production. There were about 50 of these devices produced, but only about 8–10 have survived to this day. The device was never a financial success. It was cheaper to hire workers to do the computations manually. The You Tube video below describes the operation of a Pascaline.

Vacuum Experiments

Although it seems strange to us today, most scientists at the time of Pascal agreed with Aristotle that “Nature abhors a vacuum.” In 1644 Evangelista Torricelli performed an experiment that challenged this belief. He took a glass tube that was closed at one end and filled it with mercury. Covering the open end he immersed it in a dish of mercury. When the cover was removed the mercury fell until there was a column about 30 inches high remaining in the tube. Figure 4 shows this experiment.

Figure 4: Torricelli Experiment

The question was “what is the empty space above the mercury column?” Torrecelli believed it was a vacuum. His explanation was that the air exerted a pressure on the mercury in the dish that was balanced by the weight of the column of mercury. His explanation was not generally accepted. Many scientists thought there was some invisible substance in this apparently empty space. Possibly some type of vapor had leaked in.

Pascal heard about the experiment and duplicated it in 1646. Pascal duplicated the experiment with water and with wine. Since these substances weighed much less than mercury he had to construct a long glass tube about 45 feet high. The followers of Aristotle thought that wine was more vaporous than water and therefore the vapor in the void above the column should push the wine down farther than the water. However, wine is lighter than water and actually left a smaller void than water.

Pascal performed another interesting experiment. The apparatus is shown in Figure 5 below.

Figure 5: Another Vacuum Experiment

The apparatus was filled with mercury and inverted as in the other experiments. A hole near the top was initially covered. The mercury in the lower straight section formed a column as in the other experiments. However, there was some mercury left in the curved trap. When the hole was uncovered the mercury column went down, but the mercury in the trap formed a column in the upper tube. The mercury in the lower tube went down since there is now air pressure on both side of the mercury column so there is nothing to balance the weight of the mercury column. The mercury in the upper column went up since there is now nothing to balance the air pressure until the mercury column is formed.

Pascal's most famous vacuum experiment involved taking a Torricelli barometer up to the top of a 3000 ft. mountain to see how the height of the mercury column varied with altitude. Pascal reasoned that the air pressure was due to the weight of the air above us. Therefore, it was reasonable to assume that the air pressure would be less at a high altitude. On September 19, 1648 Pascal had his brother-in-law and several trusted friends take measurements at the bottom of the mountain Puy de Dome near Clermont and then take the device to the top recording measurements as they went.

Figure 6: Puy de Dome Experiment

They found that the height of the mercury column was 711 mm at the bottom of the mountain and 627 mm at the top, a difference of over 3 inches. This was added proof that it was air pressure acting on the surface of the mercury reservoir that was balancing the weight of the mercury column. Thus, Torricelli's barometer could be used to measure air pressure. A numerical value for the air pressure could be obtained by dividing the weight due to the column of mercury by the cross-sectional area of the tube. Pascal then multiplied this pressure by the surface area of the earth to obtain an estimate of the total weight of the atmosphere. He was within 30% of the generally accepted value today.

Pascal Initiates Omnibus System

In 1662 Pascal had the idea of creating an omnibus system in Paris. He secured financing from some of his friends and the king granted him monopoly status. The system started with seven horse-drawn vehicles running along regular routes. Each coach was capable of carrying six to eight passengers. An artist's rendition is shown in Figure 7 below.

Figure 7: A Pascal Omnibus Carriage.

The omnibus system was a big success at first, but soon the novelty wore off. At this time only the nobility and gentry were allowed to ride the coaches. Soldiers and peasants were not allowed. As the aristocrats were not dependent on the system, the business was not sustainable. By 1675 the omnibus system was out of business. This proved to be an idea that was ahead of its time.