Pascal’s law (Pascal’s Principle)

Pascal's law (also called Pascal's Principle) is a the fundamental law in hydrostatic. It states that "a change in the pressure at any point of an enclosed incompressible fluid is conveyed undiminished to every part of the fluid and to the surfaces of its container”. Pressure is the result of a force applied over a specific area, and that pressure is therefore measured by the formula:

where F is the magnitude of the force (in N), A is the surface of the area (in m²), and Pis the pressure (in units N/m² in the SI system). If we consider that this container and its fluid contents are subject to gravity as an additional force, then we must consider that the difference of pressure due to a difference in elevation within a fluid column is given by:

where ρ is the fluid density (kg/m³), g is acceleration due to gravity (m/s²), h1 and h2 are the heights of fluid above the point of measurement (m). The intuitive explanation of this formula is that the change in pressure between two elevations is due to the weight of the fluid between the elevations.

In honor of Pascal’s scholarly activities in this topic, another name for the SI unit of pressure is Pascal (Pa):

An important application of Pascal's law is the hydraulic press:

A force F1 is applied to a small piston of area A1. The pressure is transmitted through a liquid to a larger piston of area A2. Since the pressure is the same on both sides, we see that P = F1/A1 = F2/A2. Therefore, the force F2 is larger than F1 by multiplying factor A2/A1. Hydraulic brakes, car lifts, hydraulic jacks, and forklifts all make use of this principle.

Pascal’s rule is used to design watertowers, but scuba divers must also understand this principle. At a depth of 10 meters under water, pressure is twice the atmospheric pressure at sea surface, and increases by about 100 kPa (about 1 atm) for each increase of 10 m depth.

• 1. water pump
• 2. water
• 3. users