Pascal’s law says that pressure applied to a liquid in a closed container acts equally on every part of the container’s wall, so force on any surface equals pressure times that surface’s area. At 20 MPa a 100 mm piston carries 157 kN, and the weight of a metre of fluid changes the pressure by only about 0.05%, so in a working hydraulic system the pressure may be taken as the same everywhere.
Part of Hydraulic Systems
Pascal’s law is the rule that makes hydraulics work: a pressure created at one point in a confined liquid appears undiminished at every other point.
Pressure Is the Same in Every Direction
Think of a sealed vessel full of oil. Squeeze it at one end and every wall, in every direction, feels the same pressure. The pressure is a force per unit area, so the force on a wall depends only on its area:
Force = pressure x area. With the pressure in pascals (newtons per square metre) and the area in square metres the answer is in newtons.
This is the only formula the whole hydraulics tree needs, and it is the same one used for air (Pneumatic Principles). What is special about oil is that it is practically incompressible, so the pressure is created instantly and transmitted without lag.
Weight of the Fluid Barely Matters
In a still fluid, pressure does increase with depth by density x gravity x height. For water the corpus uses 9,810 Pa per metre (Head Calculation). Oil is lighter, so for oil this is an overestimate. Against a working pressure of 20 MPa:
- Pressure from 1 m of fluid = 9,810 Pa
- Fraction of working pressure = 9,810 / 20,000,000 = 0.00049, or 0.05%
So in a machine a metre tall the pressure at the bottom differs from the pressure at the top by less than a tenth of one percent, and Pascal’s law is exact enough. It matters only at pressures of kilopascals, as in a water tank.
Where the Law Stops Working: Moving Fluid
Pascal’s law is a statement about a fluid at rest. When oil flows through a pipe or a valve, friction removes pressure along the way, and a narrow orifice can drop most of the pressure across it. Pressure measured at the pump is therefore higher than the pressure at a distant cylinder. A gauge at the cylinder shows what the load sees.
Worked Example: The Force on a Piston and on an End Cap
A cylinder with a bore of 100 mm at 20 MPa:
- Area = π / 4 x 0.1² = 0.007854 m²
- Force on the piston = 20,000,000 x 0.007854 = 157,080 N, 157 kN, about 16 tonnes-force
- The oil pushes with the same pressure on the other end of the chamber, so the cylinder’s end cap is pushed outward with the same 157 kN. Its threads, tie rods or welds must hold that, with margin
The same law works in reverse: any load that pushes on the piston creates the pressure that must be held. A load of 157 kN on a 100 mm piston makes 20 MPa in the oil, whether or not a pump is running.
Common Mistakes
- Ignoring the end cap. The cylinder tube sees hoop stress, but the caps and their fixings see the full piston force.
- Reading the pump gauge as the load pressure. Friction and orifices separate them while oil flows.
- Thinking pressure depends on the pipe’s size. It does not; only force and flow do.
Safety
A load creates pressure even with the pump off
A raised load pressurises the oil beneath it whether or not a pump is running, and anything that connects that oil to the outside, a loosened fitting or a cut hose, releases a pinhole jet or lets the load fall. Never loosen a fitting on a cylinder holding a load. Support the load mechanically first. Never search for a leak with a hand: a fine jet at this pressure injects oil through skin, so use a piece of card or wood.
What’s Next
- Learn next: Force Multiplication — two pistons of different size
- Combine with: Hydraulic Cylinders — Pascal’s law inside a tube