A small push, a huge force
A hydraulic jack lets one person lift a car. The trick is a fluid trapped between two pistons of different sizes. In the 17th century Blaise Pascal stated the principle: pressure applied to an enclosed fluid is transmitted undiminished to every part of it. Pushing a small piston creates a pressure, and that same pressure acting on a much larger piston produces a much larger force.
The formulas
- Pressure: p = F₁ ÷ A₁
- Output force: F₂ = p × A₂ = F₁ × (A₂ ÷ A₁) = F₁ × (D₂ ÷ D₁)²
- Travel of the large piston: s₂ = s₁ × A₁ ÷ A₂
The force multiplication equals the ratio of the piston areas, so it grows with the square of the diameter ratio.
Worked example
A small piston 1 inch in diameter and a large piston 8 inches in diameter, with 50 lbf pushed on the small one:
- Area ratio: (8 ÷ 1)² = 64.
- Output force: 50 × 64 = 3,200 lbf, enough to hold up 3,200 lb.
- Fluid pressure: 50 ÷ 0.785 sq in = 63.7 psi.
- If the small piston moves 4 inches, the large one rises only 0.0625 inch.
No free energy
The work put in, 50 lbf × 4 in, equals the work done on the load, 3,200 lbf × 0.0625 in, before friction. A jack therefore uses many short pump strokes, with check valves that let fluid into the large cylinder but not back out. Opening the release valve lets the load down.
Where hydraulics are used
- Car jacks and shop presses: a handle multiplies your force again, as a lever, before the hydraulics do.
- Brakes: the pedal pushes a small master cylinder, and larger caliper pistons squeeze the brake pads.
- Construction machines: excavators, loaders and cranes use pumps that reach 3,000 to 5,000 psi.
- Aircraft: hydraulic actuators move control surfaces and landing gear.
Joseph Bramah patented the hydraulic press in England in 1795, and it powered much of the industrial age.
Practical notes
- Hydraulic oil is used because it is nearly incompressible, lubricates the seals and resists corrosion. Air in the system makes it spongy, which is why brakes are bled.
- Real systems lose a few percent to seal friction.
- Never work under a load held only by a hydraulic jack. Seals can fail without warning; always use jack stands.
- Check the pressure rating of hoses and fittings: a leak at high pressure can inject fluid through the skin, a medical emergency.