Pascal's Law and Hydraulic Machines
Pascal's law states that a pressure change applied to a confined incompressible fluid is transmitted undiminished to every part of the fluid and its containing walls.
Why this shows up in the exam
Hydraulic lifts and presses · Vehicle braking systems · Force multiplication in workshop tools
Learn the idea
An externally applied pressure increment is transmitted throughout a confined static fluid. A small piston can control a large load because both pistons experience the same added pressure; the larger force is paid for by a proportionally smaller displacement.
🧠 Memory hook: Hydraulics multiply force through area, not energy for free.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F₁/A₁ = F₂/A₂ — ideal hydraulic force relation when piston faces are at effectively equal elevation
- A₁ x₁ = A₂ x₂ — displaced-volume conservation for an incompressible leak-free machine
- F₁ x₁ = F₂ x₂ — ideal work balance when friction and other losses are neglected
How to approach it
- 1Convert every diameter or radius into area
- 2Equate pressure increments and include hydrostatic terms if needed
- 3Use displaced volume to find motion or work
Common slip-ups that cost marks
- •Using piston radius ratio instead of area ratio
- •Assuming the large piston moves the same distance
- •Ignoring a stated height difference between piston faces
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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