Mechanics & Simple Machines · GCSE Physics Pressure in Fluids
Pascal's Law Hydraulic Lift & Pressure Simulator
Core concept: Pressure applied to an enclosed liquid is transmitted undiminished in all directions. Force multiplies by area ratio F2/F1 = A2/A1, while displacement scales inversely h2/h1 = A1/A2.
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- Live Derivation
- Projector Mode
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3D Simulation Stage● 60 FPS
Parameter Controls
N
cm²
cm²
cm
Live Derivations & Metrics
Output Force F2
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Liquid Pressure p
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Force Multiplier
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Output Lift h2
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Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: Small piston has A1=10cm², large piston A2=200cm². A 200N force pushes small piston down 20cm. Find lift force and rise height.
Step-by-Step Derivation:
- Pressure p = 200/10 = 20N/cm². Output force F2 = 20*200 = 4000N. Volume displacement h2 = (10*20)/200 = 1cm.
Worked Problem
Problem: List at least three everyday devices operating on the communicating vessels principle.
Step-by-Step Derivation:
- 1) Teapot and spout; 2) boiler sight glass level indicator; 3) plumbing P-trap odor water seal; 4) Three Gorges ship locks.
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: Why are dam walls constructed thicker at the base than at the top?
Answer Key: Liquid pressure p = rho*g*h increases linearly with depth, exerting far greater pressure on the dam base.
Q2. Variant 2: In a U-tube with water, 10cm of unknown oil balances 8cm of water. Find oil density.
Answer Key: Pressure equilibrium at interface: rho_oil * 10 = rho_water * 8 => rho_oil = 0.8 g/cm³.
Q3. Variant 3: A hydraulic lift has large piston radius 5x the small piston. Find output force for 100N input.
Answer Key: Area ratio scales as radius squared: A2/A1 = 5² = 25. Thus F2 = 25 * 100N = 2500N.
Frequently Asked Questions & Misconceptions
Does Pascal's principle apply to gases?
It strictly applies to incompressible liquids. Gases compress when loaded, delaying and diminishing pressure transmission, which is why hydraulic brake lines must be bled of air bubbles.
Does a hydraulic lift save energy?
No. Output force is multiplied by A2/A1, but output stroke is reduced by the exact same ratio. W1 = F1*h1 = F2*h2 = W2, obeying energy conservation.
Why does a brake fluid leak cause automobile brake failure?
Brakes transmit master cylinder pressure through hydraulic fluid to calipers via Pascal's principle. Leaks release pressure, preventing brake calipers from clamping discs.
Do communicating vessels with unequal diameters still equalize level?
Yes. Hydrostatic pressure p = rho*g*h depends only on fluid density and vertical depth, independent of tube cross-section or geometry.